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In [[mathematics]], more specifically in the area of [[modern algebra]] known as [[field theory (mathematics)|field theory]], the '''primitive element theorem''' or '''Artin's theorem on primitive elements''' is a result characterizing the finite degree [[field extension]]s that possess a '''primitive element'''. More specifically, the primitive element theorem characterizes those finite degree extensions <math>E\supseteq F</math> such that there exists <math>\alpha\in E</math> with <math>E=F[\alpha]=F(\alpha)</math>.
{{ distinguish|a priori probability}}


== Terminology ==
{{No footnotes|article|date=February 2008}}
Let <math>E\supseteq F</math> be an arbitrary field extension. An element <math>\alpha\in E</math> is said to be a ''primitive element'' for <math>E\supseteq F</math> when


:<math>E=F[\alpha].</math>
{{Bayesian statistics}}


In this situation, the extension <math>E\supseteq F</math> is referred to as a ''[[simple extension]]''. Then every element ''x'' of ''E'' can be written in the form
In [[Bayesian probability|Bayesian]] [[statistical inference]], a '''prior probability distribution''', often called simply the '''prior''', of an uncertain quantity ''p'' is the [[probability distribution]] that would express one's uncertainty about ''p'' before some evidence is taken into account. For example, ''p'' could be the proportion of voters who will vote for a particular politician in a future election. It is meant to attribute uncertainty rather than randomness to the uncertain quantity. The unknown quantity may be a [[parameter]] or [[latent variable]].


:<math>x=f_{n-1}{\alpha}^{n-1}+\cdots+f_1{\alpha}+f_0</math> where <math>f_i\in F</math>
One applies [[Bayes' theorem]], multiplying the prior by the [[likelihood function]] and then normalizing, to get the ''[[posterior probability distribution]]'', which is the conditional distribution of the uncertain quantity given the data.


for all ''i'', and <math>\alpha\in E</math> is fixed. That is, if <math>E\supseteq F</math> is separable of degree ''n'', there exists <math>\alpha\in E</math> such that the set
A prior is often the purely subjective assessment of an experienced expert. Some will choose a ''[[conjugate prior]]'' when they can, to make calculation of the posterior distribution easier.


:<math>\{1,\alpha,\cdots,{\alpha}^{n-1}\}</math>
Parameters of prior distributions are called ''[[hyperparameter]]s,'' to distinguish them from parameters of the model of the underlying data. For instance, if one is using a [[beta distribution]] to model the distribution of the parameter ''p'' of a [[Bernoulli distribution]], then:
* ''p'' is a parameter of the underlying system (Bernoulli distribution), and
* ''α'' and ''β'' are parameters of the prior distribution (beta distribution), hence ''hyper''parameters.


is a basis for ''E'' as a [[vector space]] over ''F''.
== Informative priors ==


For instance, the extensions <math>\mathbb{Q}(\sqrt{2})\supseteq \mathbb{Q}</math> and <math>\mathbb{Q}(x)\supseteq \mathbb{Q}</math> are simple extensions with primitive elements <math>\sqrt{2}</math> and ''x'', respectively (<math>\mathbb{Q}(x)</math> denotes the field of rational functions in the indeterminate ''x'' over <math>\mathbb{Q}</math>).
An ''informative prior'' expresses specific, definite information about a variable.
An example is a prior distribution for the temperature at noon tomorrow.
A reasonable approach is to make the prior a [[normal distribution]] with [[expected value]] equal to today's noontime temperature, with [[variance]] equal to the day-to-day variance of atmospheric temperature,
or a distribution of the temperature for that day of the year.


== Existence statement ==
This example has a property in common with many priors,
namely, that the posterior from one problem (today's temperature) becomes the prior for another problem (tomorrow's temperature); pre-existing evidence which has already been taken into account is part of the prior and as more evidence accumulates the prior is determined largely by the evidence rather than any original assumption, provided that the original assumption admitted the possibility of what the evidence is suggesting. The terms "prior" and "posterior" are generally relative to a specific datum or observation.


The interpretation of the theorem changed with the formulation of the theory of [[Emil Artin]], around 1930. From the time of Galois, the role of primitive elements had been to represent a [[splitting field]] as generated by a single element. This (arbitrary) choice of such an element was bypassed in Artin's treatment.<ref>Israel Kleiner, ''A History of Abstract Algebra'' (2007), p. 64.</ref> At the same time, considerations of construction of such an element receded: the theorem becomes an [[existence theorem]].
== Uninformative priors ==<!-- This section is linked from [[Non-informative prior]] -->


The following theorem of Artin then takes the place of the classical ''primitive element theorem''.
An ''uninformative prior'' expresses vague or general information about a variable.
The term "uninformative prior" may be somewhat of a misnomer; often, such a prior might be called a ''not very informative prior'', or an ''objective prior'', i.e. one that's not subjectively elicited.
Uninformative priors can express "objective" information such as "the variable is positive" or "the variable is less than some limit".


;Theorem
The simplest and oldest rule for determining a non-informative prior is the [[principle of indifference]], which assigns equal probabilities to all possibilities.


Let <math>E\supseteq F</math> be a finite degree field extension. Then <math>E=F[\alpha]</math> for some element <math>\alpha\in E</math> if and only if there exist only finitely many intermediate fields ''K'' with <math>E\supseteq K\supseteq F</math>.
In parameter estimation problems, the use of an uninformative prior typically yields results which are not too different from conventional statistical analysis, as the likelihood function often yields more information than the uninformative prior.


A corollary to the theorem is then the primitive element theorem in the more traditional sense (where separability was usually tacitly assumed):
Some attempts have been made at finding [[a priori probability|a priori probabilities]], i.e. probability distributions in some sense logically required by the nature of one's state of uncertainty; these are a subject of philosophical controversy, with Bayesians being roughly divided into two schools: "objective Bayesians", who believe such priors exist in many useful situations, and "subjective Bayesians" who believe that in practice priors usually represent subjective judgements of opinion that cannot be rigorously justified (Williamson 2010).  Perhaps the strongest arguments for objective Bayesianism were given by [[Edwin T. Jaynes]], based mainly on the consequences of symmetries and on the principle of maximum entropy.


;Corollary
As an example of an a priori prior, due to Jaynes (2003), consider a situation in which one knows a ball has been hidden under one of three cups, A, B or C, but no other information is available about its location.  In this case a ''uniform prior'' of ''p''(''A'')&nbsp;= ''p''(''B'')&nbsp;= ''p''(''C'')&nbsp;= 1/3 seems intuitively like the only reasonable choice.  More formally, we can see that the problem remains the same if we swap around the labels ("A", "B" and "C") of the cups.  It would therefore be odd to choose a prior for which a permutation of the labels would cause a change in our predictions about which cup the ball will be found under; the uniform prior is the only one which preserves this invariance.  If one accepts this invariance principle then one can see that the uniform prior is the logically correct prior to represent this state of knowledge.  It should be noted that this prior is "objective" in the sense of being the correct choice to represent a particular state of knowledge, but it is not objective in the sense of being an observer-independent feature of the world: in reality the ball exists under a particular cup, and it only makes sense to speak of probabilities in this situation if there is an observer with limited knowledge about the system.


Let <math>E\supseteq F</math> be a finite degree [[separable extension]]. Then <math>E=F[\alpha]</math> for some <math>\alpha\in E</math>.
As a more contentious example, Jaynes published an argument (Jaynes 1968) based on [[Lie group]]s that
suggests that the prior representing complete uncertainty about a probability should be the [[Haldane prior]] ''p''<sup>&minus;1</sup>(1&nbsp;&minus;&nbsp;''p'')<sup>&minus;1</sup>.  The example Jaynes gives is of finding a chemical in a lab and asking whether it will dissolve in water in repeated experiments.  The Haldane prior<ref>This prior was proposed by [[J.B.S. Haldane]] in "A note on inverse probability", Mathematical Proceedings of the Cambridge Philosophical Society 28, 55–61, 1932, available online at http://journals.cambridge.org/action/displayAbstract?aid=1733860. See also J. Haldane, "The precision of observed values of small frequencies", Biometrika, 35:297–300, 1948, available online at http://www.jstor.org/pss/2332350.</ref> gives by far the most weight to <math>p=0</math> and <math>p=1</math>, indicating that the sample will either dissolve every time or never dissolve, with equal probability.  However, if one has observed samples of the chemical to dissolve in one experiment and not to dissolve in another experiment then this prior is updated to the [[uniform distribution (continuous)|uniform distribution]] on the interval [0, 1].  This is obtained by applying [[Bayes' theorem]] to the data set consisting of one observation of dissolving and one of not dissolving, using the above prior.  The Haldane prior has been criticized{{By whom|date=July 2010}} on the grounds that it yields an improper posterior distribution that puts 100% of the probability content at either ''p'' = 0 or at ''p'' = 1 if a finite number of observations have given the same result.  The [[Jeffreys prior]] ''p''<sup>&minus;1/2</sup>(1&nbsp;&minus;&nbsp;''p'')<sup>&minus;1/2</sup> is therefore preferred{{By whom|date=July 2010}} (see below).


The corollary applies to [[algebraic number field]]s, i.e. finite extensions of the rational numbers '''Q''', since '''Q''' has [[characteristic (algebra)|characteristic]] 0 and therefore every extension over '''Q''' is separable.
Priors can be constructed which are proportional to the [[Haar measure]] if the parameter space ''X'' carries a [[transformation group|natural group structure]] which leaves invariant our Bayesian state of knowledge (Jaynes, 1968). This can be seen as a generalisation of the invariance principle used to justify the uniform prior over the three cups in the example above. For example, in physics we might expect that an experiment will give the same results regardless of our choice of the origin of a coordinate system. This induces the group structure of the [[translation group]] on ''X'', which determines the prior probability as a constant [[improper prior]]. Similarly, some measurements are naturally invariant to the choice of an arbitrary scale (i.e., it doesn't matter if we use centimeters or inches, we should get results that are physically the same). In such a case, the scale group is the natural group structure, and the corresponding prior on ''X'' is proportional to 1/''x''. It sometimes matters whether we use the left-invariant or right-invariant Haar measure. For example, the left and right invariant Haar measures on the [[affine group]] are not equal. Berger (1985, p.&nbsp;413) argues that the right-invariant Haar measure is the correct choice.


==Counterexamples==
Another idea, championed by [[Edwin T. Jaynes]], is to use the [[principle of maximum entropy]] (MAXENT). The motivation is that the [[Shannon entropy]] of a probability distribution measures the amount of information contained in the distribution. The larger the entropy, the less information is provided by the distribution. Thus, by maximizing the entropy over a suitable set of probability distributions on ''X'', one finds the distribution that is least informative in the sense that it contains the least amount of information consistent with the constraints that define the set. For example, the maximum entropy prior on a discrete space, given only that the probability is normalized to 1, is the prior that assigns equal probability to each state. And in the continuous case, the maximum entropy prior given that the density is normalized with mean zero and variance unity is the standard [[normal distribution]].  The principle of ''[[minxent|minimum cross-entropy]]'' generalizes MAXENT to the case of "updating" an arbitrary prior distribution with suitability constraints in the maximum-entropy sense.


For non-separable extensions, necessarily in [[characteristic p]] with ''p'' a prime number, then at least when the degree [''L''&nbsp;:&nbsp;''K''] is ''p'', ''L''&nbsp;/&nbsp;''K'' has a primitive element, because there are no intermediate subfields. When [''L''&nbsp;:&nbsp;''K''] = ''p''<sup>2</sup>, there may not be a primitive element (and therefore there are infinitely many intermediate fields). This happens, for example if ''K'' is
A related idea, [[reference prior]]s, was introduced by [[José-Miguel Bernardo]]. Here, the idea is to maximize the expected [[Kullback–Leibler divergence]] of the posterior distribution relative to the prior. This maximizes the expected posterior information about ''X'' when the prior density is ''p''(''x''); thus, in some sense, ''p''(''x'') is the "least informative" prior about X. The reference prior is defined in the asymptotic limit, i.e., one considers the limit of the priors so obtained as the number of data points goes to infinity. Reference priors are often the objective prior of choice in multivariate problems, since other rules (e.g., [[Jeffreys prior|Jeffreys' rule]]) may result in priors with problematic behavior.


:''F<sub>p</sub>''(''T'',&nbsp;''U''),
Objective prior distributions may also be derived from other principles, such as [[information theory|information]] or [[coding theory]] (see e.g. [[minimum description length]]) or [[frequentist statistics]] (see [[frequentist matching]]).


the field of rational functions in two indeterminates ''T'' and ''U'' over the [[finite field]] with ''p'' elements, and ''L'' is obtained from ''K'' by adjoining a ''p''-th root of ''T'', and of ''U''. In fact one can see that for any &alpha; in ''L'', the element ''&alpha;''<sup>''p''</sup> lies in ''K'', but a primitive element must have degree ''p''<sup>2</sup> over ''K''.
Philosophical problems associated with uninformative priors are associated with the choice of an appropriate metric, or measurement scale. Suppose we want a prior for the running speed of a runner who is unknown to us. We could specify, say, a normal distribution as the prior for his speed, but alternatively we could specify a normal prior for the time he takes to complete 100 metres, which is proportional to the reciprocal of the first prior. These are very different priors, but it is not clear which is to be preferred.  Jaynes' often-overlooked method of transformation groups can answer this question in some situations.<ref>Jaynes (1968), pp. 17, see also Jaynes (2003), chapter 12.  Note that chapter 12 is not available in the online preprint but can be previewed via Google Books.</ref>


==Constructive results==
Similarly, if asked to estimate an unknown proportion between 0 and 1, we might say that all proportions are equally likely and use a uniform prior. Alternatively, we might say that all orders of magnitude for the proportion are equally likely, the '''{{visible anchor|logarithmic prior}}''', which is the uniform prior on the logarithm of proportion. The [[Jeffreys prior]] attempts to solve this problem by computing a prior which expresses the same belief no matter which metric is used. The Jeffreys prior for an unknown proportion ''p'' is ''p''<sup>&minus;1/2</sup>(1&nbsp;&minus;&nbsp;''p'')<sup>&minus;1/2</sup>, which differs from Jaynes' recommendation.


Generally, the set of all primitive elements for a finite separable extension ''L''&nbsp;/&nbsp;''K'' is the complement of a finite collection of proper ''K''-subspaces of&nbsp;''L'', namely the intermediate fields. This statement says nothing for the case of [[finite field]]s, for which there is a computational theory dedicated to finding a generator of the [[multiplicative group]] of the field (a [[cyclic group]]), which is ''a fortiori'' a primitive element. Where ''K'' is infinite, a [[pigeonhole principle]] proof technique considers the linear subspace generated by two elements and proves that there are only finitely many linear combinations
Priors based on notions of [[algorithmic probability]] are used in [[inductive inference]] as a basis for induction in very general settings.


:<math>\gamma = \alpha + c \beta\ </math>
Practical problems associated with uninformative priors include the requirement that the posterior distribution be proper. The usual uninformative priors on continuous, unbounded variables are improper. This need not be a problem if the posterior distribution is proper. Another issue of importance is that if an uninformative prior is to be used ''routinely'', i.e., with many different data sets, it should have good [[frequentist]] properties. Normally a [[Bayesian probability|Bayesian]] would not be concerned with such issues, but it can be important in this situation. For example, one would want any [[decision theory|decision rule]] based on the posterior distribution to be [[admissible decision rule|admissible]] under the adopted loss function. Unfortunately, admissibility is often difficult to check, although some results are known (e.g., Berger and Strawderman 1996). The issue is particularly acute with [[hierarchical Bayes model]]s; the usual priors (e.g., Jeffreys' prior) may give badly inadmissible decision rules if employed at the higher levels of the hierarchy.


with ''c'' in ''K'' in it, that fail to generate the subfield containing both elements. This is almost immediate as a way of showing how Artin's result implies the classical result, and a bound for the number of exceptional ''c'' in terms of the number of intermediate fields results (this number being something that can be bounded itself by Galois theory and ''a priori''). Therefore in this case trial-and-error is a possible practical method to find primitive elements. See the Example.
==Improper priors==


== Example ==
If Bayes' theorem is written as
It is not, for example, immediately obvious that if one adjoins to the field '''Q''' of [[rational number]]s roots of both [[polynomial]]s
:<math>P(A_i|B) = \frac{P(B | A_i) P(A_i)}{\sum_j P(B|A_j)P(A_j)}\, ,</math>
then it is clear that the same result would be obtained if all the prior probabilities ''P''(''A''<sub>''i''</sub>) and ''P''(''A''<sub>''j''</sub>) were multiplied by a given constant; the same would be true for a [[continuous random variable]].  If the summation in the denominator converges, the posterior probabilities will still sum (or integrate) to 1 even if the prior values do not, and so the priors may only need to be specified in the correct proportion. Taking this idea further, in many cases the sum or integral of the prior values may not even need to be finite to get sensible answers for the posterior probabilities.  When this is the case, the prior is called an '''improper prior'''.  However, the posterior distribution need not be a proper distribution if the prior is improper. This is clear from the case where event ''B'' is independent of all of the ''A''<sub>''j''</sub>.


:<math>x^2 - 2\ </math>
Some statisticians{{Citation needed|date=December 2008}} use improper priors as [[uninformative prior]]s.  For example, if they need a prior distribution for the mean and variance of a random variable, they may assume ''p''(''m'',&nbsp;''v'')&nbsp;~&nbsp;1/''v'' (for ''v''&nbsp;>&nbsp;0) which would suggest that any value for the mean is "equally likely" and that a value for the positive variance becomes "less likely" in inverse proportion to its value.  Many authors (Lindley, 1973; De Groot, 1937; Kass and Wasserman, 1996){{Citation needed|date=December 2008}} warn against the danger of over-interpreting those priors since they are not probability densities. The only relevance they have is found in the corresponding posterior, as long as it is well-defined for all observations. (The [[Beta distribution#Haldane.27s prior probability .28 Beta.280.2C0.29 .29|Haldane prior]] is a typical counterexample.{{Clarify|reason=counterexample of what?|date=May 2011}}{{Citation needed|date=May 2011}})


and
=== Examples ===
Examples of improper priors include:
* Beta(0,0), the [[beta distribution]] for α=0, β=0.
* The [[uniform distribution (continuous)|uniform distribution]] on an infinite interval (i.e., a half-line or the entire real line).
* The logarithmic prior on the positive reals.{{Citation needed|date=October 2010}}


:<math>x^2 - 3,\ </math>
==Other priors==
The concept of [[algorithmic probability]] provides a route to specifying prior probabilities based on the relative complexity of the alternative models being considered.


say &alpha; and &beta; respectively, to get a field ''K''&nbsp;=&nbsp;'''Q'''(&alpha;,&nbsp;&beta;) of [[Degree of a field extension|degree]] 4 over '''Q''', that the extension is simple and there exists a primitive element &gamma; in ''K'' so that ''K''&nbsp;=&nbsp;'''Q'''(&gamma;). One can in fact check that with
== Notes ==


:<math>\gamma = \alpha + \beta\ </math>
<references/>


the powers &gamma;<sup>&nbsp;''i''</sup> for 0&nbsp;&le;&nbsp;''i''&nbsp;&le;&nbsp;3 can be written out as [[linear combination]]s of&nbsp;1,&nbsp;&alpha;,&nbsp;&beta; and ''&alpha;&beta;'' with integer coefficients. Taking these as a [[system of linear equations]], or by factoring, one can solve for &alpha; and &beta; over&nbsp;'''Q'''(''&gamma;'') (one gets, for instance, &alpha;=<math>\scriptstyle\frac{\gamma^3-9\gamma}2</math>), which implies that this choice of &gamma; is indeed a primitive element in this example. A simpler argument, assuming the knowledge of all the subfields as given by Galois theory, is to note the independence of 1,&nbsp;&alpha;,&nbsp;&beta; and &alpha;&beta; over the rationals; this shows that the subfield generated by &gamma; cannot be that generated &alpha; or &beta;, nor in fact that generated by &alpha;&beta;, exhausting all the subfields of degree 2. Therefore it must be the whole field.
== References ==


== See also ==
* {{cite book |author=Rubin, Donald B.; [[Andrew Gelman|Gelman, Andrew]]; John B. Carlin; Stern, Hal |title=Bayesian Data Analysis |edition=2nd |publisher=Chapman & Hall/CRC |location=Boca Raton |year=2003 |pages= |isbn=1-58488-388-X |doi= |accessdate= |mr=2027492 }}
* [[Primitive element (finite field)]]
* {{cite book |last=Berger |first=James O. |title=Statistical decision theory and Bayesian analysis |publisher=Springer-Verlag |location=Berlin |year=1985 |pages= |isbn=0-387-96098-8 |doi= |accessdate= |mr=0804611 }}
* {{cite journal
|first1=James O. |last1=Berger
|first2=William E. |last2=Strawderman
|title=Choice of hierarchical priors: admissibility in estimation of normal means
|journal=[[Annals of Statistics]]
|volume=24 |issue=3 |pages=931&ndash;951 |year=1996
|doi=10.1214/aos/1032526950
|mr=1401831 | zbl = 0865.62004
}}
* {{cite journal |first=Jose M. |last=Bernardo
|title=Reference Posterior Distributions for Bayesian Inference
|journal=[[Journal of the Royal Statistical Society]], Series B
|volume=41 |issue= 2 |pages=113&ndash;147 |year=1979
|mr=0547240 | jstor = 2985028
}}
* {{cite journal | title=The formal definition of reference priors
|author1=James O. Berger
|authorlink1=James Berger (statistician)
|author2=José M. Bernardo
|authorlink2=José-Miguel Bernardo
|author3=Dongchu Sun
|journal=Annals of Statistics
|year=2009
|volume=37
|issue=2
|pages=905–938
|arxiv=0904.0156 | doi=10.1214/07-AOS587
}}
* {{cite journal|last=Jaynes |first=Edwin T. |authorlink= Edwin T. Jaynes |title=Prior Probabilities |journal=IEEE Transactions on Systems Science and Cybernetics |volume=4 |issue=3 |pages=227&ndash;241 |date=Sep 1968 |doi=10.1109/TSSC.1968.300117 |url=http://bayes.wustl.edu/etj/articles/prior.pdf |accessdate=2009-03-27}}
** Reprinted in {{cite book |author=Rosenkrantz, Roger D. |title=E. T. Jaynes: papers on probability, statistics, and statistical physics |publisher=Kluwer Academic Publishers |location=Boston |year=1989 |isbn=90-277-1448-7 |doi= |accessdate= |pages=116&ndash;130}}
* {{cite book |last=Jaynes |first=Edwin T. |authorlink= Edwin T. Jaynes |title= Probability Theory: The Logic of Science |publisher=Cambridge University Press |year=2003 |pages= |isbn=0-521-59271-2 |doi= |accessdate= |url=http://www-biba.inrialpes.fr/Jaynes/prob.html }}
* {{cite journal|last=Williamson |first=Jon |title=review of Bruno di Finetti. Philosophical Lectures on Probability |journal=Philosophia Mathematica |volume=18 |issue=1 |pages=130&ndash;135 |year=2010 |doi=10.1093/philmat/nkp019  |url=http://www.kent.ac.uk/secl/philosophy/jw/2009/deFinetti.pdf |accessdate=2010-07-02}}


==References==
{{DEFAULTSORT:Prior Probability}}
 
[[Category:Bayesian statistics]]
* [http://www.mathreference.com/fld-sep,pet.html The primitive element theorem at mathreference.com]
[[Category:Probability assessment]]
* [http://planetmath.org/encyclopedia/ProofOfPrimitiveElementTheorem2.html The primitive element theorem at planetmath.org]
* [http://www.math.cornell.edu/~kbrown/6310/primitive.pdf The primitive element theorem on the site of Cornell's university (pdf file)]
 
==Notes==
{{Reflist}}
 
[[Category:Field theory]]
[[Category:Theorems in abstract algebra]]
 
[[de:Satz vom primitiven Element]]
[[fr:Théorème de l'élément primitif]]
[[it:Teorema dell'elemento primitivo]]
[[pt:Teorema do elemento primitivo]]
[[uk:Теорема про первісний елемент]]
[[zh:本原元定理]]

Revision as of 03:23, 12 August 2014

Template:Distinguish

Template:No footnotes

Template:Bayesian statistics

In Bayesian statistical inference, a prior probability distribution, often called simply the prior, of an uncertain quantity p is the probability distribution that would express one's uncertainty about p before some evidence is taken into account. For example, p could be the proportion of voters who will vote for a particular politician in a future election. It is meant to attribute uncertainty rather than randomness to the uncertain quantity. The unknown quantity may be a parameter or latent variable.

One applies Bayes' theorem, multiplying the prior by the likelihood function and then normalizing, to get the posterior probability distribution, which is the conditional distribution of the uncertain quantity given the data.

A prior is often the purely subjective assessment of an experienced expert. Some will choose a conjugate prior when they can, to make calculation of the posterior distribution easier.

Parameters of prior distributions are called hyperparameters, to distinguish them from parameters of the model of the underlying data. For instance, if one is using a beta distribution to model the distribution of the parameter p of a Bernoulli distribution, then:

  • p is a parameter of the underlying system (Bernoulli distribution), and
  • α and β are parameters of the prior distribution (beta distribution), hence hyperparameters.

Informative priors

An informative prior expresses specific, definite information about a variable. An example is a prior distribution for the temperature at noon tomorrow. A reasonable approach is to make the prior a normal distribution with expected value equal to today's noontime temperature, with variance equal to the day-to-day variance of atmospheric temperature, or a distribution of the temperature for that day of the year.

This example has a property in common with many priors, namely, that the posterior from one problem (today's temperature) becomes the prior for another problem (tomorrow's temperature); pre-existing evidence which has already been taken into account is part of the prior and as more evidence accumulates the prior is determined largely by the evidence rather than any original assumption, provided that the original assumption admitted the possibility of what the evidence is suggesting. The terms "prior" and "posterior" are generally relative to a specific datum or observation.

Uninformative priors

An uninformative prior expresses vague or general information about a variable. The term "uninformative prior" may be somewhat of a misnomer; often, such a prior might be called a not very informative prior, or an objective prior, i.e. one that's not subjectively elicited. Uninformative priors can express "objective" information such as "the variable is positive" or "the variable is less than some limit".

The simplest and oldest rule for determining a non-informative prior is the principle of indifference, which assigns equal probabilities to all possibilities.

In parameter estimation problems, the use of an uninformative prior typically yields results which are not too different from conventional statistical analysis, as the likelihood function often yields more information than the uninformative prior.

Some attempts have been made at finding a priori probabilities, i.e. probability distributions in some sense logically required by the nature of one's state of uncertainty; these are a subject of philosophical controversy, with Bayesians being roughly divided into two schools: "objective Bayesians", who believe such priors exist in many useful situations, and "subjective Bayesians" who believe that in practice priors usually represent subjective judgements of opinion that cannot be rigorously justified (Williamson 2010). Perhaps the strongest arguments for objective Bayesianism were given by Edwin T. Jaynes, based mainly on the consequences of symmetries and on the principle of maximum entropy.

As an example of an a priori prior, due to Jaynes (2003), consider a situation in which one knows a ball has been hidden under one of three cups, A, B or C, but no other information is available about its location. In this case a uniform prior of p(A) = p(B) = p(C) = 1/3 seems intuitively like the only reasonable choice. More formally, we can see that the problem remains the same if we swap around the labels ("A", "B" and "C") of the cups. It would therefore be odd to choose a prior for which a permutation of the labels would cause a change in our predictions about which cup the ball will be found under; the uniform prior is the only one which preserves this invariance. If one accepts this invariance principle then one can see that the uniform prior is the logically correct prior to represent this state of knowledge. It should be noted that this prior is "objective" in the sense of being the correct choice to represent a particular state of knowledge, but it is not objective in the sense of being an observer-independent feature of the world: in reality the ball exists under a particular cup, and it only makes sense to speak of probabilities in this situation if there is an observer with limited knowledge about the system.

As a more contentious example, Jaynes published an argument (Jaynes 1968) based on Lie groups that suggests that the prior representing complete uncertainty about a probability should be the Haldane prior p−1(1 − p)−1. The example Jaynes gives is of finding a chemical in a lab and asking whether it will dissolve in water in repeated experiments. The Haldane prior[1] gives by far the most weight to and , indicating that the sample will either dissolve every time or never dissolve, with equal probability. However, if one has observed samples of the chemical to dissolve in one experiment and not to dissolve in another experiment then this prior is updated to the uniform distribution on the interval [0, 1]. This is obtained by applying Bayes' theorem to the data set consisting of one observation of dissolving and one of not dissolving, using the above prior. The Haldane prior has been criticizedTemplate:By whom on the grounds that it yields an improper posterior distribution that puts 100% of the probability content at either p = 0 or at p = 1 if a finite number of observations have given the same result. The Jeffreys prior p−1/2(1 − p)−1/2 is therefore preferredTemplate:By whom (see below).

Priors can be constructed which are proportional to the Haar measure if the parameter space X carries a natural group structure which leaves invariant our Bayesian state of knowledge (Jaynes, 1968). This can be seen as a generalisation of the invariance principle used to justify the uniform prior over the three cups in the example above. For example, in physics we might expect that an experiment will give the same results regardless of our choice of the origin of a coordinate system. This induces the group structure of the translation group on X, which determines the prior probability as a constant improper prior. Similarly, some measurements are naturally invariant to the choice of an arbitrary scale (i.e., it doesn't matter if we use centimeters or inches, we should get results that are physically the same). In such a case, the scale group is the natural group structure, and the corresponding prior on X is proportional to 1/x. It sometimes matters whether we use the left-invariant or right-invariant Haar measure. For example, the left and right invariant Haar measures on the affine group are not equal. Berger (1985, p. 413) argues that the right-invariant Haar measure is the correct choice.

Another idea, championed by Edwin T. Jaynes, is to use the principle of maximum entropy (MAXENT). The motivation is that the Shannon entropy of a probability distribution measures the amount of information contained in the distribution. The larger the entropy, the less information is provided by the distribution. Thus, by maximizing the entropy over a suitable set of probability distributions on X, one finds the distribution that is least informative in the sense that it contains the least amount of information consistent with the constraints that define the set. For example, the maximum entropy prior on a discrete space, given only that the probability is normalized to 1, is the prior that assigns equal probability to each state. And in the continuous case, the maximum entropy prior given that the density is normalized with mean zero and variance unity is the standard normal distribution. The principle of minimum cross-entropy generalizes MAXENT to the case of "updating" an arbitrary prior distribution with suitability constraints in the maximum-entropy sense.

A related idea, reference priors, was introduced by José-Miguel Bernardo. Here, the idea is to maximize the expected Kullback–Leibler divergence of the posterior distribution relative to the prior. This maximizes the expected posterior information about X when the prior density is p(x); thus, in some sense, p(x) is the "least informative" prior about X. The reference prior is defined in the asymptotic limit, i.e., one considers the limit of the priors so obtained as the number of data points goes to infinity. Reference priors are often the objective prior of choice in multivariate problems, since other rules (e.g., Jeffreys' rule) may result in priors with problematic behavior.

Objective prior distributions may also be derived from other principles, such as information or coding theory (see e.g. minimum description length) or frequentist statistics (see frequentist matching).

Philosophical problems associated with uninformative priors are associated with the choice of an appropriate metric, or measurement scale. Suppose we want a prior for the running speed of a runner who is unknown to us. We could specify, say, a normal distribution as the prior for his speed, but alternatively we could specify a normal prior for the time he takes to complete 100 metres, which is proportional to the reciprocal of the first prior. These are very different priors, but it is not clear which is to be preferred. Jaynes' often-overlooked method of transformation groups can answer this question in some situations.[2]

Similarly, if asked to estimate an unknown proportion between 0 and 1, we might say that all proportions are equally likely and use a uniform prior. Alternatively, we might say that all orders of magnitude for the proportion are equally likely, the Template:Visible anchor, which is the uniform prior on the logarithm of proportion. The Jeffreys prior attempts to solve this problem by computing a prior which expresses the same belief no matter which metric is used. The Jeffreys prior for an unknown proportion p is p−1/2(1 − p)−1/2, which differs from Jaynes' recommendation.

Priors based on notions of algorithmic probability are used in inductive inference as a basis for induction in very general settings.

Practical problems associated with uninformative priors include the requirement that the posterior distribution be proper. The usual uninformative priors on continuous, unbounded variables are improper. This need not be a problem if the posterior distribution is proper. Another issue of importance is that if an uninformative prior is to be used routinely, i.e., with many different data sets, it should have good frequentist properties. Normally a Bayesian would not be concerned with such issues, but it can be important in this situation. For example, one would want any decision rule based on the posterior distribution to be admissible under the adopted loss function. Unfortunately, admissibility is often difficult to check, although some results are known (e.g., Berger and Strawderman 1996). The issue is particularly acute with hierarchical Bayes models; the usual priors (e.g., Jeffreys' prior) may give badly inadmissible decision rules if employed at the higher levels of the hierarchy.

Improper priors

If Bayes' theorem is written as

then it is clear that the same result would be obtained if all the prior probabilities P(Ai) and P(Aj) were multiplied by a given constant; the same would be true for a continuous random variable. If the summation in the denominator converges, the posterior probabilities will still sum (or integrate) to 1 even if the prior values do not, and so the priors may only need to be specified in the correct proportion. Taking this idea further, in many cases the sum or integral of the prior values may not even need to be finite to get sensible answers for the posterior probabilities. When this is the case, the prior is called an improper prior. However, the posterior distribution need not be a proper distribution if the prior is improper. This is clear from the case where event B is independent of all of the Aj.

Some statisticiansPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. use improper priors as uninformative priors. For example, if they need a prior distribution for the mean and variance of a random variable, they may assume p(m, v) ~ 1/v (for v > 0) which would suggest that any value for the mean is "equally likely" and that a value for the positive variance becomes "less likely" in inverse proportion to its value. Many authors (Lindley, 1973; De Groot, 1937; Kass and Wasserman, 1996)Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. warn against the danger of over-interpreting those priors since they are not probability densities. The only relevance they have is found in the corresponding posterior, as long as it is well-defined for all observations. (The Haldane prior is a typical counterexample.Template:ClarifyPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.)

Examples

Examples of improper priors include:

  • Beta(0,0), the beta distribution for α=0, β=0.
  • The uniform distribution on an infinite interval (i.e., a half-line or the entire real line).
  • The logarithmic prior on the positive reals.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

Other priors

The concept of algorithmic probability provides a route to specifying prior probabilities based on the relative complexity of the alternative models being considered.

Notes

  1. ↑ This prior was proposed by J.B.S. Haldane in "A note on inverse probability", Mathematical Proceedings of the Cambridge Philosophical Society 28, 55–61, 1932, available online at http://journals.cambridge.org/action/displayAbstract?aid=1733860. See also J. Haldane, "The precision of observed values of small frequencies", Biometrika, 35:297–300, 1948, available online at http://www.jstor.org/pss/2332350.
  2. ↑ Jaynes (1968), pp. 17, see also Jaynes (2003), chapter 12. Note that chapter 12 is not available in the online preprint but can be previewed via Google Books.

References

  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
    • Reprinted in 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
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