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{{multiple issues|
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{{refimprove|date=November 2013}}
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{{Bayesian statistics}}{{Probability fundamentals}}
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'''Bayesian Programming''' is a formalism and a methodology to specify probabilistic models and solve problems when all the necessary information is not available.
 
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[[Edwin Thompson Jaynes|Edwin T. Jaynes]] proposed that probability could be considered as an alternative and an extension of logic for rational reasoning with incomplete and uncertain information. In his founding book ''Probability Theory: The Logic of Science''<ref name=Jaynes2003>{{cite book|last=Jaynes|first=Edwin T.|title=Probability Theory: The Logic of Science|year=2003|publisher=Cambridge University Press|isbn=0-521-59271-2}}</ref>  he developed this theory and proposed what he called “the robot,” which was not
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a physical device, but an inference engine to automate probabilistic reasoning
— a kind of [[Prolog]] for probability instead of logic. Bayesian Programming<ref name=Bessiere2013>{{cite book|last=Bessière|first=P.|title=Bayesian Programming|year=2013|publisher=Chapman & Hall/CRC|isbn=9781439880326|coauthors=Mazer, E.; Ahuactzin, J-M. & Mekhnacha, K.}}</ref> is a formal and concrete implementation of this "robot".


Bayesian programming may also be seen as an algebraic formalism to specify [[graphical model]]s such as, for instance, [[Bayesian network|Bayesian networks]], [[Dynamic Bayesian network|Dynamic Bayesian networks]], [[Kalman filter|Kalman filters]] or [[Hidden Markov Model|Hidden Markov Models]]. Indeed, Bayesian Programming is more general than [[Bayesian network|Bayesian networks]] and has a power of expression equivalent to [[Factor graph|probabilistic factor graphs]].
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== Formalism ==
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A Bayesian program is a means of specifying a family of probability distributions.
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The constituent elements of a Bayesian program are presented below:
== In messy Mbt Shoes ==


<math>
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Program
 
\begin{cases}
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Description
 
  \begin{cases}
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  Specification (\pi)
 
      \begin{cases}
   <li>[http://bbs.0714.cn/forum.php?mod=viewthread&tid=6580521&extra= http://bbs.0714.cn/forum.php?mod=viewthread&tid=6580521&extra=]</li>
      Variables\\
 
      Decomposition\\
   <li>[http://verdamilio.net/tonio/spip.php?article1739/ http://verdamilio.net/tonio/spip.php?article1739/]</li>
      Forms\\
 
      \end{cases}\\
</ul>
   Identification\ (based\ on\ \delta)
   \end{cases}\\
Question
\end{cases}
</math>


# A program is constructed from a description and a question.
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# A description is constructed using some specification (<math>\pi</math>) as given by the programmer and an identification or learning process for the parameters not completely specified by the specification, using a data set (<math>\delta</math>).
# A specification is constructed from a set of pertinent variables, a decomposition and a set of forms.
# Forms are either parametric forms or questions to other Bayesian programs.
# A question specifies which probability distribution has to be computed.


=== Description ===
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The purpose of a description is to specify an effective method of computing a [[joint probability distribution]]
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on a set of [[Random variable|variables]] <math>\left\{ X_{1},X_{2},\cdots,X_{N}\right\}</math> given a set of experimental data <math>\delta</math> and some
specification <math>\pi</math>. This [[Joint probability distribution|joint distribution]] is denoted as: <math>P\left(X_{1}\wedge X_{2}\wedge\cdots\wedge X_{N}|\delta\wedge\pi\right)</math>.


To specify preliminary knowledge <math>\pi</math>, the programmer must undertake the following:
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  <li>[http://www.indesign-podcast.de/2013/05/17/272-neu-in-indesign-cc-dokumente-anlegen-mit-vorschau/#comments http://www.indesign-podcast.de/2013/05/17/272-neu-in-indesign-cc-dokumente-anlegen-mit-vorschau/#comments]</li>
 
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</ul>


# Define the set of relevant [[Random variable|variables]] <math>\left\{ X_{1},X_{2},\cdots,X_{N}\right\}</math> on which the joint distribution is defined.
== AP Vibram Ireland ==
# Decompose the joint distribution (break it into relevant [[Independence (probability theory)|independant]] or [[Conditional probability|conditional probabilities]]).
# Define the forms each of the distributions (e.g., for each variable, one of the [[list of probability distributions]]).


==== Decomposition ====
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Given a partition <math>\left\{ X_{1},X_{2},\cdots,X_{N}\right\}</math> containing <math>K</math> subsets, <math>K</math> variables are defined
  <li>[http://www.688680.com/read.php?tid=185610 http://www.688680.com/read.php?tid=185610]</li>
<math>L_{1},\cdots,L_{K}</math>, each corresponding to one of these subsets.
 
Each variable <math>L_{k}</math> is obtained as the conjunction of the variables <math>\left\{ X_{k_{1}},X_{k_{2}},\cdots\right\}</math>
  <li>[http://verdamilio.net/tonio/spip.php?article1970/ http://verdamilio.net/tonio/spip.php?article1970/]</li>
belonging to the <math>k^{th}</math> subset. Recursive application of [[Bayes' theorem]] leads to:
 
 
  <li>[http://www.christophegreffet.fr/blog/index.php?2013/07/09/81-une-semaine-cruciale-pour-le-finances-departementales/ http://www.christophegreffet.fr/blog/index.php?2013/07/09/81-une-semaine-cruciale-pour-le-finances-departementales/]</li>
<math>
 
\begin{array}{rl}
  <li>[http://www.52jiaoyou.com/forum.php?mod=viewthread&tid=2417902&fromuid=54125 http://www.52jiaoyou.com/forum.php?mod=viewthread&tid=2417902&fromuid=54125]</li>
& P\left(X_{1}\wedge X_{2}\wedge\cdots\wedge X_{N}|\delta\wedge\pi\right)\\
 
= & P\left(L_{1}\wedge\cdots\wedge L_{K}|\delta\wedge\pi\right)\\
</ul>
= & P\left(L_{1}|\delta\wedge\pi\right)\times P\left(L_{2}|L_{1}\wedge\delta\wedge\pi\right) \times\cdots\times P\left(L_{K}|L_{K-1}\wedge\cdots\wedge L_{1}\wedge\delta\wedge\pi\right)\end{array}
</math>
 
[[Conditional independance|Conditional independence]] hypotheses then allow further simplifications. A conditional
independence hypothesis for variable <math>L_{k}</math> is defined by choosing some variable <math>X_{n}</math>
among the variables appearing in the conjunction <math>L_{k-1}\wedge\cdots\wedge L_{2}\wedge L_{1}</math>, labelling <math>R_{k}</math> as the
conjunction of these chosen variables and setting:
 
<math>
P\left(L_{k}|L_{k-1}\wedge\cdots\wedge L_{1}\wedge\delta\wedge\pi\right)=P\left(L_{k}|R_{k}\wedge\delta\wedge\pi\right)
</math>
 
We then obtain:
 
<math>
\begin{array}{rl}
& P\left(X_{1}\wedge X_{2}\wedge\cdots\wedge X_{N}|\delta\wedge\pi\right)\\
= & P\left(L_{1}|\delta\wedge\pi\right)\times P\left(L_{2}|R_{2}\wedge\delta\wedge\pi\right)\times\cdots\times P\left(L_{K}|R_{K}\wedge\delta\wedge\pi\right)\end{array}
</math>
 
Such a simplification of the joint distribution as a product of simpler distributions is
called a decomposition, derived using the [[Chain rule (probability)|chain rule]].
 
This ensures that each variable appears at the most once on the left of a conditioning
bar, which is the necessary and sufficient condition to write mathematically valid
decompositions{{Citation needed|date=November 2013}}.
 
==== Forms ====
 
Each distribution <math>P\left(L_{k}|R_{k}\wedge\delta\wedge\pi\right)</math> appearing in the product is then associated
with either a parametric form (i.e., a function <math>f_{\mu}\left(L_{k}\right)</math>) or a question to another Bayesian program <math>P\left(L_{k}|R_{k}\wedge\delta\wedge\pi\right) = P\left(L|R\wedge\widehat{\delta}\wedge\widehat{\pi}\right)</math>.
 
When it is a form <math>f_{\mu}\left(L_{k}\right)</math>, in general, <math>\mu</math> is a vector of parameters that may depend on <math>R_{k}</math> or <math>\delta</math> or both. Learning
takes place when some of these parameters are computed using the data set <math>\delta</math>.
 
An important feature of Bayesian Programming is this capacity to use questions to other Bayesian programs as components of the definition of a new Bayesian program. <math>P\left(L_{k}|R_{k}\wedge\delta\wedge\pi\right)</math> is obtained by some inferences done by another Bayesian program defined by the specifications <math>\widehat{\pi}</math> and the data <math>\widehat{\delta}</math>. This is similar to calling a subroutine in classical programming and provides an easy way to build [[Bayesian network#Hierarchical models|hierarchical models]].
 
=== Question ===
 
Given a description (i.e., <math>P\left(X_{1}\wedge X_{2}\wedge\cdots\wedge X_{N}|\delta\wedge\pi\right)</math>), a question is obtained by partitioning <math>\left\{ X_{1},X_{2},\cdots,X_{N}\right\}</math>
into three sets: the searched variables, the known variables and
the free variables.
 
The 3 variables <math>Searched</math>, <math>Known</math> and <math>Free</math> are defined as the
conjunction of the variables belonging to
these sets.
 
A question is defined as the set
of distributions:
 
<math>
P\left(Searched|Known\wedge\delta\wedge\pi\right)
</math>
 
made of many "instantiated questions" as the cardinal of <math>Known</math>,
each instantiated question being the distribution:
 
<math>
P\left(Searched|Known\wedge\delta\wedge\pi\right)
</math>
 
=== Inference ===
 
Given the joint distribution
<math>P\left(X_{1}\wedge X_{2}\wedge\cdots\wedge
X_{N}|\delta\wedge\pi\right)</math>, it is always possible to compute
any possible question using the following
general inference:
 
<math>
\begin{array}{cl}
& P\left(Searched|Known\wedge\delta\wedge\pi\right)\\
= & \sum_{Free}\left[P\left(Searched\wedge Free|Known\wedge\delta\wedge\pi\right)\right]\\
= & \frac{\displaystyle \sum_{Free}\left[P\left(Searched\wedge Free\wedge Known|\delta\wedge\pi\right)\right]}{\displaystyle P\left(Known|\delta\wedge\pi\right)}\\
= & \frac{\displaystyle \sum_{Free}\left[P\left(Searched\wedge Free\wedge Known|\delta\wedge\pi\right)\right]}{\displaystyle \sum_{Free\wedge Searched}\left[P\left(Searched\wedge Free\wedge Known|\delta\wedge\pi\right)\right]}\\
= & \frac{1}{Z}\times\sum_{Free}\left[P\left(Searched\wedge Free \wedge Known | \delta\wedge\pi\right)\right]\end{array}
</math>
 
where the first equality results from the marginalization rule, the second
results from [[Bayes' theorem]] and the third corresponds to a second application of marginalization. The denominator appears to be a normalization term and can be replaced by a constant <math>Z</math>.
 
Theoretically, this allows to solve any Bayesian inference problem. In practice,
however, the cost of computing exhaustively and exactly <math>P\left(Searched|Known\wedge\delta\wedge\pi\right)</math>
is too great in almost all cases.
 
Replacing the joint distribution but its decomposition we get:
 
<math>
\begin{array}{cl}
& P\left(Searched|Known\wedge\delta\wedge\pi\right)\\
= & \frac{1}{Z}\sum_{Free}\left[\prod_{k=1}^{K}\left[P\left(L_{i}|K_{i}\wedge\pi\right)\right]\right]
\end{array}
</math>
 
which is usually a much simpler expression to compute, as the dimensionality of the problem is considerably reduced by the decomposition into a product of lower dimension distributions.
 
== Example ==
 
===Bayesian spam detection===
 
The purpose of [[Bayesian spam filtering]] is to eliminate junk e-mails.
 
The problem is very easy to formulate. E-mails should be classified
into one of two categories: non-spam or spam. The only available information to classify the e-mails is their content: a set of words. Using these words without taking the order into account is commonly called a [[Bag of words|bag of words model]].
 
The classifier should furthermore be able to adapt to its user and to learn
from experience. Starting from an initial standard setting, the classifier should
modify its internal parameters when the user disagrees with its own decision.
It will hence adapt to the user’s criteria to differentiate between non-spam and
spam. It will improve its results as it encounters increasingly classified e-mails.
 
==== Variables ====
 
The variables necessary to write this program are as follows:
# <math>Spam</math>: a binary variable, false if the e-mail is not spam and true otherwise.
# <math>W_0,W_1, ..., W_{N-1}</math>: <math>N</math> binary variables. <math>W_n</math> is true if the <math>n^{th}</math> word of the dictionary is present in the text.
 
These <math>N + 1</math> binary variables sum up all the information
about an e-mail.
 
==== Decomposition ====
 
Starting from the joint distribution and applying recursively [[Bayes' theorem]] we obtain:
 
<math>
\begin{array}{ll}
& P\left(Spam\wedge W_{0}\wedge\cdots\wedge W_{N-1}\right)\\
= & P\left(Spam\right)\times P\left(W_{0}|Spam\right)\times P\left(W_{1}|Spam\wedge W_{0}\right)\\
& \times\cdots\\
& \times P\left(W_{N-1}|Spam\wedge W_{0}\wedge\cdots\wedge W_{N-2}\right)\end{array}
</math>
 
This is an exact mathematical expression.
 
It can be drastically simplified by assuming that the probability of
appearance of a word knowing the nature of the text (spam or not) is
independent of the appearance of the other words. This is the [[Naive bayes|naive Bayes]] assumption and this makes this spam filter a [[Naive bayes|naive Bayes model]].
 
For instance, the programmer can assume that:
 
<math>
P(W_1|Spam \land W_0) = P(W_1|Spam)
</math>
 
to finally obtain:
 
<math>
P(Spam \land W_0 \land \ldots
      \land W_{N-1}) = P(Spam)\prod_{n=0}^{N-1}[P(W_n|Spam)]
</math>
 
This kind of assumption is known as the [[Naive Bayes classifier|naive Bayes' assumption]].
It  is "naive" in the sense that the independence between words is clearly
not completely true. For instance, it completely neglects that the
appearance of pairs of words may be more significant than isolated
appearances. However, the programmer may assume this hypothesis and
may develop the model and the associated inferences to test how
reliable and efficient it is.
 
==== Parametric forms ====
 
To be able to compute the joint distribution, the programmer must now specify the
<math>N + 1</math> distributions appearing in the decomposition:
 
# <math>P(Spam)</math> is a prior defined, for instance, by <math>P([Spam=1])=0.75</math>
# Each of the <math>N</math>  forms <math>P(W_n|Spam)</math> may be specified using [[Laplace rule of succession]] (this is a pseudocounts-based [[N-gram#Smoothing techniques|smoothing technique]] to counter the [[PPM compression algorithm|zero-frequency problem]] of words never-seen-before):
## <math>P(W_n|[Spam=false])=\frac{1+a^n_f}{2+a_f}</math>
## <math>P(W_n|[Spam=true])=\frac{1+a^n_t}{2+a_t}</math>
 
where <math>a^n_f</math> stands for the number of appearances of the <math>n^{th}</math> word in non-spam e-mails
and <math>a_f</math> stands for the total number of non-spam e-mails. Similarly, <math>a_t^n</math>
stands for the number of appearances of the <math>n^{th}</math> word in spam
e-mails and <math>a_t</math> stands for the total number of spam
e-mails.
 
==== Identification ====
 
The <math>N</math>  forms <math>P(W_n|Spam)</math> are not yet completely specified because the <math>2N + 2</math> parameters
<math>a_f^{n=0, \ldots, N-1}</math>, <math>a_t^{n=0, \ldots, N-1}</math>, <math>a_f</math> and <math>a_t</math> have no values yet.
 
The identification of these parameters could be done either by batch processing a
series of classified e-mails or by an incremental updating of the
parameters using the user's classifications of the e-mails as they
arrive.
 
Both methods could be combined: the system could start with initial standard values
of these parameters issued from a generic database, then some
incremental learning customizes the classifier to each individual
user.
 
==== Question ====
 
The question asked to the program is: "what is the probability for a given text to be spam knowing which words appear and don't appear in this text?"
It can be formalized by:
<math>P\left(Spam|w_{0}\wedge\cdots\wedge w_{N-1}\right)</math>
 
which can be computed as follows:
 
<math>\begin{array}{ll}
& P\left(Spam|w_{0}\wedge\cdots\wedge w_{N-1}\right)\\
= & \frac{\displaystyle P\left(Spam\right)\prod_{n=0}^{N-1}\left[P\left(w_{n}|Spam\right)\right]}{\displaystyle \sum_{Spam}\left[P\left(Spam\right)\prod_{n=0}^{N-1}\left[P\left(w_{n}|Spam\right)\right]\right]}\end{array}</math>
 
The denominator appears to be a [[Normalizing constant|normalization constant]]. It is not necessary to compute it to
decide if we are dealing with spam. For instance, an easy trick is to compute the
ratio:
 
<math>
\begin{array}{ll}
& \frac{P\left(\left[Spam=true\right]|w_{0}\wedge\cdots\wedge w_{N-1}\right)}{P\left(\left[Spam=false\right]|w_{0}\wedge\cdots\wedge w_{N-1}\right)}\\
= & \frac{P\left(\left[Spam=true\right]\right)}{P\left(\left[Spam=false\right]\right)}\times\prod_{n=0}^{N-1}\left[\frac{P\left(w_{n}|\left[Spam=true\right]\right)}{P\left(w_{n}|\left[Spam=false\right]\right)}\right]\end{array}
</math>
 
This computation is faster and easier because it requires only <math>2N</math>
products.
 
==== Bayesian program ====
 
The Bayesian spam filter program is completely defined by:
 
<math>
Pr
\begin{cases}
  Ds
  \begin{cases}
    Sp (\pi)
    \begin{cases}
      Va: Spam,W_0,W_1 \ldots W_{N-1} \\
      Dc:
        \begin{cases}
          P(Spam \land W_0 \land \ldots \land W_n \land \ldots \land W_{N-1})\\
        = P(Spam)\prod_{n=0}^{N-1}P(W_n|Spam)
      \end{cases}\\
      Fo:
      \begin{cases}
          P(Spam):
          \begin{cases}
            P([Spam=false])=0.25 \\
            P([Spam=true])=0.75
          \end{cases}\\
          P(W_n|Spam):
          \begin{cases}
              P(W_n|[Spam=false])\\
              =\frac{1+a^n_f}{2+a_f} \\
              P(W_n|[Spam=true])\\
              =\frac{1+a^n_t}{2+a_t}
          \end{cases} \\
        \end{cases}\\
      \end{cases}\\
  Identification\ (based\ on\ \delta)
  \end{cases}\\
  Qu: P(Spam|w_0 \land \ldots \land w_n \land \ldots \land w_{N-1})
\end{cases}
</math>
 
===Bayesian filter, Kalman filter and  Hidden Markov model===
 
Bayesian filters (often called [[Recursive Bayesian estimation]]) are generic probabilistic models for time evolving processes. Numerous models are particular instances of this generic approach, for instance: the [[Kalman filter]] or the [[Hidden Markov model]].
 
==== Variables ====
 
* Variables <math>S^{0},\cdots,S^{T}</math> are a time series of state variables considered to be on a time horizon ranging from <math>0</math> to <math>T</math>.
* Variables <math>O^{0},\cdots,O^{T}</math> are a time series of observation variables on the same horizon.
 
==== Decomposition ====
 
The decomposition is based:
* on <math>P\left(S^{t}|S^{t-1}\right)</math>, called the system model, transition model or dynamic model, which formalizes the transition from the state at time <math>t-1</math> to the state at time <math>t</math>;
* on <math>P\left(O^{t}|S^{t}\right)</math>, called the observation model, which expresses what can be observed at time <math>t</math> when the system is in state <math>S^{t}</math>;
* on an initial state at time <math>0</math>: <math>P\left(S^{0}\wedge O^{0}\right)</math>.
 
==== Parametrical forms ====
 
The parametrical forms are not constrained and different choices lead to different well-known models: see Kalman filters and Hidden Markov models just below.
 
==== Question ====
 
The question usually asked of these models is <math>P\left(S^{t+k}|O^{0}\wedge\cdots\wedge O^{t}\right)</math>: what is the
probability distribution for the state at time <math>t + k</math> knowing the observations from
instant <math>0</math> to <math>t</math>?
 
The most common case is Bayesian filtering where <math>k=0</math>, which
means that one searches for the present state, knowing the past observations.
 
However
it is also possible to do a prediction <math>(k>0)</math>, where one tries to extrapolate a
future state from past observations, or to do smoothing <math>(k<0)</math>, where one tries to
recover a past state from observations made either before or after that instant.
 
Some more complicated questions may also be asked as shown below in the HMM section.
 
Bayesian filters <math>(k=0)</math> have a very interesting recursive property, which contributes
greatly to their attractiveness. <math>P\left(S^{t}|O^{0}\wedge\cdots\wedge O^{t}\right)</math> may be computed simply from <math>P\left(S^{t-1}|O^{0}\wedge\cdots\wedge O^{t-1}\right)</math>
with the following formula:
 
<math>
\begin{array}{ll}
& P\left(S^{t}|O^{0}\wedge\cdots\wedge O^{t}\right)\\
= & P\left(O^{t}|S^{t}\right)\times\sum_{S^{t-1}}\left[P\left(S^{t}|S^{t-1}\right)\times P\left(S^{t-1}|O^{0}\wedge\cdots\wedge O^{t-1}\right)\right]\end{array}
</math>
 
Another interesting point of view for this equation is to consider that there are two phases: a
prediction phase and an estimation phase:
* During the prediction phase, the state is predicted using the dynamic model and the estimation of the state at the previous moment:
<math>
\begin{array}{ll}
& P\left(S^{t}|O^{0}\wedge\cdots\wedge O^{t-1}\right)\\
= & \sum_{S^{t-1}}\left[P\left(S^{t}|S^{t-1}\right)\times P\left(S^{t-1}|O^{0}\wedge\cdots\wedge O^{t-1}\right)\right]\end{array}
</math>
* During the estimation phase, the prediction is either confirmed or invalidated using the last observation:
<math>
\begin{array}{ll}
& P\left(S^{t}|O^{0}\wedge\cdots\wedge O^{t}\right)\\
= & P\left(O^{t}|S^{t}\right)\times P\left(S^{t}|O^{0}\wedge\cdots\wedge O^{t-1}\right)\end{array}
</math>
 
==== Bayesian program ====
 
<math>
Pr\begin{cases}
Ds\begin{cases}
Sp(\pi)\begin{cases}
Va:\\
S^{0},\cdots,S^{T},O^{0},\cdots,O^{T}\\
Dc:\\
\begin{cases}
& P\left(S^{0}\wedge\cdots\wedge S^{T}\wedge O^{0}\wedge\cdots\wedge O^{T}|\pi\right)\\
= & P\left(S^{0}\wedge O^{0}\right)\times\prod_{t=1}^{T}\left[P\left(S^{t}|S^{t-1}\right)\times P\left(O^{t}|S^{t}\right)\right]\end{cases}\\
Fo:\\
\begin{cases}
P\left(S^{0}\wedge O^{0}\right)\\
P\left(S^{t}|S^{t-1}\right)\\
P\left(O^{t}|S^{t}\right)\end{cases}\end{cases}\\
Id\end{cases}\\
Qu:\\
\begin{cases}
\begin{array}{l}
P\left(S^{t+k}|O^{0}\wedge\cdots\wedge O^{t}\right)\\
\left(k=0\right)\equiv Filtering\\
\left(k>0\right)\equiv Prediction\\
\left(k<0\right)\equiv Smoothing\end{array}\end{cases}\end{cases}
</math>
 
====Kalman Filter====
 
The very well-known [[Kalman filter]]s<ref>{{cite journal|last=Kalman|first=R. E.|title=A New Approach to Linear Filtering and Prediction Problems|journal=Transactions of the ASME--Journal of Basic Engineering|year=1960|volume=82|page=33––45}}</ref> are a special case of Bayesian
filters.
 
They are defined by the following Bayesian program:
 
<math>
Pr\begin{cases}
Ds\begin{cases}
Sp(\pi)\begin{cases}
Va:\\
S^{0},\cdots,S^{T},O^{0},\cdots,O^{T}\\
Dc:\\
\begin{cases}
& P\left(S^{0}\wedge\cdots\wedge O^{T}|\pi\right)\\
= & \left[\begin{array}{c}
P\left(S^{0}\wedge O^{0}|\pi\right)\\
\prod_{t=1}^{T}\left[P\left(S^{t}|S^{t-1}\wedge\pi\right)\times P\left(O^{t}|S^{t}\wedge\pi\right)\right]\end{array}\right]\end{cases}\\
Fo:\\
\begin{cases}
P\left(S^{t}|S^{t-1}\wedge\pi\right)\equiv G\left(S^{t},A\bullet S^{t-1},Q\right)\\
P\left(O^{t}|S^{t}\wedge\pi\right)\equiv G\left(O^{t},H\bullet S^{t},R\right)\end{cases}\end{cases}\\
Id\end{cases}\\
Qu:\\
P\left(S^{T}|O^{0}\wedge\cdots\wedge O^{T}\wedge\pi\right)\end{cases}
</math>
* Variables are continuous.
* The transition model <math>P\left(S^{t}|S^{t-1}\wedge\pi\right)</math> and the observation model <math>P\left(O^{t}|S^{t}\wedge\pi\right)</math> are both specified using Gaussian laws with means that are linear functions of the conditioning variables.
 
With these hypotheses and by using the recursive formula, it is possible to solve
the inference problem analytically to answer the usual <math>P\left(S^{T}|O^{0}\wedge\cdots\wedge O^{T}\wedge\pi\right)</math> question.
This leads to an extremely efficient algorithm, which explains the popularity of Kalman filters and the number of their everyday applications.
 
When there are no obvious linear transition and observation models, it is still often
possible, using a first-order Taylor's expansion, to treat these models as locally linear.
This generalization is commonly called the [[Extended Kalman filter]].
 
====Hidden Markov model====
 
[[Hidden Markov model]]s (HMMs) are another very popular specialization of Bayesian filters.
 
They are defined by the following Bayesian program:
 
<math>
Pr\begin{cases}
Ds\begin{cases}
Sp(\pi)\begin{cases}
Va:\\
S^{0},\cdots,S^{T},O^{0},\cdots,O^{T}\\
Dc:\\
\begin{cases}
& P\left(S^{0}\wedge\cdots\wedge O^{T}|\pi\right)\\
= & \left[\begin{array}{c}
P\left(S^{0}\wedge O^{0}|\pi\right)\\
\prod_{t=1}^{T}\left[P\left(S^{t}|S^{t-1}\wedge\pi\right)\times P\left(O^{t}|S^{t}\wedge\pi\right)\right]\end{array}\right]\end{cases}\\
Fo:\\
\begin{cases}
P\left(S^{0}\wedge O^{0}|\pi\right)\equiv Matrix\\
P\left(S^{t}|S^{t-1}\wedge\pi\right)\equiv Matrix\\
P\left(O^{t}|S^{t}\wedge\pi\right)\equiv Matrix\end{cases}\end{cases}\\
Id\end{cases}\\
Qu:\\
Max_{S^{1}\wedge\cdots\wedge S^{T-1}}\left[P\left(S^{1}\wedge\cdots\wedge S^{T-1}|S^{T}\wedge O^{0}\wedge\cdots\wedge O^{T}\wedge\pi\right)\right]\end{cases}
</math>
* Variables are treated as being discrete.
* The transition model <math>P\left(S^{t}|S^{t-1}\wedge\pi\right)</math> and the observation model <math>P\left(O^{t}|S^{t}\wedge\pi\right)</math> are
both specified using probability matrices.
* The question most frequently asked of HMMs is:
<math>
Max_{S^{1}\wedge\cdots\wedge S^{T-1}}\left[P\left(S^{1}\wedge\cdots\wedge S^{T-1}|S^{T}\wedge O^{0}\wedge\cdots\wedge O^{T}\wedge\pi\right)\right]
</math>
What is the most
probable series of states that leads to the present state, knowing the past observations?
 
This particular question may be answered with a specific and very efficient algorithm
called the [[Viterbi algorithm]].
 
A specific learning algorithm called the [[Baum–Welch algorithm]] has also been developed
for HMMs.
 
== Applications ==
 
=== Academic applications ===
 
For the last 15 years, Bayesian programming approach has been used in various universities to develop both robotics applications and life sciences models.<ref name=Bessiere2008>{{cite book|last=Bessière, P.; Laugier, C. & Siegwart, R.|title=Probabilistic Reasoning and Decision Making in Sensory-Motor Systems|year=2008|publisher=Springer|isbn=978-3-540-79007-5}}</ref>
 
==== Robotics ====
 
In robotics, Bayesian Programming has been applied to [[autonomous robotics]],<ref>{{cite journal|last=Lebeltel|first=O.|coauthors=Bessière, P.; Diard, J. & Mazer, E.|title=Bayesian Robot Programming|journal=Advanced Robotics|year=2004|volume=16|issue=1|page=49––79}}</ref><ref>{{cite journal|last=Diard|first=J.|coauthors=Gilet, E.; Simonin, E. & Bessière, P.|title=Incremental learning of Bayesian sensorimotor models: from low-level behaviours to large-scale structure of the environment|journal=Connection Science|year=2010|volume=22|issue=4|page=291––312|doi=10.1080/09540091003682561}}</ref><ref>{{cite journal|last=Pradalier|first=C.|coauthors=Hermosillo, J.; Koike, C., Braillon, C.; Bessière, P. & Laugier, C.|title=The CyCab: a car-like robot navigating autonomously and safely among pedestrians|journal=Robotics and Autonomous Systems|year=2005|volume=50|issue=1|page=51––68|doi=10.1016/j.robot.2004.10.002}}</ref><ref>{{cite journal|last=Ferreira|first=J.|coauthors=Lobo, J.; Bessière, P.; Castelo-Branco, M. & Dias, J.|title=A Bayesian Framework for Active Artificial Perception|journal=IEEE Transactions on Systems, IEEE Transactions on Systems, Man, and Cybernetics, Part B|year=2012|volume=99|page=1––13}}</ref><ref name=Ferreira2014>{{cite book|last=Ferreira|first=J. F.|title=Probabilistic Approaches to Robotic Perception|year=2104|publisher=Springer|coauthors=Dias, J. M.}}</ref> robotic [[Computer-aided design|CAD]] systems,<ref>{{cite journal|last=Mekhnacha|first=K.|coauthors=Mazer, E. & Bessière, P.|title=The design and implementation of a Bayesian CAD modeler for robotic applications|journal=Advanced Robotics|year=2001|volume=15|issue=1|page=45––69|doi=10.1163/156855301750095578}}</ref> [[Advanced driver assistance systems]],<ref>{{cite journal|last=Coué|first=C.|coauthors=Pradalier, C.; Laugier, C.; Fraichard, T. & Bessière, P.|title=Bayesian Occupancy Filtering for Multitarget Tracking: an Automotive Application|journal=International Journal of Robotics Research|year=2006|volume=25|issue=1|page=19––30|doi=10.1177/0278364906061158}}</ref> robotic arm control, [[mobile robot]]ics,<ref>{{cite journal|last=Vasudevan|first=S.|coauthors=Siegwart, R.|title=Bayesian space conceptualization and place classification for semantic maps in Bayesian space conceptualization and place classification for semantic maps in mobile robotics|journal=Robotics and Autonomous Systems|year=2008|volume=56|page=522––537|doi=10.1016/j.robot.2008.03.005|issue=6}}</ref><ref>{{cite journal|last=Perrin|first=X.|coauthors=Chavarriaga, R.; Colas, F.; Seigwart, R. & Millan, J.|title=Brain-coupled interaction for semi-autonomous navigation of an assistive robot|journal=Robotics and Autonomous Systems|year=2010|volume=58|page=1246––1255|doi=10.1016/j.robot.2010.05.010|issue=12}}</ref> Human-robots interactions,<ref>{{cite journal|last=Rett|first=J.|coauthors=Dias, J. & Ahuactzin, J-M.|title=Bayesian reasoning for Laban Movement Analysis used in human-machine interaction|journal=Int. J. of Reasoning-based Intelligent Systems|year=2010|volume=2|issue=1|page=13––35|doi=10.1504/IJRIS.2010.029812}}</ref>
Human-vehicle interactions (Bayesian autonomous driver models)
<ref>
{{Citation
| last1 = Möbus | first1 = C.
| last2 = Eilers | first2 = M.
| last3 = Garbe | first3 = H.
| last4 = Zilinski | first4 = M.
| editor-last = Duffy
| editor-first = Vincent G.
| booktitle = Digital Human Modeling
| title = Probabilistic and Empirical Grounded Modeling of Agents in (Partial) Cooperative Traffic Scenarios
| contribution-url = http://link.springer.com/chapter/10.1007%2F978-3-642-02809-0_45
| series = Lecture Notes in Computer Science, Volume 5620
| year = 2009
| pages = 423-432
| place = Second International Conference, ICDHM 2009, San Diego, CA, USA
| publisher = Springer
| isbn = 978-3-642-02808-3
| doi = 10.1007/978-3-642-02809-0_45 }}
</ref>
<ref>
{{Citation
| last1 = Möbus | first1 = C.
| last2 = Eilers | first2 = M.
| editor-last = Duffy
| editor-first = Vincent G.
| booktitle = Digital Human Modeling
| title = Further Steps Towards Driver Modeling according to the Bayesian Programming Approach
| contribution-url = http://link.springer.com/chapter/10.1007%2F978-3-642-02809-0_44
| series = Lecture Notes in Computer Science, Volume 5620
| year = 2009
| pages = 413-422
| place = Second International Conference, ICDHM 2009, San Diego, CA, USA
| publisher = Springer
| isbn = 978-3-642-02808-3
| doi = 10.1007/978-3-642-02809-0_44 }}
</ref>
<ref>
{{cite conference
| last = Eilers
| first = M.
| authorlink =
| coauthors = Möbus, C.
| title = Lernen eines modularen Bayesian Autonomous Driver Mixture-of-Behaviors (BAD MoB) Modells
| booktitle = Fahrermodellierung - Zwischen kinematischen Menschmodellen und dynamisch-kognitiven Verhaltensmodellen
| pages = 61 - 74
| editor-last1 = Kolrep
| editor-first1 = H.
| editor-last2 = Jürgensohn
| editor-first2 = Th.
| publisher = VDI-Verlag
| series = Fortschrittsbericht des VDI in der Reihe 22 (Mensch-Maschine-Systeme)
| year = 2010
| location = Düsseldorf, Germany
| contribution-url = http://www.lks.uni-oldenburg.de/download/Publikationen/2010/Eilers&PCM2010_BFFM_BAD_MoB_Modells2010.pdf
| isbn = 978-3-18-303222-8
| issn =
| accessdate = }}
</ref>
<ref>
{{cite book
| last = Möbus
| first = C.
| authorlink =
| coauthors = Eilers, M.
| title = Prototyping Smart Assistance with Bayesian Autonomous Driver Models
| booktitle = Handbook of Research on Ambient Intelligence and Smart Environments: Trends and Perspectives
| pages = 460-512
| editor-last1 = Mastrogiovanni
| editor-first1 = F.
| editor-last2 = Chong
| editor-first2 = N.-Y.
| publisher = IGI Global publications
| series =
| year = 2011
| location = Hershey, Pennsylvania (USA)
| contribution-url = http://www.igi-global.com/chapter/prototyping-smart-assistance-bayesian-autonomous/54671
| isbn = 9781616928575
| doi = 10.4018/978-1-61692-857-5.ch023
| issn =
| accessdate = }}
</ref>
<ref>
{{cite conference
| last = Eilers
| first = M.
| authorlink =
| coauthors = Möbus, C.
| title = Learning the Relevant Percepts of Modular Hierarchical Bayesian Driver Models Using a Bayesian Information Criterion
| booktitle = Digital Human Modeling
| pages = 463 - 472
| editor-last = Duffy
| editor-first = V.G.
| publisher = Springer
| series = LNCS 6777
| year = 2011
| location = Heidelberg, Germany
| contribution-url = http://www.lks.uni-oldenburg.de/46350.html
| isbn = 978-3-642-21798-2
| doi = 10.1007/978-3-642-21799-9_52
| issn =
| accessdate = }}
</ref>
<ref>
{{cite conference
| last = Eilers
| first = M.
| authorlink =
| coauthors = Möbus, C.
| title = Learning of a Bayesian Autonomous Driver Mixture-of-Behaviors (BAD-MoB) Model
| booktitle = Advances in Applied Digital Human Modeling
| pages = 436 - 445
| editor-last = Duffy
| editor-first = V.G.
| publisher = CRC Press, Taylor & Francis Group
| series = LNCS 6777
| year = 2011
| location = Boca Raton, USA
| url = http://www.crcpress.com/product/isbn/9781439835111
| contribution-url = http://www.lks.uni-oldenburg.de/46350.html
| isbn = 978-1-4398-3511-1
| accessdate = }}
</ref>
video game avatar programming and training <ref>{{cite journal|last=Le Hy|first=R.|coauthors=Arrigoni, A.; Bessière, P. & Lebetel, O.|title=Teaching Bayesian Behaviours to Video Game Characters|journal=Robotics and Autonomous Systems|year=2004|volume=47|page=177––185|doi=10.1016/j.robot.2004.03.012|issue=2–3}}</ref> and real-time strategy games (AI).<ref>{{cite book|title=Bayesian Programming and Learning for Multiplayer Video Games|last=Synnaeve|first=G.|year=2012|url=http://tel.archives-ouvertes.fr/docs/00/78/06/35/PDF/29588_SYNNAEVE_2012_archivage.pdf}}</ref>
 
==== Life sciences ====
 
In life sciences, Bayesian Programming has been used in vision to reconstruct shape from motion,<ref>{{cite journal|last=Colas|first=F.|coauthors=Droulez, J.; Wexler, M. & Bessière, P.|title=A unified probabilistic model of the perception of three-dimensional structure from optic flow|journal=Biological Cybernetics|year=2008|page=132––154}}</ref> to model visuo-vestibular interaction<ref>{{cite journal|last=Laurens|first=J.|coauthors=Droulez, J.|title=Bayesian processing of vestibular information|journal=Biological Cybernetics|year=2007|volume=96|page=389––404|doi=10.1007/s00422-006-0133-1|issue=4}}</ref> and to study saccadic eye movements;<ref>{{cite journal|last=Colas|first=F.|coauthors=Flacher, F.; Tanner, T.; Bessière, P. & Girard, B.|title=Bayesian models of eye movement selection with retinotopic maps|journal=Biological Cybernetics|year=2009|volume=100|issue=3|page=203––214|doi=10.1007/s00422-009-0292-y}}</ref> in speech perception and control to study early acquisition of speech<ref>{{cite journal|last=Serkhane|first=J.|coauthors=Schwartz, J-L. & Bessière, P.|title=Building a talking baby robot A contribution to the study of speech acquisition and evolution|journal=Interaction Studies|year=2005|volume=6|issue=2|page=253––286|doi=10.1075/is.6.2.06ser}}</ref> and the emergence of articulatory-acoustic systems;<ref>{{cite journal|last=Moulin-Frier|first=C.|coauthors=Laurent, R.; Bessière, P.; Schwartz, J-L. & Diard, J.|title=Adverse conditions improve distinguishability of auditory, motor and percep-tuo-motor theories of speech perception: an exploratory Bayesian modeling study|journal=Language and Cognitive Processes|year=2012|volume=27|issue=7–8|page=1240––1263|doi=10.1080/01690965.2011.645313}}</ref> and to model handwriting perception and control.<ref>{{cite journal|last=Bessière|first=E.|coauthors=Diard, J. & Bessière, P.|title=Bayesian Action--Perception Computational Model: Interaction of Production and Recognition of Cursive Letters|journal=Plos ONE|year=2011|volume=6|issue=6|page=e20387|bibcode=2011PLoSO...620387G|doi=10.1371/journal.pone.0020387|editor1-last=Sporns|editor1-first=Olaf}}</ref>
 
== Bayesian programming versus possibility theories ==
 
The comparison between probabilistic approaches (not only Bayesian programming) and possibility theories has been debated for a long time and is, unfortunately, a very controversial matter.
 
Possibility theories like, for instance, [[fuzzy set]]s,<ref>{{cite journal|last=Zadeh|first=Lofti, A.|journal=Information and Control|year=1965|volume=8|issue=3|page=338––353|doi=10.1016/S0019-9958(65)90241-X|title=Fuzzy sets}}</ref>
[[Fuzzy logic]]<ref>{{cite journal|last=Zadeh|first=Lofti, A.|journal=Synthese|year=1975|volume=30|issue=3––4|page=407––428|doi=10.1007/BF00485052|title=Fuzzy logic and approximate reasoning}}</ref> and [[Possibility theory]]<ref>{{cite journal|last=Dubois|first=D.|coauthors=Prade, H.|journal=Ann. Math. Artif. Intell.|year=2001|volume=32|issue=1––4|page=35––66|doi=10.1023/A:1016740830286}}</ref> propose different alternatives to probability
to model uncertainty. They argue that probability
is insufficient or inconvenient to model certain aspects of incomplete
and uncertain knowledge.
 
The defense of probability is mainly based on [[Cox's theorem]] which, starting
from four postulates
concerning rational reasoning in the presence of
uncertainty, demonstrates that the only mathematical
framework that satisfies these postulates is probability theory. The
argument then goes like this: if you use a different approach than
probability, then you necessarily infringe on one of these postulates.
Let us see which one and discuss its utility.
 
== Bayesian programming versus probabilistic programming ==
 
The purpose of [[Probabilistic relational programming language|probabilistic programming]] is to unify the scope of classical programming languages with probabilistic modeling (especially [[Bayesian network]]s) in order to be able to deal with uncertainty but still profit from the power of expression of programming languages to describe complex models.
 
The extended classical programming languages can be logical languages as proposed in Probabilistic Horn Abduction,<ref>{{cite journal|last=Poole|first=D.|title=Probabilistic Horn abduction and Bayesian networks|journal=Artificial Intelligence|year=1993|volume=64|page=81––129|doi=10.1016/0004-3702(93)90061-F}}</ref> Independent Choice
Logic,<ref>{{cite journal|last=Poole|first=D.|title=The Independent Choice Logic for modelling multiple agents under uncertainty|journal=Artficial Intelligence|year=1997|volume=94|page=7––56|doi=10.1016/S0004-3702(97)00027-1}}</ref> PRISM,<ref>{{cite journal|last=Sato|first=T.|coauthors=Kameya, Y.|journal=Journal of Artificial Intelligence Research|year=2001|volume=15|page=391––454}}</ref> and ProbLog which propose an extension of Prolog.
 
It can also be extensions of functional programming languages (essentially [[Lisp (programming language)|Lisp]] and [[Scheme (programming language)|Scheme]]) such as IBAL or CHURCH. The inspiring programming languages can even be object oriented like in BLOG and FACTORIE or more standard ones like in CES and FIGARO.
 
The purpose of Bayesian programming is different. Jaynes' precept of "probability as logic" defends that probability is an extension of and an alternative to logic above which a complete theory of rationality, computation and programming can be rebuilt. Bayesian programming does not search to extend classical languages but rather to replace them by a new programming approach based on probability and taking fully into account [[Incompleteness#Logical completeness|incompleteness]] and [[Uncertainty quantification|uncertainty]].
 
The precise comparison between the semantic and power of expression of Bayesian and probabilistic programming is still an open question.
 
== See also ==
 
{{Portal|Artificial intelligence|Statistics}}
{{columns-list|2|width=95%|
* [[Bayes' rule]]
* [[Bayesian inference]]
* [[Bayesian probability]]
* [[Bayesian spam filtering]]
* [[Belief propagation]]
* [[Cox's theorem]]
* [[Expectation-maximization algorithm]]
* [[Factor graph]]
* [[Graphical model]]
* [[Hidden Markov model]]
* [[Judea Pearl]]
* [[Kalman filter]]
* [[Naive Bayes classifier]]
* [[Pierre-Simon Laplace|Pierre-Simon de Laplace]]
* [[Probabilistic logic]]
* [[Probabilistic programming language]]
* [[Subjective logic]]
}}
 
== References ==
 
{{Reflist|2}}
 
== External links ==
* [http://www.probayes.com/Bayesian-Programming-Book A companion site to the ''Bayesian programming'' book where to download ProBT an inference engine dedicated to Bayesian programming.]
* The [http://Bayesian-programming.org Bayesian-programming.org site] for the promotion of Bayesian programming with detailed information and numerous publications.
 
[[Category:Bayesian statistics]]
[[Category:Probability theory]]
[[Category:Artificial intelligence]]

Revision as of 21:37, 15 February 2014

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Windsor Star earns multiple Nation's Newspaper Award nominations

This mosaic of Ambassador Bridge owner Matty Moroun was developed using about 175 images of properties his companies have bought in Windsor. (Photo Illustration/The Windsor Star)

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Original source article:Windsor Star earns multiple National Classifieds Award nominations

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With the obstacles and camaraderie now affectionate towards memories, Zimmer is embracing retirement living, having hit Whitewater's slopes all winter. Now the local dude known for his smile along with fairness is heading definately not his Kootenay home to use her honed skills to help a different community in need New Zealand's next largest city.

Amos's retired use of volunteering at his grandchildren's school, working on home projects in addition to daily walks is a long way away from early days at her Nelson Hydro post. Back then, when staff Cheap Nike Free Runs Australia was so frequently needed on-site to check the old school generating systems, Amos simply made his your bed right at the power plant.

"During Mike's career with the city, your dog oversaw the period of time during which the energy plant was Pandora Charms Ireland automated plus staff no longer needed to go on site," smiles Alex Love, Nelson Hydro general manager. "Considering that Mike's career spanned more than one quarter of the 118 calendar year history of Nelson Hydro, it's no wonder he's a permanent piece of the utility's history.In

In his 30 plus season career with Nelson Hydro, Amos worked on the actual downtown voltage conversion undertaking, the Granite terminal, Rosemont substation as well as generator five installations. Positioning five different titles, the past nine years of his employment were spent as functions manager. For Amos, staying in budget meant keeping a lean, efficient and organized producers.

"I enjoyed the variety of work greatly," says Amos. "From traffic alerts to building electrical servicing, to revenue metering, to generators maintenance, to substation maintenance, to computer control systems, to new station construction, for you to power line construction, most people did it all."

From power lines to guitar strings, Amos' aim is on family and his love of Abercrombie Australia music.

Although they are headed in very different guidance, he and Zimmer both voice the song of 2 men happy to have more time for loved ones and new escapades, both with long, successful careers well worth recollecting.

In messy Mbt Shoes

'Lone Survivor' a brutal tribute to help Navy SEALs

This 12 ,. 5, 2013 photo displays director Peter Berg, from remaining, actor Mark Wahlberg and past Navy SEAL Marcus Luttrell in The big apple. In the age of the Mbt Shoes superhero, the movies' most reliable real life good guy has been the Navy Close off. "Lone Survivor," starring Mark Wahlberg, is the latest in a stringed of films, including "Zero Dark Thirty" along with "Act of Valor" to honor the particular Navy's special operations force using as much faithfulness as the filmmakers may possibly muster. (Victoria Will/Invision/AP)

Marcus Luttrell, the former Navy Closure whose deadly mission with Afghanistan has been turned into the film Survivor, strides into a hotel room for an interview, trailed by his services dog, Mr. Rigby.

The extra tall, hulking, goateed Navy Cross recipient greets a journalist with a steel solid grip, and nods to director Peter Berg and star Indicate Wahlberg, who plays him while in the film. This is clearly never what he wants to be doing.

Based on Luttrell's best selling 2007 precious moment, Survivor is about a The year 2005 four man operation around northeastern Afghanistan's Kunar province that droped apart when a trio regarding goat herders stumbled upon the staked out and about SEALs.

After releasing the civilians and aborting the goal, the SEALs were promptly ambushed by the Taliban in a firefight that tumbled all the way down a rocky gulch, killed Luttrell's 3 fellow SEALs, left Luttrell horribly injured and, in an attempted rescue, killed 16 more men.

Survivor, which opens up like a recruitment video together with documentary footage of strong SEAL training, is the hottest in a series of films this pays tribute to the Navy's specific forces: In messy, uncertain wars, they're elite experts of precision. In the time of the superhero film, the Navy SEALs have influenced filmmakers as the genuine article.

Luttrell would rather not necessarily talk about any of it. He / she went along with Survivor plus wrote the book at the advocating of his superiors. Compared to the genuine events, the movie is no stressful experience for Luttrell.

went through this in real life, so a movie concerning this isn't going to affect me in any way, says the 38 yr old Texan.

Hollywood and the American Uggs Ireland armed forces are worlds apart. Although Survivor is a uniquely close up collaboration, one in which Berg and Wahlberg (both producers) worked underneath significant pressure from the groups of those who died and effective duty SEALs to carefully render the soldiers' lives, in battle and in brotherhood.

was at the actual screening when there were 100 moms and dads of dead soldiers, says Berg. I was at a testing where there were 500 effective members of special operations, like Admiral (William) McRaven. And those are different. Simply because when those lights show up, those people are going to look anyone in the eye. the years, Notary seals have been played by the enjoys of Bruce Willis, Steven Seagal and Demi Moore, and recently been a mainstay in online games ( of Duty, Gear Stable But the movies, often with close consultation with the military services, have come a long way since 1990's SEALs, with Charlie Sheen.

2012's of Valor was acted out through active duty SEALs and used live ammo sequences to portray a fictional hidden mission. Kathryn Bigelow's Dark Thirty dramatized the most common SEAL mission, the raid around Abbottabad that killed Osama bin Packed. The recent docudrama Phillips recreated the saving of the kidnapped mariner by SEAL snipers, together with Tom Hanks' most moving scene improvised with a real life Naval officer.

These types of productions, though, have given go up to questions of exactness and charges of propaganda. senators, including Dianne Feinstein as well as John McCain, claimed that too much information was shared with the filmmakers with Dark Thirty, and many belittled the film for suggesting pain aided the hunt for trash Laden. Phillips showed only a several the 19 shots that were fired on the three Somali devils, and didn't mention a $30,000 that went lost in the aftermath. Retired Army lieutenant general James B. Vaught argued that surrounding Valor revealed too much about tactics: the hell out of the media channels! he implored.

But the military views in the movies a chance to contour its image and guarantee some degree of authenticity with depictions of its service men and women. Heir has largely drawn encouragement as a brutal ode to Navy blue SEALs and a faithful depiction of the moral confusion associated with combat.

films like 'Black Hawk Down' along with 'Lone Survivor,' the commonality is the notion that this is really a opportunity to set the record straight or at least to depict things as they believe people happened, says Philip Strub, head with the Defense Department's Film and tv Liaison Office.

It can make for any thorny mix of fictionalization, artist license in addition to classification issues. Berg consulted often with military liaisons and the Group Office of Information while creating the script.

read the following action reports, says Berg. considered the autopsies. I went to Irak. I met all these people. We just followed the blue print out that Latrell laid out in his book. We never set out to make a move non Hollywood or Hollywood. We just literally told the story plot. Wahlberg: fell in line with what the goals were, what the agenda was and how high the standard was set by not only your SEAL team guys however families. It was a lot of pressure, although everybody took a lot of satisfaction in the fact that we were involved in this thing. the film, which expands nationally in theaters Feb 5th, premiered at the AFI Festival around November, Wahlberg made emotional responses about actors who boast about military training for the big game.

was really talking about myself, since I've been guilty of it many times, talking about how hard I had to work, says Wahlberg. nothing compared to they do. Luttrell emerged from Heir with admiration for Berg and Wahlberg: virtually all relative, he says. I do for income and what he does for a living is exactly the same. We both wake up every day, put out as hard as possible and then go to bed at night, aiming to see the next day. took this kind Michael Kors Australia of under their wing plus they worked with it and brought it to life from the internet pages in the book, from the blood vessels on the Moncler Jackets mountain.

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Woman cut free from Charlesworth lock up

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Del. Nike Store Ireland

Salisbury Officer Cleared in Nike Store Ireland Fatal Shooting

SALISBURY, Md. A Salisbury police officer will not face charges in connection with your fatal shooting of a Delaware fugitive during a February traffic end, according to a report released by way of the Wicomico County State's Attorney's Company on Tuesday. Wicomico State's Attorney Matthew Maciarello reported Tiffany And Co Usa the report concludes there isn't a probable cause to charge Specialist 1st Class Milton Rodriguez with a criminal offense, and that Rodriguez' deadly use of compel in the killing of 25 year old James New Balance Runners L. Norris, associated with Wilmington, Del., was justified to Vibram Ireland prevent the clear and present chance that Norris presented. The crash happened on Monday, The month of february. According to the report, members of your Maryland State Apprehension Company stopped a car Norris was a passenger in on North Salisbury Blvd at Philadelphia Avenue inside Salisbury. The report said your officer ordered Norris not to fit his hands in his purses but Norris who it turns out received his hands clenched around two .38 caliber revolvers in both jacket wallets refused and told Rodriguez and another officer, "You better kill/shoot me initially or I'm gonna kill/shoot people." The report said that is when Rodriguez, who was in concern for his safety, pulled apart his weapon. "The taking from a life is tragic. It is, however under circumstances justified; and this is such a case," the actual report said. "Pfc.

AP Vibram Ireland

Suspect 'entrapped' in Christmas tree bomb plot

PORTLAND, Ore. (AP) The defense team of your 21 year old Somali American plans to argue that he was entrapped simply by government agents who exploited his religious zeal as well as financial problems to cause him into attempting to detonate a weapon of mass destruction at a Portland Christmas tree light ceremony in 2010. Government prosecutors Vibram Ireland say such theories are "untethered from reality."

The back and forth has, until now, recently been kept to a series of filings in cases where. Defense attorneys for Mohamed Mohamud thrust for more evidence; the government does respond that such evidence possibly doesn't exist, or the security isn't entitled to it.

Mohamud found believe he could detonate a weapon of mass destruction during the Christmas tree lighting service by dialing a number upon his cell phone, but there wasn't any bomb waiting for the band. The men he thought have been his co conspirators were undercover FBI agents. citizens.

Federal investigators began looking into Mohamud during the past year, when he was 17 as well as 18. Undercover agents called him, posing as radical Islamic Abercrombie And Fitch Australia jihadists which wanted to bring Christian Louboutin Australia Mohamud into the times.

They pretended to show Mohamud how to detonate a new bomb and offered your pet cash to buy bomb doing parts and an apartment to hide in.

The defense statements these efforts are evidence how the government entrapped Mohamud. To prove it, Mohamud's lawyers must show at least 3 things: That Mohamud wasn't likely to be able to terrorism before government real estate agents sought him out, how the government used sophisticated methods to induce Mohamud to participate in the criminal offenses and that they exploited Mohamud's specific vulnerabilities his reliance on their money and the adherence to his belief.

The prosecution's case boils down to a disagreement they'll offer repeatedly to some trial jury: No sensible person, no matter the inducements of money as well as appeal to religious glory, may be led to commit what they understood would be an act of terrorism.

A prosecutors urged the judge New Balance Runners with filings not to compel them to earnings more evidence, arguing that they've gone above and beyond what the federal government law requires them to start.

The defense will also improve another theory: The entire exploration was part of a larger politics effort to convince Portland's urban center council that it should rejoin the federal anti terror job force. The city dropped outside 2005 over civil liberties concerns.

"That's a bit of hardball that (the actual defense is) playing, but it's well within bounds of what they can do," said Lewis Clark school professor Tung Yin, who has closely put into practice the case. "It's always a challenge when you are writing these motions of the way much of a kitchen sink to include."

The defense law firms also say the government couldn't back off when Mohamud resisted, illustrating into question how far he previously have taken the plot with out persistent enticement.

"The government strategies appear to be unprecedented," Mohamud's law firms wrote. "When Mr. Mohamud agreed with his father to complete his undergrad degree . the FBI extended the inducement by using a face to face meeting, invoking The lord's will, claiming, I'm sure provides good reason for you to stay where you're.' "

Prosecutors replied towards the defense by repeating their original claim, that no matter the particular inducement, Mohamud's actions in 2010 display he intended to kill hundreds of people.

"The investigation and timing of your case were driven by one factor," prosecutors had written. "Defendant's selection of the tree lighting effects ceremony on November Twenty-six, 2010 as his designed target."