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Questions tagged [bayesian-network]

For questions related to Bayesian networks, the generic example of a directed probabilistic graphical model. Includes dynamic Bayesian networks, e.g. Hidden Markov Models (HMMs) and Kalman Filters. For applications of Bayesian networks in any field, e.g. machine learning. NOT for general questions about Bayes' theorem, Bayesian statistics, conditional probabilities, networks, or graph theory.

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Bayesian network: how to speed up inference(s)?

I'm experimenting with open-source python libraries that can handle Bayesian networks easily. However the inference is slower compared to the commercial solution (SMILE). One slower inference would ...
bartfer's user avatar
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Conceptual question on Bayesian networks conditional probability

In bayesian networks we often represent conditional independence assumptions within the network like the following: $$ (eq.1)P(X|A, B, C) = P(X|A) $$ This is assuming that B, C are conditionally ...
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Probability calculation with bayesian belief network

Trying to calculate the $P(A|\bar{C})$ based on below BBN and wondering if someone can help me confirm the correct setup from below approaches. Approach 1: $P(A|\bar{C}) = \sum_{B,D,E} P(B|\bar{C})P(...
biostat's user avatar
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(Bayesian probability) Show that $P(H|E) = \frac{h (c +a \overline c)}{hc+a\overline c}$

The question, briefly How does the calculation $P(H|E) = \frac{h (c +a \overline c)}{hc+a\overline c}$ work? Some background I'm trying to work through the proof of the following theorem in ...
snofelet's user avatar
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What assumptions are needed to "un-marginalize" this conditional distribution?

I want to prove the identity: $$p(y|D,x)=\int p(y|W,x)p(W|D)dW$$ using the conditional independences given by one of the following two graphical models: I believe I have a proof that assumes model (A)...
LYB's user avatar
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In a Bayesian network, does the removal of an edge ever remove existing conditional independences?

I am wondering if the removal of any edge in a acyclic Bayesian network ever removes an existing conditional independence? Intuitively, I would think not, but I was wondering if there is a formal ...
ajl123's user avatar
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Prior BPN based on Multi Linear Regression Model Output and Monte Carlo Simulations

On page 286 in the Prediction of road accidents: A Bayesian hierarchical approach paper. The passage describes the construction and parameter learning of Bayesian Probability Networks (BPNs), ...
Mike's user avatar
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Equivalence of DAGs after conditioning on the identity of two variables

Let $(G,p)$ be a Bayesian network* with a leaf (child-less node) $X$, such that there is a root (parent-less node) $Y$ in $G$ which has the same range as $X$. Moreover, suppose that we can "...
Jens's user avatar
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DAGs, d-separation, paths of two vertices: confusion

I'm taking a class on Bayesian probability. Briefly, my question is about directed acyclical graphs (DAGs) and d-separation of parent and child vertices, conditional on the parent. (This question ...
snofelet's user avatar
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If $X \perp Y$ and $X \perp Y | Z$ , is that true that $X \perp Z$ or $Y \perp Z$ if $X$ and $Y$ can take 3 values but $Z$ only takes two.

I have the following problem : If $X \perp Y$ and $(X \perp Y )| Z$ , is that true that $X \perp Z$ or $Y \perp Z$ if $X$ and $Y$ can take 3 values but $Z$ only takes two. $X \perp Y $ means $X$ and $...
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is the assumption If X⊥⊥Y | Z and X⊥⊥Y then (X⊥⊥Z or Y ⊥⊥Z) true? [duplicate]

is the assumption If X⊥⊥Y | Z and X⊥⊥Y then (X⊥⊥Z or Y ⊥⊥Z) true ? where X⊥⊥Y means is independent of Y and X⊥⊥Y means that X is independent of Y given Z? I have been trying to prove or disprove the ...
MproBoss's user avatar
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Average of two discrete random variables

I have this graph B<-A->C and I have the joint probability distribution of A and B , P(A,B), and the joint probability distribution of A and C, P(A,C). I want to compute the average of B and C. ...
Moh's user avatar
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Russell & Norvig: Connecting models of probabilistic reasoning to Stochastic Differential Equations

Artificial Intelligence: A Modern Approach, 4th Global ed. by Stuart Russell and Peter Norvig contains the following footnote on page 480 of chapter 14: Uncertainty over continuous time can be ...
BrentKylling's user avatar
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Probability of complement as fraction

I am trying to work through the paper "Repairing Neural Networks by Leaving the Right Past Behind" (arxiv). And really struggle working through the mathematics. The paper states that the key ...
MrWombat's user avatar
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Bayesian belief network - calculate probability

Given the following Bayesian belief network, what is the probability that a non-smoking patient with a smoking parent will develop lung tumor? In this question, isn't the answer already provided ...
DanielG's user avatar
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Given a Bayes Net, compute $p(A|B,C)$

I am given the following Bayes Net: and I am asked to compute $p(A|B,C)$. This is what I've done: \begin{align} p(A|B,C) & := \frac{p(A,B,C)}{p(B,C)} \\ & = \frac{p(A,B,C)}{p(B)\ p(C|A)} \\ &...
tail's user avatar
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Given a decision network, compute the EU of buying a book

I am given this homework: And this is what I have done up to now: (a) This is the decision network for that problem While I think the decision network is correct, I am having struggles with part (b)....
tail's user avatar
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Given a Bayesian Network, calculate $p(a)$

I am given this Bayesian Network: I need to calculate $p(+d|+a)$ What I have done up to now is: $$ p(+d|+a) := \frac{p(+d,+a)}{p(+a)} $$ where \begin{align} p(+d,+a) & = \sum_X p(+d,+a,X) \\ &...
tail's user avatar
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Given a Bayes Network, calculate $p(a | b, \neg c)$

I am assigned a homework but I cannot figure out how to solve it. Given this Bayes' Network: calculate $p(a | b, \neg c)$. This is what I have done up to now: \begin{align} p(a | b, \neg c) & \...
tail's user avatar
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A Bayesian network with 4 nodes question

Hello. I need to find the following probabilities: $ \qquad a. P(\neg A, B, \neg C, D) \\ \qquad b. P(A|B,C,D) $ This is my solution: I would like to get an opinion on my solution.
Maor Cohen's user avatar
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Bayesian network probability problem. Rainy on 3rd day given it rains on 1st day

Given the above bayesian network constructed in order to predict rain during successive days and the conditional probability tables. What would be the probability of P( Rain3∣ Rain1 )? My approach: ...
MatiasC's user avatar
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Posterior probability, Dynamic Bayesian Network

I need help with part c). However, these are the answers I got for a) & b): a) P(S1) = P(S1 | S0) * P(S0) + P(S1 | ¬S0) * P(¬S0) = 0.65 b) P(¬Red_eyes and ¬Yawn | S1) = P(¬Red_eyes | S1) * (¬Yawn |...
kim120's user avatar
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Calculation of conditional probability in Probabilistic Graphical Model.

I'm reading through the Koeller and Friedman PGM book and there's an example PGM in Chapter 3. The student example. On page 54 the authors calculate $P(i^1|g^3) \approx 0.079$. The text states a ...
user720609's user avatar
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128 views

What does it mean to marginalize and condition a causal graph?

In causal inference and Bayesian graphical models, the idea of "marginalization" and being "closed under marginalization and conditioning" is brought up and referred to in "...
ajl123's user avatar
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Why is log(p(x)) important in mathematics?

I read many papers for Bayesian Learning, and I can see that in every probabilistic formula they use a logarithm of a distribution p(x) (i.e. log(p(x))) or the negative logarithm of p(x) (i.e. -log((p(...
dogo's user avatar
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Bayesian Network: Calculate probability of a parent node given child node

I have a Question about Bayesian Networks. Given a child node, how to calculate probability of the given parent node(using probability of all nodes). The bayes net is : I was able to solve for P(E | ¬...
user17420392's user avatar
1 vote
1 answer
247 views

Conditional Probability in Bayesian Network

I am working on exercise 13.5 from Nong Ye's Data Mining - Theories, Algorithms, and Examples. The problem gives the following Bayesian network as well as conditional probability tables showing the ...
greelious's user avatar
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What is the difference between $p(a|b)$ and $p(a)$?

I know that $$p(a|b)=\frac{p(a, b)}{p(b)}$$ And I also know $$p(a, b) = p(a)p(b)$$ So, algebraically, it all seems to me that $$p(a|b)=p(a)$$ I know something is wrong with this situation that I'm ...
Ramtin Barzkar's user avatar
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Independence in Belief Networks

The belief network for the following questions is given below: Q1: Which variables must be independent of A given C and S according to the belief network above? My ans: Since C is given, there is no ...
Alex Williams's user avatar
3 votes
1 answer
59 views

How to simplify integrals in the conditionals/marginals in a Bayesian Network

I'm trying to calculate the conditionals within a Bayesian network as shown in the picture, e.g. $P(X_t|X_{t-1}, S)$, which resorts to the calculation of the marginals $P(X_{t-1}, S)$ and $P(X_t, X_{t-...
bcloud2022's user avatar
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Checking for independence in simple Bayessian network

Having the simple model, for example $P(W\mid R)= 0.8$ Is probability of wet grass given rain and $P(W\mid S)= 0.6$ Is probability of wet grass given sprinkler, It is correct, that the $P(W \mid S,R)$,...
user184868's user avatar
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1 answer
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Doesnt seem right; Conditional Probability question

So heres my working out for the question. I figured that I need to find three probabilities: P(c|x), P(y|c) and P(z'|c) as it is the probability they ate contaminated food given they have symptoms X ...
Toast's user avatar
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Conditional Independence, Bayes Network and d-separation

I have a diagram of a Bayes network as shown below: $$\begin{array}{c}A&&&&B&&&&C\\&\searrow&&\swarrow\\&&D&&&&E\\&&&\...
Pengibaby's user avatar
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Bayesian Network calculations given dependence of variables

I've been given this bayesian network 1 where $P(A) = P(A = t) = 0.2, P(B) = 0.5, P(C) = 0.8.$ $$\require{enclose}\begin{array}{c}\enclose{circle}{~~A~~}&&&&\enclose{circle}{~~B~~}&...
Kiley Kearns's user avatar
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Bayes Net. How are the values P(G | D,I) calculated?

Example Bayes Net I have been looking into Bayesian Networks but I keep getting hung up on a simple dependence in most example problems which is how are the values in the conditional probability ...
rgalt's user avatar
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2 answers
140 views

chain rule ordering

suppose I want to compute the joint probability $P(X,Y,Z)$ with chain rule. Is it true that there will be $3!$ possible factorization ? or is there more ? I got 6 for this example: $P(X|YZ)P(Y|Z)P(Z)$...
Cav's user avatar
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calculate probability using variable elimination

Consider the following Conditional probability for the Bayesian Network: By using variable elimination, how to calculate the following probability? I am summing all the terms related to $E$, then ...
Toey's user avatar
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Algorithm for computing joint probability distribution from conditional probability table using tensor multiplication in Bayesian Network?

I get stuck on this problem. If in a Bayesian network, how can we do tensor multiplication on the conditional probability table so that it eventually gives the joint probability distribution? If a ...
Sebastian Li's user avatar
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1 answer
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How to calculate an intersection in bayesian network

I was trying to solve this question, but i don't know how to proceed from there. And i am not sure how to compute $P(A|X_1,X_2,\neg X_3)$ or $P(A \cap X_1\cap X_2)$. It seems like i don't understand ...
osbm's user avatar
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Bayes Rule combining two sensors

You are programming a demining robot. As the robot drives along, the prior probability of a mine being in its immediate vicinity is 0.001 The robot is equipped with a mine detecting sensor which ...
Arnaiz's user avatar
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3 votes
2 answers
499 views

Why does the conditional independent rule of INTERSECTION require STRICT POSITIVE DISTRIBUTION?

Recently, I was confused with the proofs of some conditional independent rules (decomposition, weak union, contraction, intersection), particularly the conditional independent rule of INTERSECTION. In ...
bigbiggentleman's user avatar
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1 answer
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Minimal Bayesian network for a given subset of variables?

Let $G=(V, E)$ be a DAG. Let $\mathrm{dom}$ be a domain for each node in $V$ and $P$ be a joint probabiliy distribution over those domains, that factors as a product of conditional probability ...
user56834's user avatar
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How do I find the P(B | D = T) in this bayesina netowrk?

How to find P(B | D = T) in the following Bayesian network?
ali msvn's user avatar
1 vote
1 answer
80 views

Shortest path with jumps (dynamic Bayesian network)?

Suppose I have the following graph structure: It has the following properties: There are four states $\mathcal{S} = {q,s_1,s_2,s_3}$ where $q$ is some origin state where we start from (though it is ...
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Directed edges in Bayes net could have no effect?

After taking a risk analysis course, I am getting myself familiar with Bayes nets. Currently, I am looking at a common example of whether to take an umbrella on a walk. This is in the context of ...
user2153235's user avatar
1 vote
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107 views

True Loss for Bayes Classifier with Two Classes

For a Bayes classifier of two classes (say 0 and 1), I'm not understanding how the largest possible true risk would be 0.5? I'm assuming that we assign a 0 loss for a correct classification and a loss ...
M. Fire's user avatar
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Property between probability spaces

$\textit{Q1:}$ Why the statement below holds? If someone could give the intuition and/or a proof I would appreciate it. (this one is answered already so check $Q2$) Suppose that $\mathcal{I}=(X,\mu)$ ...
Nav89's user avatar
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How do I calculate the diagnostic inference for Bayes Net with multiple evidence and hidden variable?

I have a Bayes Net for a tsunami alarm at nuclear power plants that looks like this: Top node is "Tsunami" = (T or F) is the ground truth of whether there is a Tsunami approaching. There is ...
webStudent33's user avatar
1 vote
0 answers
41 views

Computing value of noisy-MAX model

I am having trouble computing the remaining probabilities with the use of an interaction model called the noisy-MAX. The noisy-MAX model is an interaction model which helps a network engineer ...
LK4's user avatar
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Peripheralization of Conditional Distributions of head to tail model

If we peripheralize the concurrent probability of the head to tail graphical model for c, we get the following equation. $p(a,b) = p(a)Σ_{c}p(a|c)p(c|b) = p(a)p(b|a)$ The question is, does the ...
pie's user avatar
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