# 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 ...
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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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### 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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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)} \\ &...
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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)....
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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) \\ &...
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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) & \...
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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.
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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: ...
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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 |...
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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 ...
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### 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 "...
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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(...
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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 | ¬...
1 vote
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### 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 ...
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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 ...