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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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Is it okay to not provide a whitelist when using the Hill-Climbing algorithm?

So, I'm trying to use Hill-Climbing for a Bayesian learning network. For some reasons, I do not know all of the variables that I'm going to use and hence, I cannot provide a whitelist or a blacklist ...
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A question about functions from binary inputs to binary outputs

The following is a distillation of part of a larger research problem. (I have several clunky proofs for special cases, but an elegant method for the general case is somehow escaping me.) Consider a ...
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16 views

Evidences in Bayesian Networks

When inferring the probability for a random variable to outcome a particular value in a Bayesian Network, one may assign a set of evidence. A set of evidence is basically a set of random variables ...
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14 views

Bayesian network prediction model in rjags

I have a text to predict log-level of a poisonous gas in houses in different counties in Minnesota. This is the part of the table I have been given: The whole table is located here: https://ufile.io/...
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2answers
30 views

Compute a probability given a Bayesian network using variable elimination

Having the following Bayesian Network: A -> B, A -> C, B -> D, B -> F, C -> F, C -> G $$\begin{array}{l} A&\to&B&\to& D\\\...
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19 views

Uncertain about definition of Bayesian Network

If I have a Bayesian network of the form: $A\rightarrow B\rightarrow C\rightarrow D$ is it necessarily true that $P(B,D|C)=P(B|C)P(D|C)$? Wikipedia gives the following defining condition for a ...
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18 views

Complete a Bayesian Network by specifying the probability distributions

I have a hierarchical Bayesian Network like this: Here: $R≡$ log level of poisonous gas (radon) in a house $B≡$ type of house (With a basement or without) $C≡$ a county in Minnesota where the ...
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1answer
68 views

Compute probability given a Bayesian Network

Having the following Bayesian Network: A -> B, A -> C, B -> D, B -> F, C -> F, C -> G $$\begin{array}{l} A&\to&B&\to& D\\\...
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1answer
65 views

Calculate probability using brute-force method

I have to calculate a probability using the following probabilities from a Bayesian network: $$P(+a)=...$$ $$P(+a|+b)=..., P(+a|¬b)=...$$ $$P(+b|+a)=..., P(+b|¬a)=...$$ $$P(+d|+b)=..., P(+d|¬b)=...$$ $...
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1answer
36 views

Bayesian Model with Hierarchical Structure

I asked this on Cross Validated but found no answers, so i will try here. I have a table with the following variables: level of poisonous gas (radon) in a house type of house (With a basement or ...
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1answer
19 views

Inference in probabilistic graphical models (Bayesian networks)

I've been given a practice final exam that uses this network from CMU and was given some probabilities to determine. I'll attach some pictures below of the information at the link above. I've been ...
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21 views

How to aggregate the normal distributions of two Kalman populations?

Suppose I have the following Bayesian Network: It's given by the following probability distributions: $$\begin{aligned}X_1&\sim \mathcal N(\mu, \delta^2)\\ \forall i, 2\leq i\leq n: X_i|X_{i-1}&...
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Bayesian Network vs MultiVariate Analysis vs Induction

I work with JS programmer on the logic for a web app. We have factors that influence a composition of a set. Envision rows in Excel that tell a set to have 5 members or 10, etc. Each row has certain ...
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1answer
33 views

Finding an unconditional joint probability in a Bayesian Belief Network

I have a Bayesian network as drawn in the picture: We can see that $B$ and $C$ are conditionally independent given $A$. My goal is to find $P(B\cap C)$. My first thought was to use the Law of Total ...
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1answer
18 views

Different order of insertion - different Bayesian network ? how to prove formally?

I have some Bayesian network which i constructed from some data, say it consists of nodes A, B, C and D and that was the initial order of insertion. If i ...
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1answer
62 views

solve $P(C = 0, F = 1)$ bayes network

given this: And I want to solve $P(C = 0, W = 1)$. Which I did below: $$P(C = 0, W = 1) = P(C = 0)P(W = 1 | C = 0)$$ $$= P(C = 0) \big[P(W = 1 | R = 0, S = 0) \cdot P(R = 0 | C = 0) \cdot P(S = 0 | ...
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1answer
20 views

Apparent paradox on d-separation and conditioning in Bayesian Networks

Two random variables $A$ and $B$ are conditionally independent (when conditioned on a set of random variables $\mathcal{C}$), if the variables are d-separated, i.e. if all the paths from $A$ to $B$ ...
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1answer
90 views

Bayesian network probability diamond shape

I am looking to find $P(A=0,D=1)$. We will have something like $(0.5)(.......)$ The dots are the following: $P(D=1|C=0,B=0)*P(C=0,B=0|A=1) + \dots + P(D=1|C=1,B=1)*P(C=1,B=1|A=1)$ How am I ...
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1answer
23 views

Bayesian belief network

A child inherits a gene X with probability 50%. A disease will develop if child inherited gene from both parents. The disease will not develop if child got gene from just one of parents. Jain and Max ...
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1answer
44 views

Bayesian network network problem

I want to find: $P(C=0,A=1,D=1)$. I know the following: $P(C=0,A=1,D=1) = P(C=0|A=1, D=1)*P(A=1|D=1)*P(D=1)$ From the image, we can see $P(D=1)$ is $P(D=1) = P(D=1|A=0)*P(A=0) + P(D=1|A=1)*P(A=1) =...
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How does marginalizing over one variable affect independencies in the distribution?

I was requested to find a general algorithm which, given a Bayesian network graph $\mathcal{G}$ over a set of random variables $\mathcal{X}$ and a node to remove $X\in \mathcal{X}$, builds a new ...
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1answer
32 views

Dynamic Bayesian Networks and cycles

I am aware that Bayesian Networks and Dynamic Bayesian Networks do not allow cycles. However, there is something I can't figure out and which is simple: what is a cycle in a DBN? Consider two nodes, $...
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2answers
33 views

How to calculate P(X|W,Z) in a Bayesian network?

Bayesian net I can see that $P(X,Y,W,Z)$ = $P(X|Y,Z)P(Y|W,Z)P(W)P(Z)$. I did the following till now to calculate $P(X|W,Z)$: $P(X|W,Z)$ = $P(X|Y,W,Z)$ + $P(X|\overline{Y},W,Z)$ = $P(X,Y,W,Z)P(Y,W,Z)...
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1answer
28 views

Variable Elimination Bayesian Belief Network

I'm rather confused on how to perform variable elimination in the following bayesian believe network. If I have the following query queryP(B|G, E) with a variable ordering of G, E, A, B, C, D, F. My ...
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53 views

Bayes Rule - Expanding the conditional probabilties

Suppose I am generating a sample for $P(A=0|B=0,C=0,AvB=0,CvA=2,BvC=0)$ The pseudo probability for this would be given as: $P'(A=0|B=0,C=0,AvB=0,CvA=2,BvC=0) = P(A=0)P(B=0,C=0,AvB=0,CvA=2,BvC=0|A=0)$ ...
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0answers
22 views

conditional probability for a simple Bayes network

I have a very simple, and maybe trivial question about this Bayes net. Given a Bayes net, $A \rightarrow B \leftarrow C$ and the probability distribution $p(B|A,C)$. How do we compute $P(B = b| A = a,...
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0answers
10 views

forward sampling for Bayesian network with continuous variables and equation based causal relationship

I have a physical system which can be represented by the following Bayesian network. It has the following characteristics The encoded variables are continuous variables. The causal relationships ...
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1answer
32 views

Understanding how to read Bayesian networks

Below is an example that I want to talk about: I'm going to define variable names based on the first letter as described in the bubbles. One question I have is how would I calculate $P(M|B)$? This is ...
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20 views

What statistical network allows to pick where to take the values from?

I am looking for a mathematical framework similar to Bayesian Network that would allow me to solve next class of problems: Ann and Ron are running towards one of 2 closed baskets with apples. if in ...
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1answer
34 views

Bayesian Probability solving

The above diagram is the Bayesian Network. I want to find P(M=t|A=t && E=f) I have followed the follwoing steps. P(M=t|A=t && E=f) = P(M=t && A=t && E=f)/ P(A=t &&...
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1answer
47 views

Why Bayesian Approach don't use test data for model validation?

Up to I know the usual way of thinking in machine learning approach is to split the data in a train and test subsets. The first one is for fitting the model (with the support of a validation subset) ...
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1answer
22 views

Is this Bayesian Network Probability calculation correct?

I think I understand how to calculate BN and why it is so, but complex net still confuses me. Currently how I understand it is that, if there is any 'result' variable in the probability, it can be ...
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1answer
23 views

Is this Bayesian Network probability correct?

I just extended a bayesian network that was on a ppt into this form. I'm trying to get P(A,B,C,D,E) and I think it's p(A)P(B)P(C|A,B)P(D|C)P(E|C) but as I'm not sure, just wanted to check if it is ...
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1answer
25 views

Conditional Probability Calculation in Bayes Net

Say I have a simple Bayes Net that appears like that in the picture and am giving the following probabilities: $P(y|x) = 0.5$ $P(z|x)=0.4$ $P(y|\bar{x})=0.8$ $P(z|\bar{x}) = 0.9 $ How would I ...
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1answer
26 views

Directed vs undirected graphs in Bishop's PRML

In Bishop's PRML, chapter 8 is dedicated to graphical models. In figure 8.32, we have the following figure showing a directed and an undirected graph: These two graphs are said to be "equivalent". ...
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27 views

Conditional probability table for two parents, one chilld

Assuming: Bayesian network with 3 variables: $A$, $B$, $C$ $C$ is dependent on $A$ and $B$ $A$ and $B$ are conditionally independent given $C$ Following (conditional) probabilities $$P(a), P(b), P(c)...
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1answer
82 views

Optimisation vs. Bayes' Theorem not coinciding

Suppose I have the following Bayesian Network: It's given by the following relations: $$\begin{aligned}X_1&\sim \mathcal N(\mu, 1/\sigma^2)\\ \forall k, 2\leq k\leq n: X_k|X_{k-1}&\sim \...
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1answer
58 views

Struggling with Bayes network

Im in a machine learning course and bayes networks was presented in such an abstract way I find it really difficult to understand how to use it. And all examples I can find, the final numbers seem ...
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1answer
29 views

Bayesian Network 1 Parent 2 Children

I've been attempting this problem for a good while now, and I was wondering if somebody could help me figure this one out. I am currently attempting to write a program that tests $p(B|G, D)$ and ...
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1answer
58 views

Bayes network probability question

I'm looking at this problem as I review for an exam and I would appreciate it if anyone can give me work/answers to Pr(c), Pr(b), Pr(b,c) and Pr(c,d) so I can check my solutions, and use the work to ...
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1answer
150 views

How to find conditional probability, given parent node and child node

Currently I am working on a sample question for my course: Calculate P(Sprinkler | Cloudy=True, WetGrass=True) based on . My process is as follows: Given the conditional probability table of ...
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23 views

Writing the distribution of this random vector (Markov random field).

All the random variables in this problem are taking values in $\{0,1\}$. Imagine a cross. The intersection point of the cross is a random variable $X_1$, and the extremities of the cross are random ...
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1answer
29 views

Conditional probability from Bayesian network

Based on the Bayesian network given below: https://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html How would I calculate p(S = T|C = F, R = T, W = F)?
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I wake up in a random class and hear 6 biology-related words. How certain should I be that I'm in Biology class?

Suppose I'm sleeping in some class. I wake up and I hear 6 topic-specific words that seem related to biology. I'm asked to guess whether I'm in Biology class? How confident should I be? I think this ...
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0answers
25 views

How to construct a simple Bayes network?

Suppose I'm interested in the probability that event $A$ will occur. I'm uncertain about $P(A)$, but I believe that it has a uniform distribution on $[0.1,.9]$. Moreover, I know that event $B$ and $C$ ...
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0answers
15 views

Derive rankings from a paired probability matrix

Similar to this question, I have a matrix of pairwise probabilities (say, p(a > b), p(b > c), p(a > c)) with which I'd like to calculate the probability of each possible ranking (p(a > b > c), p(b > a ...
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22 views

Question regarding Conditional Probability Tables (CPTs)

I'm a beginner in Bayesian networks. How were the numbers inside the highlighted area calculated? This is all the information I am given.
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19 views

How were these probability values calculated?

I'm learning about Bayesian Networks and am an absolute beginner and I stumbled upon this. My question is (might sound stupid), how were these values inside the red box calculated? What formula was ...
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19 views

Terminology: Dynamic Bayesian network with hidden process

I came across a problem which can be modelled using a special type of dynamic Bayesian network. I'm looking for a name for this kind of network, but could not find anything so far. It resembles a "...
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28 views

The invariant property of Kalman filter

I came a cross a property for Kalman filter known as invariant property. I could only find some information about it on a wikipedia article but I still struggle to understand it. The property is ...