Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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 ...

0
votes
0answers
13 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 ...
0
votes
1answer
15 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 ...
0
votes
0answers
7 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 ...
0
votes
1answer
18 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". ...
0
votes
0answers
10 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)...
1
vote
1answer
68 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 \...
0
votes
1answer
44 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 ...
0
votes
0answers
15 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 ...
-1
votes
1answer
36 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 ...
0
votes
0answers
28 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 this simple Bayesian Network diagram. My process is as follows: Given the ...
0
votes
0answers
20 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 ...
0
votes
0answers
14 views

Conditional probability from Bayesian network

Based on the Bayesian network given below: Network https://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html How would I calculate p(S = T|C = F, R = T, W = F)?
6
votes
2answers
165 views

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 ...
0
votes
0answers
19 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 $C$ ...
0
votes
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 ...
0
votes
0answers
9 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.
0
votes
0answers
18 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 ...
0
votes
0answers
17 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 "...
1
vote
0answers
16 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 ...
0
votes
0answers
15 views

Maximum of marginal probabilty vs Maximum a posteriori

Given the conditional probability distribution $P(i|j)$ and the probability distribution $P(j)$ we can compute the PD $P(i)$ via marginalization: $P(i) = \sum_j P(i|j)P(j).$ We then can find the ...
0
votes
0answers
18 views

Factorization implies I-map in Bayesian Network

Theorem: Let $G$ be a Bayesian Network structure over a set of random variables $X$ and let $P$ be a joint distribution over the same space. If $P factorizes according to $G$, then $G is an I-map for $...
1
vote
1answer
57 views

Find probability $P(X|A,B)$ given conditionals

Let $A,B,X$ be discrete random variables taking values on finite spaces, and where $A$ and $B$ are statistically independent. By the law of total probability one has $$P(x_i|A=a)=\sum_b P(x_i | A=a, ...
0
votes
0answers
16 views

Inference in Bayesian network

Consider the following Now, I need to calculate $P(l^1)$ and $P(l^1 \mid i^o)$ $$P(l^1) = P(l^1, g^1) + P(l^1, g^2) + P(l^1, g^3) $$ $$= P(g^1)P(l^1\mid g^1) + P(g^2)P(l^1\mid g^2) + P(g^3)P(l^...
0
votes
0answers
19 views

How to create a Bayesian network?

I have a question regarding a research article titles "Modeling Individualization in a Bayesian Networks Implementation of Knowledge Tracing". I am trying to create a bayesian network for the model ...
1
vote
0answers
35 views

Calculating Conditional Probabilities and the Path where they come from

I have following Problem: Given is the Bayesian Graph of Picture 1. I want to calculate the probability that the goal is reached, which can be calculated as: Since State 1 only requires either A or ...
0
votes
0answers
65 views

Probability Calculation in Bayesian Networks

I'm currently working on a formula to calculate the Mean Time To Compromise (MTTC) for specified attack graphs (In Figure 1 you can see an example). So I'm searching for an efficient way to calculate ...
0
votes
0answers
12 views

Inference in multiply connected Bayesian Networks

I have a Bayes Net with loops (not cycles) and I would like to perform inference in it. By "performing inference" I mean given some evidence what can I infer about the probabilities of the various ...
0
votes
0answers
9 views

Practical computation time needed to perform approximate inferences with a trained Bayesian network.

I have a task of estimating probabilities of events occurring for which a Bayesian Network appears to be an excellent modelling choice. Ample data and computational time will be available for training....
0
votes
0answers
71 views

Can Random Variables be written $P(X)$ instead of $P(X=x)$ as a shorthand?

Recently I asked a question and used the shorthand $P(A)$ for a random variable $A$ to quickly reason about conditional probabilities. However, I was informed that this must be written $P(A=a)$ for ...
0
votes
0answers
20 views

KL-Divergence between approximate and true posteriors with 2 latent causes

Assume I have a directed latent-variable model where $y\in \mathbb{R} \to x$ and $z \in \mathbb{R}^k \to x$. Something like the following: ...
2
votes
0answers
61 views

Total variation distance, bayesian networks and dependence

Consider the following bayesian network depicted below If $X_{1:L}$ are i.i.d. random variables where, for any $i \in [1:L]$, $X_i \in \mathcal{X}$ is uniformly distributed, we can factorize $q^{(1)}...
3
votes
1answer
49 views

How is is Bayes Rule being applied to arrive at the following formula?

In Sebastian Thrun's Intro to Atificial Intelligence course on Udacity, Problem Set 2, Simple Bayes Net, he asks the following question. Given a simple Bayes network with a single causal variable, A, ...
1
vote
1answer
40 views

Derivatives of Gaussian in deriving Kalman filter

Reading Probabilistic robotics by Thrun et al, and in chapter 3 the derivation of a Kalman filter describes in two places setting the first derivative of the quadratic to 0 to find the mean. And that ...
0
votes
0answers
25 views

Diagnostic Inference using Bayes' Theorem

I have a Bayes' net A-->C<--B I want to calculate the Probability of B given C. Since C is the effect of B, I am looking at B as a cause, hence, a diagnostic inference. using Bayes Theorem P(...
1
vote
0answers
26 views

How to define the conditional probability table of $D$ which depends on $A$, $B$ and $C$?

$A$, $B$ and $C$ are independent variables. The probabilities of occurrence are taken as contribution percentage on the variable $D$. The probability of occurrence of $D$ is known. I found on a master ...
1
vote
1answer
15 views

Producing a custom activation function

I have two matrices of equal dimensions with values [0,1]. Basically two gray scale images which are predictions from a neural network. One matrix is the prediction output of a particular object given ...
1
vote
0answers
26 views

Maximum A Posteriori example

In Maximum A Posteriori estimation, $p(D|\theta)p(\theta)$ Can anyone give me a very simple example of above distributions with estimation process by MCMC?
0
votes
0answers
20 views

Random variables in Bayesian Networks

I got a code to generate random number from a Directed Acyclic Graph at https://rdrr.io/rforge/pcalg/man/rmvDAG.html. ...
2
votes
4answers
62 views

Conditional probability with two coin tosses with two possible coins

Let's say I have in front of me two coins. One of them is unbiased, and the second is biased with P(H) = 0.9 I do not know which coin is which. Let's say I pick up 1 coin and have to flip it twice. ...
0
votes
0answers
22 views

“Causality” and independence in Bayesian Networks

I'm a little confused about the notion of "causality" as encoded in directed edges in Bayesian Networks (I'm a newcomer to graphical models, so be gentle). Generally, in my mind, causality and ...
0
votes
0answers
21 views

A variant of the minimal hitting set problem for bipartite graphs

This question is similar to the set cover problem / minimum hitting set / vertex cover in hypergraphs, but less constrained and so Im hoping a tractable algorithm exists.. Basically, you have a ...
0
votes
0answers
26 views

Conditional probability: The probability of an event ( A ) given that another multiple events have already occurred

I am trying to understand the derivation of conditional probability as discussed in the book by Duda " Pattern Classification" Specifically, the topic is about Bayesian Network. Given the network as ...
0
votes
3answers
38 views

Converting joint probability to conditional: Is P(A and B | C) = P(A| B,C)P(B)?

This question came up in the context of Bayesian networks. If I have a network where variable C is dependent on both A and B, and I want to find P(A,B|C) (probability of A and B are true given C is ...
1
vote
0answers
39 views

Bayesian Network Probability

Question # 1: On the network which I posted above, I am having trouble determining what the probability of: P(A,F) is and how it is derived? My thinking was that if you have this event (A) that is ...
0
votes
0answers
13 views

Could someone give me an example of Bayesian updating in a Bayesian network?

Essentially, title. I have a basic understanding of Bayesian updating. I have a basic understanding of Bayesian networks. I'm now trying to create my own (very small, only 5-6 nodes) sample Bayesian ...
0
votes
0answers
34 views

How do I make sure that the nodes in a Bayesian network that I'm building all satisfy the Markov condition without painful trial-and-error?

I think that I understand the fundamentals of a Bayesian network and am trying to put that into practice by making a sample one, its size being about 20 nodes. But I'm struggling to see how to assign ...
0
votes
1answer
12 views

Counting DOF according to a probabilistic graphical model (MRF, BN)

Given the graphical model of a probability distribution, either a Markov Random field (MRF) or a Bayesian Net (BN), how does one count the maximal number of degrees of freedom for all probability ...
0
votes
0answers
13 views

Common cause of two independent nodes

I have two independent nodes, Gary and Nigel that have the states: Shot and stabbing. Both of these states are mutually exclusive and exhaustive. The probability of getting shot is 0.079 and the ...
0
votes
0answers
27 views

Can I use independence for bayesian network?

I'm struggling trying to understand bayesian network. Having trouble finding P(F&G) I know independence and conditional independence are different things. Conditional independence is when A ...
3
votes
1answer
47 views

Real time bayesian analysis

Currently our memcached cluster shields our database from heavy load. If the cache were to go down, it would take our application down with it. With a cold cache, we could avoid this downtime by ...