# Questions tagged [bayesian-network]

A Bayesian network is a probabilistic directed acyclic graph. Nodes represent random variables in the Bayesian sense (observable or unobservable); edges represent conditional dependencies between nodes.

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### Background on notation for generative models

In many papers on generative modeling and Bayesian inference in statistics, I come across the following kind of notation, in particular for hierarchical models. For variables $x_1, \dots, x_n$, it ...
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### Mutual Information of nonadjacent nodes in Bayesian Network

How do you compute the mutual information of two non-adjacent nodes in a Bayesian network? In this case, what would $I(D;A)$ be? Would I need to take the conditional probabilities of all intemediate ...
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### Bayesian network with partial info (4 nodes)

I have some (conditional) probabilities for a Bayesian network with binary variables, but not all. My DAG is M->F->Y->C<-F and M->Y and M->C I ...
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### Dynamic Bayesian Network with Temporal Hidden State

Can someone direct me to papers or Python packages which I can use to develop a dynamic bayesian network with temporal hidden states. I found packages that can handle discrete hidden states. But that'...
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### Time Series Prediction with Hidden Variables [closed]

I have time series data sampled every 10 seconds. I want to predict a target variable 𝑦 for 5 steps ahead using the input variable at the current time along with 10 past lags. My problem is that ...
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### What is proposal distribution in Importance sampling

I want to learn importance sampling using a simple example. Consider the following example code which implement importance sampling using python for a simple Bayesian network. I've read that we fix ...
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### Independent statements in model definition and then DAG

In this paper in Section 3.1, they give a Baysian linear regression model and then a DAG, which I show below. From my understanding a DAG tells us how the joint distribution can be factorised. But in ...
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### How to leverage the separable functions in MCMC sampling? [closed]

I'm considering the posterior of a parametric model via the Bayesian approach. More specificity, I have a parametric model $u(p_1,p_2, p_3) = u_1(p_1) \times u_2(p_2) \times u_3(p_3)$ and I want to ...
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### Bayesian network extracting further conditional independence statements then just from d-separation theorem

Given a Bayesian network $(p,\mathcal{G})$, where $p$ is our joint distribution, and $\mathcal{G}$ is a DAG. Then by the d-separation theorem we can deduce conditional independence statements, in ...
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### BN node probabilities calculation

In the paper The use of Bayes and causal modelling in decision making, uncertainty and risk by Norman Fenton and Martin Neil following BN is presented: Quote from ...
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### Do Bayesian networks have any rules with regards to zero probability RVs?

I am currently learning about Bayesian networks through Berkeley's AI course. In a Bayesian network, each node encodes the conditional probability of the random variable (RV) represented by the node ...
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### Stable violation of faithfulness

Faithfulness is often justified by the argument that any violations of it require very specific "fine-tuned" parameters (for some appropriate SCMs/SEMs/SFMs), and that such violations are ...
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### Use of composite dependent variable in Economics

I'm curious about research that employs a composite dependent variable in empirical studies. Specifically, I'm interested in analyses that utilize any composite indexing method while taking into ...
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I have got the following Network and porbabilites And I need to Calculate the probability $P(C=False)$ I triend using the formula for joint porability distributions $P(X_1,…,X_n)= \prod_{i=1}^{n}P(... 2 votes 1 answer 182 views ### Definition of$\text{do}$operator [closed] I'm looking for a hint in understanding semantics of$\text{do}$operator. Starting from the original distribution$P$, an intervention$\text{do}(X=x)$takes us to another distribution$P_x$- in ... • 129 0 votes 0 answers 14 views ### On showing indepdedence of a collider in graphical model In the following slide: it seems how it got A and B are independent is rather circular. The reason is it assumes$p(a,b,c) = p(a)p(b)p(c|a,b)$and then marginalizes over$c$to get$p(a,b) = p(a)p(b),... • 403 0 votes 0 answers 27 views ### How can I compute a counterfactual query for discrete binary variables? In computing counterfactual queries for structural causal models (SCMs), J. Pearl says to go through 3 steps. Abduction Action Prediction In his book, Causal Inference in Statistics, he shows how to ... • 1,399 0 votes 1 answer 51 views ### Optimization of fault diagnosis sequence using probability and cost [closed] I am developping the algorithm to optimize the fault diagnosis sequence using probability and cost. For exemple, I have 3 diagnosis actions possibles : option 1 : probability which can detect the root ... 1 vote 0 answers 32 views ### Explaining the approximation to the variational free energy in Bayes by Backprop In the paper Weight Uncertainty in Neural Networks, Blundell et al., 2015, the authors approximate the exact cost (variational free energy) \mathcal F(\mathcal D, \theta) = \mathrm{KL}[q(\mathbf w \... • 101 0 votes 0 answers 21 views ### Sampling from large Bayesian network of particular form I want to know whether there is an efficient way of sampling from this special kind of Bayesian networks of the following form (like thousands or millions of variables in principle). Here is a picture ... • 135 2 votes 0 answers 75 views ### 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 Belief Networks (BPNs), specifically ... • 73 0 votes 0 answers 21 views ### Marginalization BN Is my marginalization over C of P(A)P(B)P(C|A,B)P(D|C)P(E|C) below correct? Because wouldn't this imply that there are no dependencies once you marginalize over C? 0 votes 0 answers 11 views ### Why do we need the variance term in SWAG method? My question is about the SWA-Gaussian paper. I do not really understand why they need the 1/2 factor for the covariance matrix (as underlined in the picture). I understand that it is needed because ... 1 vote 0 answers 43 views ### Temperature scaling a bayesian neural network? I am trying to calibrate a Bayesian neural network. I have already approximated the posterior density for its weights. In order to make predictions the Bayesian way, I am taking samples from the ... 0 votes 0 answers 6 views ### Is i(G) equivalent to i_l(G), the local independency set of BN? Reference: Koller, D., & Friedman, N. (2010). Probabilistic graphical models: Principles and techniques (Nachdr.). MIT Press. Bayesian network \mathcal{G} encodes that for any node X_i, there ... 0 votes 1 answer 163 views ### Removing immoralities in bayesian networks In many toy examples of bayesian networks, including the ones used in university courses, there are immoralities in the graph (see here, for example). Is it common practice to leave them in the ... • 126 0 votes 0 answers 18 views ### Given a known Bayesian Belief Network or Causal DAG, how can we score the value of different pieces of evidence? Assume we know the BBN (Bayesian Belief Network), how can we score the value of each additional piece of evidence that the system ingests? In simpler terms, here are two example use cases: Make an app ... • 931 0 votes 0 answers 25 views ### How can we estimate the combined causal effect of two separate parents in a Bayesian network? Consider the following partially-defined Bayesian network: We know the probability of C given A is True and B is False We know the probability of C given A is False and B is True We know that C can ... 0 votes 1 answer 53 views ### BNN predictive distribution p(y(x)|D) = \int p(y(x)|w)p(w|D) dw, what is p(y(x)|w)? When we use approximation methods to try to approximate the predictive distribution, I am slightly troubled by p(y(x)|D) = \int p(y(x)|w)p(w|D) dw. Since y(x) = f(w, x) (as y(x) is the neural ... • 125 0 votes 0 answers 32 views ### Do we need stationarity for Bayesian network modelling? Most of the Bayesian network packages in R dealing with continuous data require data to be Gaussian. Does this necessitate the data should also be stationary in order to run the model? 2 votes 0 answers 50 views ### Causal discovery on partially known causal DAG Often in data science, we have partial knowledge of the causal DAG structure. Regarding some of the possible edges in the DAG, we are in doubt. Are there any resources to tackle this setting? The ... 0 votes 0 answers 29 views ### Markov and Faithfullness Condition in disconnected DAG/Bayesian network I'm very confused about the Markov- and the faithfulness condition in disconnected DAGs, as I've never seen such examples. Assume for example I had a DAG where X -> Y, Z. Thus, Z is disconnected ... • 11 1 vote 1 answer 101 views ### Inference in Bayesian networks with hidden variables Suppose I have the Bayesian network in the figure and the corresponding conditional probability table for each node, where A and B are the hidden variables, and C and D are the observed variables. ... • 13 1 vote 0 answers 50 views ### Prior term in SGHMC implementation I am working with SGHMC (Stochastic Gradient Hamiltonian Monte Carlo) models. I found an implimentation of the algorithm in pytorch here. The part of the code that represents momentum variable update (... 1 vote 0 answers 138 views ### Too large KL-divergence in training I tried to train bayesian network using ELBO loss function. \begin{align*} \mathcal{F}(D, \theta) = KL[q(w|\theta)||P(w)] - \mathbb{E}_{q(w|\theta)}[\log p(D|w)] \end{align*} My question is, if model ... 0 votes 1 answer 84 views ### Biased sample same like conditioning on a collider? I am studying chapter 5 "The many variables & the spurious waffles" of the book Rethinking and trying to answer the following question: How is biased sample like conditioning on a ... • 389 0 votes 0 answers 47 views ### Why implied Conditional Independencies of mediator and confounder are the same? I am trying to understand why the impliedConditionalIndependencies function of the rethinking package returns the same value for ... • 389 2 votes 1 answer 88 views ### Regarding the bayes rule derivation of posterior distribution, p(\omega|x,y), for a given dataset D over \omega. So I was going through this paper and under Uncertainty modeling it says So I tried deriving it on my own and I got p(\omega | X, Y) = \frac{p(Y | X, \omega) \cdot p(X,\omega)}{p(Y | X) \cdot P(X)} ... 1 vote 0 answers 25 views ### Is P(D | A) = P(D | A,B) * P(B | A) according to the Bayesian Network in the description? if I consider the Bayesian network in the picture below: https://i.sstatic.net/nZKN2.jpg So A is the parent of C,D and B. But B is also the parent of D. Is it then correct to write: P(D | A) = P(D | A,... 2 votes 0 answers 19 views ### Constrained optimization between two bayesian variables I have 2 separate Bayesain networks and I was hoping to maximize Value within the constraint of the Cost. What are is a good way ... 2 votes 0 answers 32 views ### Justification of definition 2.7.1 (Potential cause) in Causality by Pearl In Causality - Models, Reasoning And Inference by Pearl, definition 2.7.1 says - Potential Cause definition: A variable X has a potential causal influence on another variable Y (that is ... 5 votes 1 answer 38 views ### In what sense is one latent causal structure "preferred to" another? Definition 2.3.3 from Causality by Pearl In Causality - Models, Reasoning, And Inference by Pearl, definition 2.3.3 reads as follows - One latent structure L = \langle D,O \rangle is preferred to another L^{'} = \langle D^{'},O \... 1 vote 1 answer 91 views ### Bayesian Linear Regression on the top of deterministic neural network I understand the concepts of Bayesian linear regression and regular neural networks separately, but I cannot wrap my head around how to combine both. In a general setting, lets say I have a (... • 11 3 votes 0 answers 87 views ### How can I compute the set of interventional probability distributions compatible with a DAG? Let P be a probability distribution on a set V of variables and for any X\subseteq V and any possible realization x of X let P_x be a distribution on V\setminus X. Let P^* the ... 1 vote 0 answers 29 views ### Specifying a terminal node in a Bayesian Network I am writing R script using bnlearn package for learning a DAG from a dataset. Is it possible to define a terminal node beforehand? ie I want a node Y to be the final one in the graph, which will not ... • 11 0 votes 0 answers 61 views ### Sampling from Unnormalized Posterior in Prediction Stage Background: Given a trained model, y, parameterized by W\text{~} P and dataset D, for a testing point x_{test}, the predictive probability distribution is given byP(y(x_{test})|D) = \int P(... • 308 1 vote 0 answers 35 views ### How to chain separate models into a single unified model (where predictions of one sub-model form an input to another)? Our team is tasked with forecasting several timeseries at the daily (or hourly) level: number of calls ('demand') number of calls catergorised as important mean vehical travel time to caller mean ... • 121 1 vote 2 answers 135 views ### Bayesian Network calculation questions update The solution follows obtain the right answer now. ----------------------------------------------------------------------------- The Question is here And my answer is hereP(a_0)=P(a_0|r_0) + ...
I have a bayesian network as illustrated above and I want to calculate probability for $P(x|z).$ I am applying the formula: \begin{align}P(x|z) &= \sum\limits_{y} P(z, x, y)\\&= P(x) \times[P(...