Bayes Network

What is Bays network

A Bayesian network is a representation of a joint probability distribution of a set of random variables with a possible mutual causal relationship. The network consists of nodes representing the random variables, edges between pairs of nodes representing the causal relationship of these nodes, and a conditional probability distribution in each of the nodes. The main objective of the method is to model the posterior conditional probability distribution of outcome (often causal) variable(s) after observing new evidence. Bayesian networks may be constructed either manually with knowledge of the underlying domain, or automatically from a large dataset by appropriate software.

The goal

The goal is to calculate the posterior conditional probability distribution of each of the possible unobserved causes given the observed evidence.

Any node in a Bayesian network is always conditionally independent of its all non decendant given that node's parents.

Difference between markov and Bayesian network

A Markov model is an example of a graph which represents only one random variable and the nodesrepresent possible realizations of that random variable in distinct time points. In contrast, a Bayesian network represents a whole set of random variables and each node represents a particular causal relationship among them.

six rules of bayes net/six rules of d seperation

link

d in d seperation stands for directional

path in nodes means:

any consecutive sequence of edges, disregarding their directionalities.

unbocked path means:

a path that can be traced without traversing a pair of arrows that collide "head-to-head"

the head to head nodes are called "colliders"

Rule 1

x and y are _d-_connected if there is an unblocked path between them.

Rule 2

x and y are _d-_connected, conditioned on a set Z of nodes, if there is a collider-free path between x and y that traverses no member of Z. If no such path exists, we say that x and y are _d-_separated by Z, We also say then that every path between x and y is "blocked" by Z.

Rule 3

If a collider is a member of the conditioning set Z, or has a descendant in Z, then it no longer blocks any path that traces this collider.

without knowing anything:

• C is dependent on A
  

• A and C is both dependent on c, which make them conditionally independent but not independent
  

• A and C is independent
  

Given B:

• A and C are independent
  

• A and C are independent
  

• A and C is dependent