Prior Samples

Context

BayesiaLab can take into account Priors when estimating parameters using Maximum Likelihood Estimation.
Priors reflect any a priori knowledge of an analyst regarding the domain, in other words, expert knowledge. See also Prior Knowledge for Structural Learning.
These priors are expressed with an analyst-specified, initial Bayesian network (structure and parameters), plus analyst-specified Prior Samples.
Prior Samples represent the analyst's subjective degree of confidence in the Priors.

\hat{P}(X = {x_i} | Pa = p{a_i}) = \frac{{N(X = {x_i}, Pa = p{a_i}) + {M_0} \times {P_0}(X = {x_i}, Pa = p{a_i})}}{{\sum_j \left( N(X = {x_j}, Pa = p{a_i}) + {M_0} \times {P_0}(X = {x_j}, Pa = p{a_i}) \right)}}

where

is the degree of confidence in the Prior.
is the joint probability returned by the prior Bayesian network.
BayesiaLab uses these two terms to generate virtual samples that are subsequently combined with the observed samples from the dataset.