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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.
P^(X=xi∣Pa=pai)=N(X=xi,Pa=pai)+M0×P0(X=xi,Pa=pai)∑j(N(X=xj,Pa=pai)+M0×P0(X=xj,Pa=pai))\hat{P}(X = {x_i} \mid Pa = p{a_i}) = \\[1em] \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

  • $M_0$ is the degree of confidence in the prior.
  • $P_0$ 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.
Step 5 — Import ReportGenerate Prior Samples