Algebraic Statistics in Model Selection

Understand

We develop the necessary theory in computational algebraic geometry to place Bayesian networks into the realm of algebraic statistics.

• We present an algebra{statistics dictionary focused on statistical modeling.
• In particular, we link the notion of effiective dimension of a Bayesian network with the notion of algebraic dimension of a variety.
• We also obtain the independence and non{independence constraints on the distributions over the observable variables implied by a Bayesian network with hidden variables, via a generating set of an ideal of polynomials associated to the network.