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arXiv · 1207.4112

Algebraic Statistics in Model Selection

Luis David Garcia
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Abstract

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. These results extend previous work on the subject. Finally, the relevance of these results for model selection is discussed.

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Luis David Garcia. 2012-07-11. Algebraic Statistics in Model Selection. https://arxiv.org/abs/1207.4112

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