Abstract des Vortrages von Johannes Rauh
Algebraic Statistics and Conditional Independence
Many problems in statistics and information theory can be reformulated in terms of algebraic equations. This observation has led to many fruitful interactions between statisticians and algebraists summarized under the name ``algebraic statistics.''
One of the topics of algebraic statistics is conditional independence (CI). CI is an important concept in statistics that allows to model the interaction between several random variables, for example, in the framework of graphical models.
CI constraints can be formulated as algebraic equations, and reasoning with CI constraints can be done by analyzing the corresponding CI ideals. Natural algebraic questions are to decide radicality or regularity of these CI ideals. A primary decomposition of the CI ideal is useful to characterize the set of probability distributions that satisfy the corresponding CI constraints.