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Abstract: Focusing on the discrete probabilistic setting we generalize thecombinatorial definition of cumulants to L-cumulants. This generalization keepsall the desired properties of the classical cumulants like semi-invariance andvanishing for independent blocks of random variables. These properties makeL-cumulants useful for the algebraic analysis of statistical models. Weillustrate this for general Markov models and hidden Markov processes in thecase when the hidden process is binary. The main motivation of this work is tounderstand cumulant-like coordinates in algebraic statistics and to give a moreinsightful explanation why tree cumulants give such an elegant description ofbinary hidden tree models. Moreover, we argue that L-cumulants can be used inthe analysis of certain classical algebraic varieties.



Author: Piotr Zwiernik

Source: https://arxiv.org/







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