Stochastic metrology and the empirical distribution

We study the problem of parameter estimation in time series stemming from general stochastic processes, where the outcomes may exhibit arbitrary temporal correlations. In particular, we address the question of how much Fisher information is lost if the stochastic process is compressed into a single...

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Bibliographic Details
Published inPhysical review research Vol. 5; no. 3; p. 033150
Main Authors Smiga, Joseph A., Radaelli, Marco, Binder, Felix C., Landi, Gabriel T.
Format Journal Article
LanguageEnglish
Published American Physical Society 01.09.2023
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Summary:We study the problem of parameter estimation in time series stemming from general stochastic processes, where the outcomes may exhibit arbitrary temporal correlations. In particular, we address the question of how much Fisher information is lost if the stochastic process is compressed into a single histogram, known as the empirical distribution. As we show, the answer is nontrivial due to the correlations between outcomes. We derive practical formulas for the resulting Fisher information for various scenarios, from generic stationary processes to discrete-time Markov chains to continuous-time classical master equations. The results are illustrated with several examples.
ISSN:2643-1564
2643-1564
DOI:10.1103/PhysRevResearch.5.033150