Stochastic metrology and the empirical distribution

• URL: http://arxiv.org/abs/2305.16480v1
• Date: Thu, 25 May 2023 21:22:34 GMT
• Title: Stochastic metrology and the empirical distribution
• Authors: Joseph A. Smiga, Marco Radaelli, Felix C. Binder, Gabriel T. Landi
• Abstract summary: We study the problem of parameter estimation in time series stemming from general processes, where the outcomes may exhibit arbitrary correlations. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 non-trivial 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.

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