Intuition for an Old Curiosity and an Implication for MCMC

Michael Lavine and Jim Hodges

The American Statistician, 2021, vol. 75, issue 1, 1-6

Abstract: Morris and Ebey reported the following curiosity. “The unweighted sample mean is examined as an estimator of the population mean in a first-order autoregressive model. It is demonstrated that the precision of this estimator deteriorates as the number of equally spaced observations taken within a fixed time interval increases.” Morris and Ebey proved their result but gave no intuition for it. We provide some intuition, then examine an implication: that the usual practice of estimating posterior expectations by taking the unweighted average of consecutive Markov chain Monte Carlo (MCMC) samples may not be optimal.

Date: 2021
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DOI: 10.1080/00031305.2018.1518267

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