Abstract:
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In the study of hydrologic time series, autocorrelation complicates trend detection. Using effective sample size (ESS) to modify trend detection tests can lead to better test performance; however, imprecise ESS estimation contributes to unreliable results. Focusing on AR(1) series, this study considers two alternatives: Fisher Information (FI) as a proxy for ESS, and Bayesian estimation of ESS. We find a noteworthy relationship between FI and ESS, but FI estimation is not superior to ESS estimation. In both cases, maximum likelihood estimation of the AR(1) parameter has high variance, leading in turn to high variance in the ESS estimates. Bayesian estimation of ESS is an alternative in the context of hydrologic time series, where substantial prior information is available. We use simulations to explore the effectiveness of Bayesian estimation of ESS, under non-informative, moderately informative, informative, and highly informative prior distributions. We compare Bayesian results to FI and ESS results, and see greatly reduced estimation variance, even for moderately informative priors. We then use Bayesian techniques to estimate ESS and trend for a hydrologic data set.
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