Multiple Changepoint Detection Using Metadata

Abstract

This paper examines multiple changepoint detection procedures that use station history (metadata) information. Metadata records are available for some climate time series; however, these records are notoriously incomplete and many station moves and gauge changes are unlisted (undocumented). The shift in a series must be comparatively larger to declare a changepoint at an undocumented time. Also, the statistical methods for the documented and undocumented scenarios radically differ: a simple t test adequately detects a single mean shift at a documented changepoint time, while a t max distribution is appropriate for a single undocumented changepoint analysis. Here, the multiple changepoint detection problem is considered via a Bayesian approach, with the metadata record being used to formulate a prior distribution of the changepoint numbers and their location times. This prior distribution is combined with the data to obtain a posterior distribution of changepoint numbers and location times. Estimates of the most likely number of changepoints and times are obtained from the posterior distribution. Simulation studies demonstrate the efficacy of this approach. The methods, which are applicable with or without a reference series, are applied in the analysis of an annual precipitation series from New Bedford, Massachusetts.

Multiple changepoint detection with partial information on changepoint times

“…where a, b > 0 are fixed hyper-parameters. The Beta-Binomial hierarchical priors in (4) and (5) are widely used in Bayesian model selection (Scott and Berger 2010), and have been adopted to detect changepoints (Giordani and Kohn 2008;Li and Lund 2015). Due to conjugacy, the marginal prior density of η has the following closed form, with β(·, ·) denoting the Beta function:…”

“…For notation, all quantities superscripted with (1) refer to undocumented times; quantities superscripted with (2) refer to documented times. Following Li and Lund (2015), we posit that the undocumented times have a Beta-Binomial(a, b (1) ) prior, and independently, the documented times have a Beta-Binomial(a, b (2) ) prior. To make the metadata times more likely to induce true mean shifts, we impose b (1) > b (2) so that…”

“…For different problems, one may need to modify b (1) and b (2) to reflect specific domain knowledge. Our previous paper (Li and Lund 2015) gives a detailed sensitivity analysis on the choice of Beta-Binomial hyper-parameters. It suggests that changepoint detection results are relatively stable under a range of E(ρ (2) )/E(ρ (1) ) values.…”

“…For example, multivariate series, which involve the more challenging problem of borrowing information across component series, are pursued. In this sense, Li and Lund (2015) is a special case of the current paper. This paper also includes a thorough investigation of the asymptotic consistency of the proposed methods.…”

“…The only exception to the above is Li and Lund (2015), which accounts for metadata in a univariate precipitation time series. That work was written for a climate audience and was largely void of statistical and technical detail.…”