Using the Change Point Model (CPM) Framework to Identify Windows for Water Resource Management Action in the Lower Colorado River Basin of Texas, USA

In water-stressed river basins with growing urban populations, conflicts over water resources have emerged between urban and agricultural interests, as managerial interventions occur with little warning and tend to favor urban over agricultural water uses. This research documents changes in water use along an urban-to-agricultural gradient to examine whether it is possible to leverage temporal fluctuations in key quantitative data indicators to detect periods in which we could expect substantive managerial interventions in water resource management. We employ the change point model (CPM) framework to locate shifts in water use, climate-related indicators, lake and river characteristics, and agricultural trends across urban and agricultural counties in the lower Colorado River basin of Texas. Three distinctive groupings of change points appear. Increasing water use by urban counties and a shift in local climate conditions characterize the first period. Declines in agricultural counties’ water use and crop production define the second. Drops in lake levels, lower river discharge, and an extended drought mark the third. We interpret the results relative to documented managerial intervention events and show that managerial interventions occur during and after significant change points. We conclude that the CPM framework may be used to monitor the optimal timing of managerial interventions and their effects to avoid negative outcomes.

Item Pool Quality Control in Educational Testing: Change Point Model, Compound Risk, and Sequential Detection

In standardized educational testing, test items are reused in multiple test administrations. To ensure the validity of test scores, the psychometric properties of items should remain unchanged over time. In this article, we consider the sequential monitoring of test items, in particular, the detection of abrupt changes to their psychometric properties, where a change can be caused by, for example, leakage of the item or change of the corresponding curriculum. We propose a statistical framework for the detection of abrupt changes in individual items. This framework consists of (1) a multistream Bayesian change point model describing sequential changes in items, (2) a compound risk function quantifying the risk in sequential decisions, and (3) sequential decision rules that control the compound risk. Throughout the sequential decision process, the proposed decision rule balances the trade-off between two sources of errors, the false detection of prechange items, and the nondetection of postchange items. An item-specific monitoring statistic is proposed based on an item response theory model that eliminates the confounding from the examinee population which changes over time. Sequential decision rules and their theoretical properties are developed under two settings: the oracle setting where the Bayesian change point model is completely known and a more realistic setting where some parameters of the model are unknown. Simulation studies are conducted under settings that mimic real operational tests.

An Automatic Algorithm to Date the Reference Cycle of the Spanish Economy

This paper provides an accurate chronology of the Spanish reference business cycle adapting a multiple change-point model. In that approach, each combination of peaks and troughs dated in a set of economic indicators is assumed to be a realization of a mixture of bivariate Gaussian distributions, whose number of components is estimated from the data. The means of each of these components refer to the dates of the reference turning points. The transitions across the components of the mixture are governed by Markov chain that is restricted to force left-to-right transition dynamic. In the empirical application, seven recessions in the period from 1970.2 to 2020.2 are identified, which are in high concordance with the timing of the turning point dates established by the Spanish Business Cycle Dating Committee (SBCDC).

Bayesian Inference on Regression Model with an Unknown Change Point

In this work, we describe a Bayesian procedure for detection of change-point when we have an unknown change point in regression model. Bayesian approach with posterior inference for change points was provided to know the particular change point that is optimal while Gibbs sampler was used to estimate the parameters of the change point model. The simulation experiments show that all the posterior means are quite close to their true parameter values. The performance of this method is recommended for multiple change points.

Comparing the Bayesian Unknown Change-Point Model and Simulation Modeling Analysis to Analyze Single Case Experimental Designs

Recently, there has been an increased interest in developing statistical methodologies for analyzing single case experimental design (SCED) data to supplement visual analysis. Some of these are simulation-driven such as Bayesian methods because Bayesian methods can compensate for small sample sizes, which is a main challenge of SCEDs. Two simulation-driven approaches: Bayesian unknown change-point model (BUCP) and simulation modeling analysis (SMA) were compared in the present study for three real datasets that exhibit “clear” immediacy, “unclear” immediacy, and delayed effects. Although SMA estimates can be used to answer some aspects of functional relationship between the independent and the outcome variables, they cannot address immediacy or provide an effect size estimate that considers autocorrelation as required by the What Works Clearinghouse (WWC) Standards. BUCP overcomes these drawbacks of SMA. In final analysis, it is recommended that both visual and statistical analyses be conducted for a thorough analysis of SCEDs.

Shear strength testing of consolidated claystones: breakpoint detection of shear stress versus shear displacement curves, a statistical approach

The evaluation of shear stress versus shear displacement curves is in the main focus of geotechnical engineering. Such curves, depending on the rock assessed, consist of a quasi-linear section, followed by a “kick” representing the peak shear strength, and a residual part, mostly parallel to the abscissa. The aim of the present study is to facilitate the future automatic detection of these crucial characteristics to take a step towards replacing their visual/analogue determination via modern statistical tools. Breakpoint detection methods (Cross-Entropy, Change Point Model) were applied to curves obtained from laboratory shear tests describing the shearing along discontinuities of nine Mont Terri Opalinus Claystone samples. Smooth and moderately rough claystone surfaces were studied. Results indicated that the end of the rising section and the kick observed on the shear strength curves was effectively approximated with the Change Point Model framework. An additional practical advantage of applying statistical tools such as breakpoint detection to shear strength determination is that it ensures the comparability of the obtained results.