Genetic algorithm with a Bayesian approach for the detection of multiple points of change of time series of counting exceedances of specific thresholds

TL;DR

This paper introduces a genetic algorithm combined with a Bayesian approach to automatically detect multiple change-points in time series of exceedances, improving segmentation accuracy for modeling threshold overshoots.

Contribution

It presents a novel method integrating genetic algorithms and Bayesian inference to identify multiple change-points in count-based time series, enhancing model fit and diagnostic efficiency.

Findings

Effective detection of multiple change-points in threshold exceedance data.

Reduction in computational time by focusing on promising candidate configurations.

Improved model fitting using the Minimum Description Length as an objective.

Abstract

Although the applications of Non-Homogeneous Poisson Processes to model and study the threshold overshoots of interest in different time series of measurements have proven to provide good results, they needed to be complemented with an efficient and automatic diagnostic technique to establish the location of the change-points, which, when taken into account, make the estimated model fit poorly in regards of the information contained in the real model. For this reason, we propose a new method to solve the segmentation uncertainty of the time series of measurements, where the emission distribution of exceedances of a specific threshold is the focus of investigation. One of the great contributions of the present algorithm is that all the days that overflowed are candidates to be a change-point, so all the possible configurations of overflow days are the possible chromosomes, which will unite to have offspring. Under the heuristics of a genetic algorithm, the solution to the problem of finding such change points will be guaranteed to be non-local and the best possible one, reducing wasted machine time evaluating the least likely chromosomes to be a solution to the problem. The analytical evaluation technique will be by means of the Minimum Description Length (\textit{MDL}) as the objective function, which is the joint posterior distribution function of the parameters of each regime and the change points that determines them and which account as well for the influence of the presence of said times.