Bayesian Multiple Change-point Research Articles

State-Level History of Overdose Deaths Involving Stimulants in the United States, 1999‒2020.

Objectives. To examine the state-level history of US overdose deaths involving stimulants with and without opioids from 1999 to 2020. Methods. We used death certificate data from the National Center for Health Statistics to categorize deaths into 4 groups of interest: cocaine with and without opioids, and psychostimulants with and without opioids. We used a Bayesian multiple change point model to describe the timing and magnitude of changes in overdose death rates involving stimulants for each state and year. Results. There was little change in the death rates of cocaine without opioids. Death rates involving cocaine and opioids sharply increased around 2015, particularly in the Northeast and Mid-Atlantic. We also observed steady increases in deaths involving psychostimulants without opioids just before 2010, particularly in states in the West and South. Deaths involving psychostimulants with opioids increased around 2015 with largest increases concentrated in Appalachian states. Conclusions. There is significant geographic heterogeneity in the co-involvement of stimulants in the US overdose crisis. Results can inform public health efforts to inform state-level overdose efforts such as naloxone distribution. (Am J Public Health. 2023;113(9):991-999. https://doi.org/10.2105/AJPH.2023.307337).

Bayesian multiple changepoint detection with missing data and its application to the magnitude‐frequency distributions

AbstractThe detection of abrupt changes in an evolving pattern of time series in the presence of missing data still poses a challenge to real applications. We formulate the multiple changepoint problem into a latent Markov model on a countably infinite state space. For efficiency‐enhancing, we propose a partially collapsed Gibbs sampler for the inference of the joint posterior of the number of changepoints and their locations. Variants of Viterbi algorithms are suggested for obtaining the MAP estimates of random changepoints in the presence of missing data, which provides better performances in these varying‐dimensional problems. The method is generally applicable for multiple changepoint detection under a variety of missing data mechanism. The method is applied to a case study of the magnitude‐frequency distribution of the 2010 Darfield M7.1 earthquake sequence in New Zealand. We find out some unusual features of the seismic b‐value in the Darfield earthquake sequence. It is noted that two changepoints are detected and in contrast to the background seismic b‐value, relatively low b‐values in the early aftershock propagation period are identified. We suggest that this might be a forewarning of potentially devastatingly strong aftershocks. The advance in the method of b‐value changepoint detection will enhance our understanding of earthquake occurrence and potentially lead to improved risk forecasting.

Scalable Bayesian Multiple Changepoint Detection via Auxiliary Uniformisation

SummaryIn this paper, we perform a sparse filtering recursion for efficient changepoint detection for discrete‐time observations. We attach auxiliary event times to the chronologically ordered observations and formulate multiple changepoint problems of discrete‐time observations into continuous‐time observations. Ideally, both the computational and memory costs of the proposed auxiliary uniformisation forward‐filtering backward‐sampling algorithm can be quadratically scaled down to the number of changepoints instead of the number of observations, which would otherwise be prohibitive for a long sequence of observations. To avoid model bias, a time‐varying changepoint recurrence rate across different segments is assumed to characterise diverse scales of run lengths of the changepoints. We demonstrate the methods through simulation studies and real data analysis.

Bayesian Quickest Detection of Propagating Spatial Events

Rapid detection of spatial events that propagate across a sensor network is of wide interest in many modern applications. In particular, in communications, radar, IoT, environmental monitoring, and biosurveillance, we may observe propagating fields or particles. In this paper, we propose Bayesian sequential single and multiple change-point detection procedures for the rapid detection of such phenomena. Using a dynamic programming framework we derive the structure of the optimal single-event quickest detection procedure, which minimizes the average detection delay (ADD) subject to a false alarm probability upper bound. The multi-sensor system configuration is arbitrary and sensors may be mobile. In the rare event regime, the optimal procedure converges to a more practical threshold test on the posterior probability of the change point. A convenient recursive computation of this posterior probability is derived by using the propagation characteristics of the spatial event. The ADD of the posterior probability threshold test is analyzed in the asymptotic regime, and specific analysis is conducted in the setting of detecting random Gaussian signals affected by path loss. Then, we show how the proposed procedure is easy to extend for detecting multiple propagating spatial events in parallel in a multiple hypothesis testing setting. A method that provides strict false discovery rate (FDR) control is proposed. In the simulation section, it is demonstrated that exploiting the spatial properties of the event decreases the ADD compared to procedures that do not utilize this information, even under model mismatch.

Climate teleconnections, interannual variability, and evolution of the rainfall regime in a tropical Caribbean island: case study of Barbados

A limited number of studies have focused on the hydroclimate dynamics of tropical Caribbean islands. The present study aims to analyze the rainfall regime in Barbados. CHIRPS gridded dataset, at a resolution of 0.05°×0.05°, providing daily rainfall data from January 1981 until 2018 was used. The variables analyzed were the annual and seasonal maximum rainfall, the total annual and seasonal rainfall, and the number of rainy days per year and per season. Potential change points in rainfall time-series were detected with a Bayesian multiple change point detection procedure. Time series were then analyzed for detection of trends using the modified Mann-Kendall test. The true temporal slopes of the rainfall time series were obtained with the Theil-Sen’s statistic. The links between rainfall and various global climate oscillation indices were also investigated. Results indicate that no change points or significant trends were observed in the annual rainfall time series. However, it was found that some climate indices have a strong correlation with precipitation on the island, especially for the total rainfall and the number of rainy days. A stationary and non-stationary frequency analysis is carried out on the rainfall annual variables using climate oscillation indices as covariates, and uncertainties on quantile estimates are identified. It is shown that non-stationary models lead to a better fit to rainfall data. Empirical mode decomposition (EMD) is used for the long-term prediction of hydro-climatic time series. Rainfall annual time series were extended with this method for a period of 20 years. Results indicate that, within that period, annual maximum rainfall will increase by about 12 mm (or 0.6 mm/year), total annual rainfall will increase by about 200 mm (or 10 mm/year) and the number of rainy days per year will see a slight decrease by about 3 days (or 0.15 day/year).

Bayesian Multiple Changepoint Detection for Stochastic Models in Continuous Time

A multiple changepoint model in continuous time is formulated as a continuous-time hidden Markov model, defined on a countable infinite state space. The new formulation of the multiple changepoint model allows the model complexities, i.e. the number of changepoints, to accrue unboundedly upon the arrivals of new data. Inference on the number of changepoints and their locations is based on a collapsed Gibbs sampler. We suggest a new version of forward-filtering backward-sampling (FFBS) algorithm in continuous time for simulating the full trajectory of the latent Markov chain, i.e. the changepoints. The FFBS algorithm is based on a randomized time-discretization for the latent Markov chain through uniformization schemes, combined with a discrete-time version of FFBS algorithm. It is shown that, desirably, both the computational cost and the memory cost of the FFBS algorithm are only quadratic to the number of changepoints. The new formulation of the multiple changepoint models allows varying scale of run lengths of changepoints to be characterized. We demonstrate the methods through simulations and a real data example for earthquakes.

Remaining useful life prediction: A multiple product partition approach

This article introduces a Bayesian multiple change point model for a collection of degradation signals in order to predict remaining useful life of rotational bearings. The model is designed for longitudinal data, where each trajectory is a time series segmented into multiple states of degradation using a product partition structure. An efficient Markov chain Monte Carlo algorithm is designed to implement the model. The model is run on in situ data, where vibration measurements are taken to indicate bearing degradation. The results suggest that bearing degradation exhibit an auto-correlation structure that we incorporate into the product partition model and often experience more than one degradation phase.

Bayesian multiple changepoints detection for Markov jump processes

A Bayesian multiple changepoint model for the Markov jump process is formulated as a Markov double chain model in continuous time. Inference for this type of multiple changepoint model is based on a two-block Gibbs sampling scheme. We suggest a continuous-time version of forward-filtering backward-sampling (FFBS) algorithm for sampling the full trajectories of the latent Markov chain via inverse transformation. We also suggest a continuous-time version of Viterbi algorithm for this Markov double chain model, which is viable for obtaining the MAP estimation of the set of locations of changepoints. The model formulation and the continuous-time version of forward-filtering backward-sampling algorithm and Viterbi algorithm can be extended to simultaneously monitor the structural breaks of multiple Markov jump processes, which may have either variable transition rate matrix or identical transition rate matrix. We then perform a numerical study to demonstrate the methods. In numerical examples, we compare the performance of the FFBS algorithm via inverse transformation with the FFBS algorithm via uniformization. The two algorithms performs well in different cases. These models are potentially viable for modelling the credit rating dynamics in credit risk management.

A Bayesian multiple changepoint model for marked poisson processes with applications to deep earthquakes

A multiple changepoint model for marked Poisson process is formulated as a continuous time hidden Markov model, which is an extension of Chib’s multiple changepoint models (J Econ 86:221–241, 1998). The inference on the locations of changepoints and other model parameters is based on a two-block Gibbs sampling scheme. We suggest a continuous time version of forward-filtering backward-sampling algorithm for simulating the full trajectories of the latent Markov chain without utilizing the uniformization method. To retrieve the optimal posterior path of the latent Markov chain, i.e. the maximum a posteriori estimation of changepoint locations, a continuous-time version of Viterbi algorithm (CT-Viterbi) is proposed. The set of changepoint locations is obtainable either from the CT-Viterbi algorithm or the posterior samples of the latent Markov chain. The number of changepoints is determined according to a modified BIC criterion tailored particularly for the multiple changepoint problems of a marked Poisson process. We then perform a simulation study to demonstrate the methods. The methods are applied to investigate the temporal variabilities of seismicity rates and the magnitude-frequency distributions of medium size deep earthquakes in New Zealand.

Bayesian multiple change-point estimation for exponential distribution with truncated and censored data

ABSTRACTThis paper considers the multiple change-point estimation for exponential distribution with truncated and censored data by Gibbs sampling. After all the missing data of interest is filled in by some sampling methods such as rejection sampling method, the complete-data likelihood function is obtained. The full conditional distributions of all parameters are discussed. The means of Gibbs samples are taken as Bayesian estimations of the parameters. The implementation steps of Gibbs sampling are introduced in detail. Finally random simulation test is developed, and the results show that Bayesian estimations are fairly accurate.

Dirichlet Process Hidden Markov Multiple Change-point Model

This paper proposes a new Bayesian multiple change-point model which is based on the hidden Markov approach. The Dirichlet process hidden Markov model does not require the specification of the number of change-points a priori. Hence our model is robust to model specification in contrast to the fully parametric Bayesian model. We propose a general Markov chain Monte Carlo algorithm which only needs to sample the states around change-points. Simulations for a normal mean-shift model with known and unknown variance demonstrate advantages of our approach. Two applications, namely the coal-mining disaster data and the real United States Gross Domestic Product growth, are provided. We detect a single change-point for both the disaster data and US GDP growth. All the change-point locations and posterior inferences of the two applications are in line with existing methods.

Does flower phenology mirror the slowdown of global warming?

Although recent global warming trends in air temperature are not as pronounced as those observed only one decade ago, global mean temperature is still at a very high level. Does plant phenology – which is believed to be a suitable indicator of climate change – respond in a similar way, that is, does it still mirror recent temperature variations? We explored in detail long-term flowering onset dates of snowdrop, cherry, and lime tree and relevant spring temperatures at three sites in Germany (1901–2012) using the Bayesian multiple change-point approach. We investigated whether mean spring temperature changes were amplified or slowed down in the past decade and how plant phenology responded to the most recent temperature changes. Incorporating records with different end points (i.e., 2002 and 2012), we compared differences in trends and inferred possible differences caused by extrapolating phenological and meteorological data. The new multiple-change point approach is characterized by an enhanced structure and greater flexibility compared to the one change point model. However, the highest model probabilities for phenological (meteorological) records were still obtained for the one change point (linear) model. Marked warming trends in the recent decade were only revealed for mean temperatures of March to May, here better described with one or two change point models. In the majority of cases analyzed, changes in temperatures were well mirrored by phenological changes. However, temperatures in March to May were linked to less strongly advancing onset dates for lime tree flowering during the period 1901-2012, pointing to the likely influence of photoperiodic constraints or unfulfilled chilling requirements. Due to the slowdown of temperature increase, analyses conducted on records ending in 2002 demonstrated distinct differences when compared with records ending in 2012. Extrapolation of trends could therefore (along with the choice of the statistical method) lead to distinctly different results and most recent data should be integrated in order not to over- or underestimate future phenological changes.

Patterns of late spring frost leaf damage and recovery in a European beech (Fagus sylvatica L.) stand in south-eastern Germany based on repeated digital photographs.

Damage by late spring frost is a risk deciduous trees have to cope with in order to optimize the length of their growing season. The timing of spring phenological development plays a crucial role, not only at the species level, but also at the population and individual level, since fresh new leaves are especially vulnerable. For the pronounced late spring frost in May 2011 in Germany, we studied the individual leaf development of 35 deciduous trees (mainly European beech Fagus sylvatica L.) at a mountainous forest site in the Bayerischer Wald National Park using repeated digital photographs. Analyses of the time series of greenness by a novel Bayesian multiple change point approach mostly revealed five change points which almost perfectly matched the expected break points in leaf development: (i) start of the first greening between day of the year (DOY) 108–119 (mean 113), (ii) end of greening, and (iii) visible frost damage after the frost on the night of May 3rd/4th (DOY 123/124), (iv) re-sprouting 19–38 days after the frost, and (v) full maturity around DOY 178 (166–184) when all beech crowns had fully recovered. Since frost damage was nearly 100%, individual susceptibility did not depend on the timing of first spring leaf unfolding. However, we could identify significant patterns in fitness linked to an earlier start of leaf unfolding. Those individuals that had an earlier start of greening during the first flushing period had a shorter period of recovery and started the second greening earlier. Thus, phenological timing triggered the speed of recovery from such an extreme event. The maximum greenness achieved, however, did not vary with leaf unfolding dates. Two mountain ashes (Sorbus aucuparia L.) were not affected by the low temperatures of -5°C. Time series analysis of webcam pictures can thus improve process-based knowledge and provide valuable insights into the link between phenological variation, late spring frost damage, and recovery within one stand.

Evolution of the rainfall regime in the United Arab Emirates

Arid and semiarid climates occupy more than 1/4 of the land surface of our planet, and are characterized by a strongly intermittent hydrologic regime, posing a major threat to the development of these regions. Despite this fact, a limited number of studies have focused on the climatic dynamics of precipitation in desert environments, assuming the rainfall input – and their temporal trends – as marginal compared with the evaporative component. Rainfall series at four meteorological stations in the United Arab Emirates (UAE) were analyzed for assessment of trends and detection of change points. The considered variables were total annual, seasonal and monthly rainfall; annual, seasonal and monthly maximum rainfall; and the number of rainy days per year, season and month. For the assessment of the significance of trends, the modified Mann–Kendall test and Theil-Sen’s test were applied. Results show that most annual series present decreasing trends, although not statistically significant at the 5% level. The analysis of monthly time series reveals strong decreasing trends mainly occurring in February and March. Many trends for these months are statistically significant at the 10% level and some trends are significant at the 5% level. These two months account for most of the total annual rainfall in the UAE. To investigate the presence of sudden changes in rainfall time-series, the cumulative sum method and a Bayesian multiple change point detection procedure were applied to annual rainfall series. Results indicate that a change point happened around 1999 at all stations. Analyses were performed to evaluate the evolution of characteristics before and after 1999. Student’s t-test and Levene’s test were applied to determine if a change in the mean and/or in the variance occurred at the change point. Results show that a decreasing shift in the mean has occurred in the total annual rainfall and the number of rainy days at all four stations, and that the variance has decreased for the total annual rainfall at two stations. Frequency analysis was also performed on data before and after the change point. Results show that rainfall quantile values are significantly lower after 1999. The change point around the year 1999 is linked to various global climate indices. It is observed that the change of phase of the Southern Oscillation Index (SOI) has strong impact over the UAE precipitation. A brief discussion is presented on dynamical basis, the teleconnections connecting the SOI and the change in precipitation regime in the UAE around the year 1999.

Recent trends in selected extreme precipitation indices in Senegal – A changepoint approach

Summary Precipitation regime is the number one factor in food productivity in the Sahel region. Recurrent droughts have caused several food crises in the region during the three last decades. The situation may not improve as a recent special IPCC report states that West Africa will likely experience longer and more intense droughts ( IPCC, 2012 ) in the near future. As drought adversely affects food security, Sahelian decision-makers need to understand past and current trends in Sahelian precipitation to have some insight in what can be expected for the next five years. In this paper, time series of selected precipitation indices were calculated using 1950–2007 daily precipitation data from 31 stations across Senegal and analyzed for changes in temporal trends using a Bayesian multiple change point detection procedure. The selected indices are the mean (M) and the standard deviation (SD) of precipitation, the frequency of wet days (precipitation using threshold of ⩾ 1 mm, Prcpl), the maximum number of consecutive dry days (precipitation

단일 양자점으로부터 발생한 발광세기 변화에 대한 베이지안 다중 변화점 추정

단일 분자에서 발생한 발광의 세기 변화를 분석하는 문제는 단분자 분광학에서 반드시 필요하다. 본 연구에서는 카드뮴셀레나이드/황화아연의 중심-껍질 구조를 갖는 양자점에 대한 단분자 분광학 데이터에 대해 Poisson count data로서 베이지안 접근으로 모수에 대한 공액 감마분포와 변화점 개수에 대한 절단포아송 분포로 사전분포를 주고 다중변화점을 추정하였다. In the field of single-molecule spectroscopy, it is essential to analyze luminescence Intensity changes that result from a single molecule. With the CdSe/ZnS core-shell structured quantum dot photon emission data Bayesian multiple change-point estimation is done with the gamma prior for Poisson parameters and truncated Poisson distribution for the number of change-points.

Analysis of changes in the Great Lakes hydro-climatic variables

A study of changes in hydro-climatology of the Great Lakes was performed incorporating the nonparametric Mann–Kendall trend detection test and a recently developed Bayesian multiple change point detection model. The Component Net Basin Supply (C-NBS) and its components (runoff, precipitation, evaporation) as well as water levels of Great Lakes were analyzed for gradual (i.e. trend type) and abrupt (i.e. shift type) nonstationary behaviors at seasonal and annual scales. It was found that the C-NBS experienced significant upward trends only in the lower Great Lakes (Erie, Ontario) during the summer portion of the year. At an annual scale upward trends were observed only in Lake Ontario. Change point analysis suggested an upward shift in Great Lakes C-NBS in the late 1960s and early 1970s. A combination of gradual and abrupt change analysis of Great Lakes water levels indicated a common upward shift along with a change in trend direction around the early 1970s. It was also found that precipitation and runoff are on a plateau and in some cases on a decreasing course following an increasing trend in the early twentieth century. Results obtained from this study show that the hydro-climatology of Great Lakes is characterized by nonstationary behavior. Changes in this behavior have caused the Great Lakes water levels to decrease during the last few decades. This study provides valuable insights into the nature of the nonstationary behavior of hydro-climatic variables of Great Lakes and contributes useful information to the future water management planning.

Rbrothers: R Package for Bayesian Multiple Change-Point Recombination Detection

Phylogenetic recombination detection is a fundamental task in bioinformatics and evolutionary biology. Most of the computational tools developed to attack this important problem are not integrated into the growing suite of R packages for statistical analysis of molecular sequences. Here, we present an R package, rbrothers, that makes a Bayesian multiple change-point model, one of the most sophisticated model-based phylogenetic recombination tools, available to R users. Moreover, we equip the Bayesian change-point model with a set of pre- and post- processing routines that will broaden the application domain of this recombination detection framework. Specifically, we implement an algorithm that forms the set of input trees required by multiple change-point models. We also provide functionality for checking Markov chain Monte Carlo convergence and creating estimation result summaries and graphics. Using rbrothers, we perform a comparative analysis of two Salmonella enterica genes, fimA and fimH, that encode major and adhesive subunits of the type 1 fimbriae, respectively. We believe that rbrothers, available at R-Forge: http://evolmod.r-forge.r-project.org/, will allow researchers to incorporate recombination detection into phylogenetic workflows already implemented in R.

Bayesian Multiple Change-Point Estimation of Multivariate Mean Vectors for Small Data

A Bayesian multiple change-point model for small data is proposed for multivariate means and is an extension of the univariate case of Cheon and Yu (2012). The proposed model requires data from a multivariate noncentral <TEX>$t$</TEX>-distribution and conjugate priors for the distributional parameters. We apply the Metropolis-Hastings-within-Gibbs Sampling algorithm to the proposed model to detecte multiple change-points. The performance of our proposed algorithm has been investigated on simulated and real dataset, Hanwoo fat content bivariate data.

Detecting plant seasonality from webcams using Bayesian multiple change point analysis

Phenological observations have a long tradition. By contrast, digital webcam-based phenological research has only developed in recent years, prompted by the development of cheaper user-friendly digital camera systems and by higher staff costs. Webcam photography provides spectral information in red, green and blue (RGB) wavelengths which mirror the seasonal colour changes in trees during bud burst, leaf unfolding, senescence and leaf fall.Recent publications have mainly used two types of image data analysis to define onset dates of certain phenological stages and to compare species and growing seasons. These methods work well, but require high quality of the webcam images. However, changing light and weather conditions complicate data analysis particularly at increasing camera-to-subject distances. We investigated a series of images providing colour information on different tree species, e.g. Fagus sylvatica, Populus tremula, as well as of trees at different altitudes (700–1200m) in the Bavarian Forest National Park, Germany. Webcam images were analysed by the two previously published methods and compared with results derived from a newly developed Bayesian multiple change point analysis. In particular, transition dates of leaf development were identified in the green, as well as the red, colour channel.The Bayesian analysis described phenological transition dates in spring and autumn and specified the uncertainties of the model fit. By contrast, previously employed methods have shortcomings associated with unrealistic asymptotic assumptions in logistic model fits or inability to cope with noise in data series.The change point analysis at different elevations showed how the Bayesian approach coped with increasingly degraded image quality. A delay in green-up of about 2.5 days per 100m of altitude was estimated for Fagus sylvatica in the study area. Autumn phenology at different altitudes did not show clear patterns.The Bayesian model approach allows not only the calculation of phenological change points during the year but also estimates the probability of those changes occurring on a particular day. This method appears to estimate reliably phenological events in the growing season, especially when handling low quality webcam data, either from poor weather conditions or when the subject is at a considerable distance from the camera.