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In this paper, the multiple change-point problem in the scale parameter of a sequence of independent gamma distributed observations is discussed. A reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is developed to compute the posterior probabilities of the number and positions of the multiple change-points. Four types of jumps are designed, and the acceptance probability of each type is given. The simulation studies show that the RJMCMC-based method is efficient in the detection of multiple change-points in the scale parameter in gamma distributed sequence, and performs better than a self-normalization based method. In addition, a real data example about successive rises and falls of Shanghai stock exchange composite index yield is used to illustrate the proposed methodology.

Data with a multimodal pattern can be analyzed using a mixture model. In a mixture model, the most important step is the determination of the number of mixture components, because finding the correct number of mixture components will reduce the error of the resulting model. In a Bayesian analysis, one method that can be used to determine the number of mixture components is the reversible jump Markov chain Monte Carlo (RJMCMC). The RJMCMC is used for distributions that have location and scale parameters or location-scale distribution, such as the Gaussian distribution family. In this research, we added an important step before beginning to use the RJMCMC method, namely the modification of the analyzed distribution into location-scale distribution. We called this the non-Gaussian RJMCMC (NG-RJMCMC) algorithm. The following steps are the same as for the RJMCMC. In this study, we applied it to the Weibull distribution. This will help many researchers in the field of survival analysis since most of the survival time distribution is Weibull. We transformed the Weibull distribution into a location-scale distribution, which is the extreme value (EV) type 1 (Gumbel-type for minima) distribution. Thus, for the mixture analysis, we call this EV-I mixture distribution. Based on the simulation results, we can conclude that the accuracy level is at minimum 95%. We also applied the EV-I mixture distribution and compared it with the Gaussian mixture distribution for enzyme, acidity, and galaxy datasets. Based on the Kullback–Leibler divergence (KLD) and visual observation, the EV-I mixture distribution has higher coverage than the Gaussian mixture distribution. We also applied it to our dengue hemorrhagic fever (DHF) data from eastern Surabaya, East Java, Indonesia. The estimation results show that the number of mixture components in the data is four, we also obtained the estimation results of the other parameters and labels for each observation. Based on the Kullback–Leibler divergence (KLD) and visual observation, for our data, the EV-I mixture distribution offers better coverage than the Gaussian mixture distribution.

We consider the modeling of data generated by a latent continuous-time Markov jump process with a state space of finite but unknown dimensions. Typically in such models, the number of states has to be pre-specified, and Bayesian inference for a fixed number of states has not been studied until recently. In addition, although approaches to address the problem for discrete-time models have been developed, no method has been successfully implemented for the continuous-time case. We focus on reversible jump Markov chain Monte Carlo which allows the trans-dimensional move among different numbers of states in order to perform Bayesian inference for the unknown number of states. Specifically, we propose an efficient split-combine move which can facilitate the exploration of the parameter space, and demonstrate that it can be implemented effectively at scale. Subsequently, we extend this algorithm to the context of model-based clustering, allowing numbers of states and clusters both determined during the analysis. The model formulation, inference methodology, and associated algorithm are illustrated by simulation studies. Finally, we apply this method to real data from a Canadian healthcare system in Quebec. Supplementary Information The online version supplementary material available at 10.1007/s11222-021-10032-8.

In Bayesian semi-parametric analyses of time-to-event data, non-parametric process priors are adopted for the baseline hazard function or the cumulative baseline hazard function for a given finite partition of the time axis. However, it would be controversial to suggest a general guideline to construct an optimal time partition. While a great deal of research has been done to relax the assumption of the fixed split times for other non-parametric processes, to our knowledge, no methods have been developed for a gamma process prior, which is one of the most widely used in Bayesian survival analysis. In this paper, we propose a new Bayesian framework for proportional hazards models where the cumulative baseline hazard function is modelled a priori by a gamma process. A key feature of the proposed framework is that the number and position of interval cutpoints are treated as random and estimated based on their posterior distributions.

Summary Conditional density estimation seeks to model the distribution of a response variable conditional on covariates. We propose a Bayesian partition model using logistic Gaussian processes to perform conditional density estimation. The partition takes the form of a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The methodology models data in which the density changes sharply throughout the covariate space, and can be used to determine where important changes in the density occur. The Markov chain Monte Carlo algorithm involves a Laplace approximation on the latent variables of the logistic Gaussian process model which marginalizes the parameters in each partition element, allowing an efficient search of the approximate posterior distribution of the tessellation. The method is consistent when the density is piecewise constant in the covariate space or when the density is Lipschitz continuous with respect to the covariates. In simulation and application to wind turbine data, the model successfully estimates the partition structure and conditional distribution.

Malware is computer software which has either been designed or modified with malicious intent. Hundreds of thousands of new malware threats appear on the internet each day. This is made possible through reuse of known exploits in computer systems which have not been fully eradicated; existing pieces of malware can be trivially modified and combined to create new malware which is unknown to anti-virus programs. Finding new software with similarities to known malware is therefore an important goal in cyber-security. A dynamic instruction trace of a piece of software is the sequence of machine language instructions it generates when executed. Statistical analysis of a dynamic instruction trace can help reverse engineers infer the purpose and origin of the software that generated it. Instruction traces have been successfully modeled as simple Markov chains, but empirically there are change points in the structure of the traces, with recurring regimes of transition patterns. Here, reversible jump MCMC for change point detection is extended to incorporate regime-switching, allowing regimes to be inferred from malware instruction traces. A similarity measure for malware programs based on regime matching is then used to infer the originating families, leading to compelling performance results.

This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral components may remain unchanged across segments, allowing components to evolve differently over time. Local spectra within segments are fit through Whittle likelihood based penalized spline models of modified Cholesky components, which provide flexible nonparametric estimates that preserve positive definite structures of spectral matrices. The approach is formulated in a Bayesian framework, in which the number and location of partitions are random, and relies on reversible jump Markov chain and Hamiltonian Monte Carlo methods that can adapt to the unknown number of segments and parameters. By averaging over the distribution of partitions, the approach can approximate both abrupt and slow-varying changes in spectral matrices. Empirical performance is evaluated in simulation studies and illustrated through analyses of electroencephalography during sleep and of the El Niño-Southern Oscillation.

Cox regression is one of the most commonly used methods in the analysis of interval-censored failure time data. In many practical studies, the covariate effects on the failure time may not be constant over time. Time-varying coefficients are therefore of great interest due to their flexibility in capturing the temporal covariate effects. To analyze spatially correlated interval-censored time-to-event data with time-varying covariate effects, a Bayesian approach with dynamic Cox regression model is proposed. The coefficient is estimated as a piecewise constant function and the number of jump points estimated from the data. A conditional autoregressive distribution is employed to model the spatial dependency. The posterior summaries are obtained via an efficient reversible jump Markov chain Monte Carlo algorithm. The properties of our method are illustrated by simulation studies as well as an application to smoking cessation data in southeast Minnesota.

Bayesian inference on the covariance matrix is usually performed after placing an inverse-Wishart or a multivariate Jeffreys as a prior density, but both of them, for different reasons, present some drawbacks. As an alternative, the covariance matrix can be modelled by separating out the standard deviations and the correlations. This separation strategy takes advantage of the fact that usually it is more straightforward and flexible to set priors on the standard deviations and the correlations rather than on the covariance matrix. On the other hand, the priors must preserve the positive definiteness of the correlation matrix. This can be obtained by considering the Cholesky decomposition of the correlation matrix, whose entries are reparameterized using trigonometric functions. The efficiency of the trigonometric separation strategy (TSS) is shown through an application to hidden Markov models (HMMs), with conditional distributions multivariate normal. In the case of an unknown number of hidden states, estimation is conducted using a reversible jump Markov chain Monte Carlo algorithm based on the split-and-combine and birth-and-death moves whose design is straightforward because of the use of the TSS. Finally, an example in remote sensing is described, where a HMM containing the TSS is used for the segmentation of a multi-colour satellite image.

Partial linear single-index model (PLSIM) has both the flexibility of nonparametric treatment and interpretability of linear term, yet existing literatures about it mainly focused on mean regression, and quantile regression analysis is scarce. Based on free knot spline approximation, we apply asymmetric Laplace distribution to implement Bayesian quantile regression, and perform variable selection in linear term and index vector via binary indicators. Our approach is exempt from regularity conditions in frequentist method, and could execute variable selection and quantile regression under mutual posterior correction, which is also the first work to implement them jointly for PLSIM in fully Bayesian framework. The numerical simulation manifests the superiority of our approach to previous methods, which embodied in better efficiency of variable selection, index vector estimates and link function approximation with different error distributions. For illustration of its application, we build a power co...

Volterra systems have had significant success in modelling nonlinear systems in various real-world applications. However, it is generally assumed that the nonlinearity degree of the system is known beforehand. In this paper, we contribute to the literature on Volterra system identification (VSI) with a numerical Bayesian approach which identifies model coefficients and the nonlinearity degree concurrently. Although this numerical Bayesian method, namely reversible jump Markov chain Monte Carlo (RJMCMC) algorithm has been used with success in various model selection problems, our use is in a novel context in the sense that both memory size and nonlinearity degree are estimated. The aforementioned study ensures an anomalous approach to RJMCMC and provides a new understanding on its flexible use which enables trans-structural transitions between different classes of models in addition to transdimensional transitions for which it is classically used. We study the performance of the method on synthetically generated data including OFDM communications over a nonlinear channel.

A Bayesian framework for finite mixture models to deal with model selection and the selection of the number of mixture components simultaneously is presented. For that purpose, a feasible reversible jump Markov Chain Monte Carlo algorithm is proposed to model each component as a sparse regression model. This approach is made robust to outliers by using a prior that induces heavy tails and works well under multicollinearity and with high-dimensional data. Finally, the framework is applied to cross-sectional data investigating early warning indicators. The results reveal two distinct country groups for which estimated effects of vulnerability indicators vary considerably.

For the image segmentation method based on Gaussian Mixture Model (GMM), there are some problems: 1) The number of component was usually a fixed number, i.e., fixed class and 2) GMM is sensitive to image noise. This paper proposed a RS image segmentation method that combining GMM with reversible jump Markov Chain Monte Carlo (RJMCMC). In proposed algorithm, GMM was designed to model the distribution of pixel intensity in RS image. Assume that the number of component was a random variable. Respectively build the prior distribution of each parameter. In order to improve noise resistance, used Gibbs function to model the prior distribution of GMM weight coefficient. According to Bayes' theorem, build posterior distribution. RJMCMC was used to simulate the posterior distribution and estimate its parameters. Finally, an optimal segmentation is obtained on RS image. Experimental results show that the proposed algorithm can converge to the optimal number of class and get an ideal segmentation results.

In this article, to reduce computational load in performing Bayesian variable selection, we used a variant of reversible jump Markov chain Monte Carlo methods, and the Holmes and Held (HH) algorith...

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely ignored due to a lack of methods that can assess the changing nature of the relationship through time. This article introduces a method for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates, which we refer to as conditional adaptive Bayesian spectrum analysis (CABS). The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. CABS is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The proposed methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse.

Prestack or angle stack gathers are inverted to estimate pseudologs at every surface location for building reservoir models. Recently, several methods have been proposed to increase the resolution of the inverted models. All of these methods, however, require that the total number of model parameters be fixed a priori. We have investigated an alternate approach in which we allow the data themselves to choose model parameterization. In other words, in addition to the layer properties, the number of layers is also treated as a variable in our formulation. Such transdimensional inverse problems are generally solved by using the reversible jump Markov chain Monte Carlo (RJMCMC) approach, which is a tool for model exploration and uncertainty quantification. This method, however, has very low acceptance. We have developed a two-step method by combining RJMCMC with a fixed-dimensional MCMC called Hamiltonian Monte Carlo, which makes use of gradient information to take large steps. Acceptance probability for such a transition is also derived. We call this new method “reversible jump Hamiltonian Monte Carlo (RJHMC).” We have applied this technique to poststack acoustic impedance inversion and to prestack (angle stack) AVA inversion for estimating acoustic and shear impedance profiles. We have determined that the marginal posteriors estimated by RJMCMC and RJHMC are in good agreement. Our results demonstrate that RJHMC converges faster than RJMCMC, and it therefore can be a practical tool for inverting seismic data when the gradient can be computed efficiently.

Mathematical models are frequently used to explore physical systems, but can be computationally expensive to evaluate. In such settings, an emulator is used as a surrogate. In this work, we propose a basis-function approach for computer model emulation. To combine field observations with a collection of runs from the numerical model, we use the proposed emulator within the Kennedy-O’Hagan framework of model calibration. A novel feature of the approach is the use of an over-specified set of basis functions where number of bases used and their inclusion probabilities are treated as unknown quantities. The new approach is found to have smaller predictive uncertainty and computational efficiency than the standard Gaussian process approach to emulation and calibration. Along with several simulation examples focusing on different model characteristics, we also use the method to analyze a dataset on laboratory experiments related to astrophysics.

Both Markov random field (MRF) and marked point process (MPP) models have some limitations for image analysis. While the MRF is useful for imposing local constraints, global constraints are not easily modeled. On the contrary, it is convenient to model global constraints, such as geometric shape and object interactions, within the MPP framework, but such an object-based MPP model has limited capability for imposing local constraints such as pixel-wise interactions. In this paper, we propose a combined model that incorporates both local and global constraints within a single energy function. Optimization using our model is performed using simulation schemes, including reversible jump Markov chain Monte Carlo and multiple birth and death algorithms. We also present results using iterated conditional modes for optimization. Although our model should be useful for any application that requires both global information and precise boundary localization, we consider the analysis of microscope images of materials in this paper. We present experimental results to compare our model to the MPP model for object detection and the MRF model for segmentation.

We present a reversible jump Bayesian piecewise log-linear hazard model that extends the Bayesian piecewise exponential hazard to a continuous function of piecewise linear log hazards. A simulation study encompassing several different hazard shapes, accrual rates, censoring proportion, and sample sizes showed that the Bayesian piecewise linear log-hazard model estimated the true mean survival time and survival distributions better than the piecewsie exponential hazard. Survival data from Wake Forest Baptist Medical Center is analyzed by both methods and the posterior results are compared.

In this article, we propose a novel and general dimension-hopping MCMC methodology that can update all the parameters as well as the number of parameters simultaneously using simple deterministic transformations of some low-dimensional (often one-dimensional) random variable. This methodology, which has been inspired by the recent Transformation based MCMC (TMCMC) for updating all the parameters simultaneously in general fixed-dimensional set-ups using low-dimensional random variables, facilitates great speed in terms of computation time and provides high acceptance rates, thanks to the low-dimensional random variables which effectively reduce the dimension dramatically. Quite importantly, our transformation based approach provides a natural way to automate the move-types in the variable dimensional problems. We refer to this methodology as Transdimensional Transformation based Markov Chain Monte Carlo (TTMCMC). We develop the theory of TTMCMC, illustrating it with gamma and normal mixtures with unknown number of components, for both simulated and real data sets. Comparisons with RJMCMC demonstrates far superior performance of TTMCMC in terms of mixing, acceptance rate, computational speed and automation. Furthermore, we demonstrate good performance of TTMCMC in multivariate normal mixtures, even for dimension as large as 20. To our knowledge, there exists no application of RJMCMC for such high-dimensional mixtures. Further, we propose a novel methodology to summarize the posterior, providing a way to obtain the mode of the posterior distribution of the densities and the associated highest posterior density credible regions. Based on our method we also propose a criterion to assess convergence of variable-dimensional algorithms. These methods of summarization and convergence assessment are applicable to general problems, not just to mixtures., A very significantly updated version, demonstrating superiority of TTMCMC over RJMCMC with many more simulations with respect to gamma and normal mixtures, for both simulated and real datasets, including even 20-dimensional normal mixtures. We are not aware of any successful RJMCMC applications in dimensions this large

Regular vine copulas are a flexible class of dependence models, but Bayesian methodology for model selection and inference is not yet fully developed. We propose sparsity-inducing but otherwise non-informative priors, and present novel proposals to enable reversible jump Markov chain Monte Carlo posterior simulation for Bayesian model selection and inference. Our method is the first to jointly estimate the posterior distribution of all trees of a regular vine copula. This represents a substantial improvement over existing frequentist and Bayesian strategies, which can only select one tree at a time and are known to induce bias. A simulation study demonstrates the feasibility of our strategy and shows that it combines superior selection and reduced computation time compared to Bayesian tree-by-tree selection. In a real data example, we forecast the daily expected tail loss of a portfolio of nine exchange-traded funds using a fully Bayesian multivariate dynamic model built around Bayesian regular vine copulas to illustrate our model’s viability for financial analysis and risk estimation.

Upscaling log measurements acquired at high frequencies and correlating them with corresponding low-frequency values from surface seismic and vertical seismic profile data is a challenging task. We have applied a sampling technique called the reversible jump Markov chain Monte Carlo (RJMCMC) method to this problem. A key property of our approach is that it treats the number of unknowns itself as a parameter to be determined. Specifically, we have considered upscaling as an inverse problem in which we considered the number of coarse layers, layer boundary depths, and material properties as the unknowns. The method applies Bayesian inversion, with RJMCMC sampling and uses simulated annealing to guide the optimization. At each iteration, the algorithm will randomly move a boundary in the current model, add a new boundary, or delete an existing boundary. In each case, a random perturbation is applied to Backus-average values. We have developed examples showing that the mismatch between seismograms computed from the upscaled model and log velocities improves by 89% compared to the case in which the algorithm is allowed to move boundaries only. The layer boundary distributions after running the RJMCMC algorithm can represent sharp and gradual changes in lithology. The maximum deviation of upscaled velocities from Backus-average values is less than 10% with most of the values close to zero.

A pseudo-marginal Markov chain Monte Carlo (PMCMC) method is proposed for nonnegative matrix factorization (NMF). The sampler jointly simulates the joint posterior distribution for the nonnegative matrices and the matrix dimensions which indicate the number of the nonnegative components in the NMF model. We show that the PMCMC sampler is a generalization of a version of the reversible jump Markov chain Monte Carlo. An illustrative synthetic data was used to demonstrate the ability of the proposed PMCMC sampler in inferring the nonnegative matrices and as well as the matrix dimensions. The proposed sampler was also applied to a nuclear magnetic resonance spectroscopy data to infer the number of nonnegative components.

The creeping characteristics of drought make it possible to mitigate drought’s effects with accurate forecasting models. Drought forecasts are inevitably plagued by uncertainties, making it necessary to derive forecasts in a probabilistic framework. In this study, we proposed a new probabilistic scheme to forecast droughts that used a discrete-time finite state-space hidden Markov model (HMM) aggregated with the Representative Concentration Pathway 8.5 (RCP) precipitation projection (HMM-RCP). The standardized precipitation index (SPI) with a 3-month time scale was employed to represent the drought status over the selected stations in South Korea. The new scheme used a reversible jump Markov chain Monte Carlo algorithm for inference on the model parameters and performed an RCP precipitation projection transformed SPI (RCP-SPI) weight-corrected post-processing for the HMM-based drought forecasting to perform a probabilistic forecast of SPI at the 3-month time scale that considered uncertainties. The point forecasts which were derived as the HMM-RCP forecast mean values, as measured by forecasting skill scores, were much more accurate than those from conventional models and a climatology reference model at various lead times. We also used probabilistic forecast verification and found that the HMM-RCP provided a probabilistic forecast with satisfactory evaluation for different drought categories, even at long lead times. In a drought event analysis, the HMM-RCP accurately predicted about 71.19 % of drought events during the validation period and forecasted the mean duration with an error of less than 1.8 months and a mean severity error of

In the expectation–maximization (EM) algorithm for maximum likelihood estimation from incomplete data, Markov chain Monte Carlo (MCMC) methods have been used in change-point inference for a long time when the expectation step is intractable. However, the conventional MCMC algorithms tend to get trapped in local mode in simulating from the posterior distribution of change points. To overcome this problem, in this paper we propose a stochastic approximation Monte Carlo version of EM (SAMCEM), which is a combination of adaptive Markov chain Monte Carlo and EM utilizing a maximum likelihood method. SAMCEM is compared with the stochastic approximation version of EM and reversible jump Markov chain Monte Carlo version of EM on simulated and real datasets. The numerical results indicate that SAMCEM can outperform among the three methods by producing much more accurate parameter estimates and the ability to achieve change-point positions and estimates simultaneously.

This paper presents a novel segmentation method for automatically determining the number of classes in Synthetic Aperture Radar (SAR) images by combining Voronoi tessellation and Reversible Jump Markov Chain Monte Carlo (RJMCMC) strategy. Instead of giving the number of classes a priori, it is considered as a random variable and subject to a Poisson distribution. Based on Voronoi tessellation, the image is divided into homogeneous polygons. By Bayesian paradigm, a posterior distribution which characterizes the segmentation and model parameters conditional on a given SAR image can be obtained up to a normalizing constant; Then, a Revisable Jump Markov Chain Monte Carlo(RJMCMC) algorithm involving six move types is designed to simulate the posterior distribution, the move types including: splitting or merging real classes, updating parameter vector, updating label field, moving positions of generating points, birth or death of generating points and birth or death of an empty class. Experimental results with real and simulated SAR images demonstrate that the proposed method can determine the number of classes automatically and segment homogeneous regions well.

This paper presents a Synthetic Aperture Radar (SAR) image segmentation approach with unknown number of classes, which is based on regular tessellation and Reversible Jump Markov Chain Monte Carlo (RJMCMC') algorithm. First of all, an image domain is portioned into a set of blocks by regular tessellation. The image is modeled on the assumption that intensities of its pixels in each homogeneous region satisfy an identical and independent Gamma distribution. By Bayesian paradigm, the posterior distribution is obtained to build the region-based image segmentation model. Then, a RJMCMC algorithm is designed to simulate from the segmentation model to determine the number of homogeneous regions and segment the image. In order to further improve the segmentation accuracy, a refined operation is performed. To illustrate the feasibility and effectiveness of the proposed approach, two real SAR image is tested.

In this paper we propose a prior distribution for the clique set and dependence structure of binary Markov random fields (MRFs). In the formulation we allow both pairwise and higher order interactions. We construct the prior by first defining a prior for the neighbourhood system of the MRF, and conditioned on this we define a prior for the appearance of higher order interactions. Finally, for the parameter values we adopt a prior that allows for parameter values to equal, and in this way we reduce the effective number of free parameters. To sample from a resulting posterior distribution conditioned on an observed scene we construct a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. We circumvent evaluations of the intractable normalising constant of the MRF when running this algorithm by adopting a previously defined approximate auxiliary variable algorithm. We demonstrate the usefulness of our prior in two simulation examples and one real data example.

A new transdimensional Sequential Monte Carlo (SMC) algorithm called SMCVB is proposed. In an SMC approach, a weighted sample of particles is generated from a sequence of probability distributions which 'converge' to the target distribution of interest, in this case a Bayesian posterior distribution. The approach is based on the use of variational Bayes to propose new particles at each iteration of the SMCVB algorithm in order to target the posterior more efficiently. The variational-Bayes-generated proposals are not limited to a fixed dimension. This means that the weighted particle sets that arise can have varying dimensions thereby allowing us the option to also estimate an appropriate dimension for the model. This novel algorithm is outlined within the context of finite mixture model estimation. This provides a less computationally demanding alternative to using reversible jump Markov chain Monte Carlo kernels within an SMC approach. We illustrate these ideas in a simulated data analysis and in applications.

We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology which allows for both continuous and discontinuous functional shapes and which are estimated using marked point processes and reversible jump Markov Chain Monte Carlo techniques. Geographical dependency is incorporated by a flexible prior distribution; the parametrisation allows the dependency to vary with functional level. The approach is tuned using Bayesian global optimization and cross-validation. Estimates enable variable selection, threshold detection and prediction as well as the extrapolation of the regression function. Performance and flexibility of our approach is illustrated by simulation studies and an application to a Norwegian insurance data set., 31 pages, 9 Figures

Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular, when the number of subpopulations is considered unknown, more sophisticated methods are required to perform Bayesian analysis. The Reversible Jump Markov Chain Monte Carlo is an alternative method for computing the posterior distribution by simulation in this case. Some problems associated with the Bayesian analysis of these class of models are frequent, such as the so-called “label-switching” problem. However, as the level of heterogeneity in the population increases, these problems are expected to become less frequent and the model’s performance to improve. Thus, the aim of this work is to evaluate the normal mixture model fit using simulated data under different settings of heterogeneity and prior information about the mixture proportions. A simulation study is also presented to evaluate the model’s performance considering the number of components known and estimating it. Finally, the model is applied to a censored real dataset containing antibody levels of Cytomegalovirus in individuals.

International audience; When faced with high frequency streams of data, clustering raises theoretical and algorithmic pitfalls. We introduce a new and adaptive online clustering algorithm relying on a quasi-Bayesian approach, with a dynamic (i.e., time-dependent) estimation of the (unknown and changing) number of clusters. We prove that our approach is supported by minimax regret bounds. We also provide an RJMCMC-flavored implementation (called PACBO, see https://cran.r-project.org/web/packages/PACBO/index.html) for which we give a convergence guarantee. Finally, numerical experiments illustrate the potential of our procedure.

Measurements of energy balance components (energy intake, energy expenditure, changes in energy stores) are often plagued with measurement error. Doubly-labeled water can measure energy intake (EI) with negligible error, but is expensive and cumbersome. An alternative approach that is gaining popularity is to use the energy balance principle, by measuring energy expenditure (EE) and change in energy stores (ES) and then back-calculate EI. Gold standard methods for EE and ES exist and are known to give accurate measurements, albeit at a high cost. We propose a joint statistical model to assess the measurement error in cheaper, non-intrusive measures of EE and ES. We let the unknown true EE and ES for individuals be latent variables, and model them using a bivariate distribution. We try both a bivariate Normal as well as a Dirichlet Process Mixture Model, and compare the results via simulation. Our approach, is the first to account for the dependencies that exist in individuals' daily EE and ES. We employ semiparametric regression with free knot splines for measurements with error, and linear components for error free covariates. We adopt a Bayesian approach to estimation and inference and use Reversible Jump Markov Chain Monte Carlo to generate draws from the posterior distribution. Based on the semiparameteric regression, we develop a calibration equation that adjusts a cheaper, less reliable estimate, closer to the true value. Along with this calibrated value, our method also gives credible intervals to assess uncertainty. A simulation study shows our calibration helps produce a more accurate estimate. Our approach compares favorably in terms of prediction to other commonly used models.

In this article we present a new method for performing Bayesian parameter inference and model choice for low- count time series models with intractable likelihoods. The method involves incorporating an alive particle filter within a sequential Monte Carlo (SMC) algorithm to create a novel exact-approximate algorithm, which we refer to as alive SMC2. The advantages of this approach over competing methods are that it is naturally adaptive, it does not involve between-model proposals required in reversible jump Markov chain Monte Carlo, and does not rely on potentially rough approximations. The algorithm is demonstrated on Markov process and integer autoregressive moving average models applied to real biological datasets of hospital-acquired pathogen incidence, animal health time series, and the cumulative number of prion disease cases in mule deer.

In this paper we propose a new method for the automatic extraction of tidal channels in digital terrain models (DTM) using a sampling approach based on marked point processes. In our model, the tidal channel system is represented by an undirected, acyclic graph. The graph is iteratively generated and fitted to the data using stochastic optimization based on a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler and simulated annealing. The nodes of the graph represent junction points of the channel system and the edges straight line segments with a certain width in between. In each sampling step, the current configuration of nodes and edges is modified. The changes are accepted or rejected depending on the probability density function for the configuration which evaluates the conformity of the current status with a pre-defined model for tidal channels. In this model we favour high DTM gradient magnitudes at the edge borders and penalize a graph configuration consisting of non-connected components, overlapping segments and edges with atypical intersection angles. We present the method of our graph based model and show results for lidar data, which serve of a proof of concept of our approach. Ministry of Environment, Energy, and Climate Protection Ministry of Science and Culture of Lower Saxony

We propose a Poisson mixture model for count data to determine the number of groups in a Group Life insurance portfolio consisting of claim numbers or deaths. We take a non-parametric Bayesian approach to modelling this mixture distribution using a Dirichlet process prior and use reversible jump Markov chain Monte Carlo to estimate the number of components in the mixture. Unlike Haastrup, we show that the assumption of identical heterogeneity for all groups may not hold as 88% of the posterior probability is assigned to models with two or three components, and 11% to models with four or five components, whereas models with one component are never visited. Our major contribution is showing how to account for both model uncertainty and parameter estimation within a single framework.

System identification has been applied in diverse areas over past decades. In particular, parametric modelling approaches such as linear and nonlinear autoregressive with exogenous inputs models have been extensively used due to the transparency of the model structure. Model structure detection aims to identify parsimonious models by ranking a set of candidate model terms using some dependency metrics, which evaluate how the inclusion of an individual candidate model term affects the prediction of the desired output signal. The commonly used dependency metrics such as correlation function and mutual information may not work well in some cases, and therefore, there are always uncertainties in model parameter estimates. Thus, there is a need to introduce a new model structure detection scheme to deal with uncertainties in parameter estimation. In this work, a distance correlation metric is implemented and incorporated with a bagging method. The combination of these two implementations enhances the performance of existing forward selection approaches in that it provides the interpretability of nonlinear dependency and an insightful uncertainty analysis for model parameter estimates. The new scheme is referred as bagging forward orthogonal regression using distance correlation (BFOR-dCor) algorithm. A comparison of the performance of the new BFOR-dCor algorithm with benchmark algorithms using metrics like error reduction ratio, mutual information, or the Reversible Jump Markov Chain Monte Carlo method has been carried out in dealing with several numerical case studies. For ease of analysis, the discussion is restricted to polynomial models that can be expressed in a linear-in-the-parameters form.

A statistical Bayesian approach for uncertainty quantification of multiple flaws.XFEM is employed for forward analyses so that re-meshing is alleviated.Bayes' theorem is applied to obtain posterior joint distribution of flaw parameters.RJMCMC algorithm is used for sampling the posteriors of flaw parameters.RJMCMC is guided by damage indices defined at each sensor location. We propose a guided Bayesian inference approach for detection and quantification of multiple flaws in structures without a priori knowledge on the number of flaws. Uncertainties due to modeling errors and measurement noise are explicitly considered in the Bayesian framework. Flaws are approximated by circular-shaped voids that can be easily represented by a set of parameters including the center coordinates and the radii. The extended finite element method (XFEM) is employed as the forward solver in the inverse detection framework, where re-meshing requirements in the vicinity of the flaws are completely alleviated. By comparing the measurement data and the output of the XFEM forward model, Bayes' theorem is used to update the probability distributions of the flaw parameters, leading to a full statistical quantification of flaws. Since the number of flaws is unknown beforehand, a trans-dimensional reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is employed for sampling the posterior distributions of flaw parameters within the varying parameter spaces. The RJMCMC algorithm is guided by predefined prior information which is based on damage indices defined at each sensor location. These indices are obtained by comparing the undamaged and damaged measurement states. Numerical studies are carried out to demonstrate the effectiveness of the proposed statistical multiple-flaw quantification method.

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, where the dimension p may be large. Gaussian graphical models provide an important tool in describing conditional independence through presence or absence of edges in the underlying graph. A popular non-Bayesian method of estimating a graphical structure is given by the graphical lasso. In this paper, we consider a Bayesian approach to the problem. We use priors which put a mixture of a point mass at zero and certain absolutely continuous distribution on off-diagonal elements of the precision matrix. Hence the resulting posterior distribution can be used for graphical structure learning. The posterior convergence rate of the precision matrix is obtained and is shown to match the oracle rate. The posterior distribution on the model space is extremely cumbersome to compute using the commonly used reversible jump Markov chain Monte Carlo methods. However, the posterior mode in each graph can be easily identified as the graphical lasso restricted to each model. We propose a fast computational method for approximating the posterior probabilities of various graphs using the Laplace approximation approach by expanding the posterior density around the posterior mode. We also provide estimates of the accuracy in the approximation.

This paper addresses the problem of decomposing a sequence of spectroscopic signals. Data are a series of signals modeled as a noisy sum of parametric peaks. We aim to estimate the peak parameters given that they change slowly between two contiguous signals. The key idea is to decompose the whole sequence rather than each signal independently. The problem is set within a Bayesian framework. The peaks with similar evolution are gathered into groups and a Markovian prior on the peak parameters of a same group is used to favor a smooth evolution of the peaks. In addition, the peak number and the group number are unknown and have to be estimated (the number of peaks in two contiguous signals change if peaks vanish). Therefore, the posterior distribution is sampled with a reversible jump Markov chain Monte Carlo algorithm. Simulations conducted on synthetic and real photoelectron data illustrate the performance of the method. HighlightsThis work aims at estimating the parameters of Gaussian peaks in spectroscopic signals.Data gather actually several spectroscopic signals, so the decomposition is performed jointly on the whole data.The peaks evolve slowly through the data and may appear and disappear.We propose an original Bayesian model and an implementation of the RJMCMC algorithm.The performances of the method are discussed on synthetic and real (photoelectron) data.

We propose a flexible prior model for the parameters of binary Markov random fields (MRF), defined on rectangular lattices and with maximal cliques defined from a template maximal clique. The prior model allows higher-order interactions to be included. We also define a reversible jump Markov chain Monte Carlo algorithm to sample from the associated posterior distribution. The number of possible parameters for a higher-order MRF becomes high, even for small template maximal cliques. We define a flexible parametric form where the parameters have interpretation as potentials for clique configurations, and limit the effective number of parameters by assigning apriori discrete probabilities for events where groups of parameter values are equal. To cope with the computationally intractable normalising constant of MRFs, we adopt a previously defined approximation of binary MRFs. We demonstrate the flexibility of our prior formulation with simulated and real data examples.

This paper introduces a methodology to infer the spatial variation of the acoustic characteristics of a 1D vertical elastic heterogeneous earth model via a Bayesian calibration approach, given a prescribed sequence of loading and the corresponding time history response registered at the ground level. This involves solving an inverse problem that maps the ground seismic response onto a random profile of the ground stratigraphy (i.e. a 1D continuous spatial random field). From a Bayesian point of view, the solution to an inverse problem is fully characterized by a posterior density function of the forward model random parameters, which explicitly overcomes the solution's non-uniqueness. This subsurface earth model is parameterized using a Bayesian partition model, where the number of soil layers, the location of the layers' interfaces, and their corresponding mechanical characteristics are defined as random variables. The partition model approach to an inverse problem is closely related to a Bayesian model selection problem, where the likely dimensionality of the inverse problem (number of unknowns) is inferred conditioned on the experimental observations. The main benefit of the proposed approach is that the explicit regularization of the inverted profile by global damping procedures is not required. A Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm is used to sample the target posterior of varying dimension, dependent on the number of layers. A synthetic case study is provided to indicate the applicability of the proposed methodology.

Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical method that describes extremal dependence taking advantage of the inherent tree-based dependence structure of the max-stable nested logistic distribution, and that identifies possible clusters of extreme variables using reversible jump Markov chain Monte Carlo techniques. Parsimonious representations are achieved when clusters of extreme variables are found to be completely independent. Moreover, we significantly decrease the computational complexity of full likelihood inference by deriving a recursive formula for the likelihood function of the nested logistic model. The method’s performance is verified through extensive simulation experiments which also compare different likelihood procedures. The new methodology is used to investigate the dependence relationships between extreme concentrations of multiple pollutants in California and how these concentrations are related to extreme weather conditions. Overall, we show that our approach allows for the representation of complex extremal dependence structures and has valid applications in multivariate data analysis, such as air pollution monitoring, where it can guide policymaking

Microarray technologies become a powerful technique for simultaneously monitoring expression patterns of thousands of genes under different conditions. However, it is important to identify gene groups that manifest similar expression profiles and are activated by similar conditions. ClusterMPP: Clustering by Marked Point Process is a new microarray data clustering algorithm performed in two steps. The first one detects cluster modes representing regions of high density observations in the raw space. Based on the simulation of a proposed Marked Point Process by the well-known Reversible Jump Markov Chain Monte Carlo algorithm, where we consider several movements like birth and death, this algorithm step identifies prototype observations of each cluster. The second step of ClusterMPP is the K nearest neighbors (KNN) assignation that affects the remaining observations to the corresponding clusters. We experiment ClusterMPP on several complex and scalable microarray datasets. The results show the efficiency of ClusterMPP compared to well-known microarray data clustering methods like K-means, Spectral Clustering, and Mean-Shift.

In this paper, we consider the structure and parameter identification problem for Bayesian Hammerstein system. A structure identification algorithm is proposed, in which the system order, system parameters and regularization parameters are all unknown in the considered system. The joint posterior distribution of system parameters and the value of basis functions $$k$$ are obtained via sampling theory. The proposed identification algorithm is based on the reversible jump Markov chain Monte Carlo method. There are two main characteristics of the algorithm: (i) By using the birth move and death move strategy, the parameter $$k$$ is searched quickly in the number of basis functions space until the suitable value of $$k$$ is found. (ii) The distributions of system parameters are changed with the value of $$k$$ in the Bayesian framework, and the parameters are successfully found after the value of $$k$$ is stable. Two examples are provided to show the effectiveness of the proposed algorithm. The performances of the algorithm are validated with the results of statistical analyses including parameter estimate error, MSE, NRMSE, MAD, Theils inequality coefficient, etc.

Projection reconstruction nuclear magnetic resonance (PR-NMR) is a technique for generating multidimensional NMR spectra. A small number of projections from lower-dimensional NMR spectra are used to reconstruct the multidimensional NMR spectra. In our previous work 1,2, it was shown that multidimensional NMR spectra are efficiently reconstructed using peak-by-peak based reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. We propose an extended and generalized RJMCMC algorithm replacing a simple linear model with a linear mixed model to reconstruct close NMR spectra into true spectra. This statistical method generates samples in a Bayesian scheme. Our proposed algorithm is tested on a set of six projections derived from the three-dimensional 700MHz HNCO spectrum of a protein HasA. HighlightsWe design a mathematical model for reconstructing multidimensional NMR spectra.We compare the performance of several statistical algorithms for PR-NMR.A generalized Monte Carlo algorithm is applied to restore the NMR spectra.

Automatic extraction of buildings from airborne laser scanning (ALS) point clouds is essential for 3D building reconstruction. This paper presents a two-part approach for extracting buildings from ALS data. First, building objects are extracted from ALS data by a marked point process using the Gibbs energy model of buildings and sampled by a reversible jump Markov chain Monte Carlo algorithm. Second, a refinement operation is performed to filter the non-building points and false building objects before extracting buildings from the detected building objects. Experimental results and evaluation using ISPRS benchmark data-sets showed the robustness of the proposed method.

Finite mixture of regression (FMR) models are aimed at characterizing subpopulation heterogeneity stemming from different sets of covariates that impact different groups in a population. We address the contemporary problem of simultaneously conducting covariate selection and determining the number of mixture components from a Bayesian perspective that can incorporate prior information. We propose a Gibbs sampling algorithm with reversible jump Markov chain Monte Carlo implementation to accomplish concurrent covariate selection and mixture component determination in FMR models. Our Bayesian approach contains innovative features compared to previously developed reversible jump algorithms. In addition, we introduce component-adaptive weighted g priors for regression coefficients, and illustrate their improved performance in covariate selection. Numerical studies show that the Gibbs sampler with reversible jump implementation performs well, and that the proposed weighted priors can be superior to non-adaptive...