Reversible Jump Markov Chain Monte Research Articles

BAREB: A Bayesian repulsive biclustering model for periodontal data.

Preventing periodontal diseases (PD) and maintaining the structure and function of teeth are important goals for personal oral care. To understand the heterogeneity in patients with diverse PD patterns, we develop a Bayesian repulsive biclustering method that can simultaneously cluster the PD patients and their tooth sites after taking the patient- and site-level covariates into consideration. BAREB uses the determinantal point process prior to induce diversity among different biclusters to facilitate parsimony and interpretability. Since PD progression is hypothesized to be spatially referenced, BAREB factors in the spatial dependence among tooth sites. In addition, since PD is the leading cause for tooth loss, the missing data mechanism is nonignorable. Such nonrandom missingness is incorporated into BAREB. For the posterior inference, we design an efficient reversible jump Markov chain Monte Carlo sampler. Simulation studies show that BAREB is able to accurately estimate the biclusters, and compares favorably to alternatives. For real world application, we apply BAREB to a dataset from a clinical PD study, and obtain desirable and interpretable results. A major contribution of this article is the Rcpp implementation of our methodology, available in the R package BAREB.

Procedural Reconstruction of 3D Indoor Models from Lidar Data Using Reversible Jump Markov Chain Monte Carlo

Automated reconstruction of Building Information Models (BIMs) from point clouds has been an intensive and challenging research topic for decades. Traditionally, 3D models of indoor environments are reconstructed purely by data-driven methods, which are susceptible to erroneous and incomplete data. Procedural-based methods such as the shape grammar are more robust to uncertainty and incompleteness of the data as they exploit the regularity and repetition of structural elements and architectural design principles in the reconstruction. Nevertheless, these methods are often limited to simple architectural styles: the so-called Manhattan design. In this paper, we propose a new method based on a combination of a shape grammar and a data-driven process for procedural modelling of indoor environments from a point cloud. The core idea behind the integration is to apply a stochastic process based on reversible jump Markov Chain Monte Carlo (rjMCMC) to guide the automated application of grammar rules in the derivation of a 3D indoor model. Experiments on synthetic and real data sets show the applicability of the method to efficiently generate 3D indoor models of both Manhattan and non-Manhattan environments with high accuracy, completeness, and correctness.

Detection of Multiple Change-Points in the Scale Parameter of a Gamma Distributed Sequence Based on Reversible Jump MCMC

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.

A novel Bayesian continuous piecewise linear log-hazard model, with estimation and inference via reversible jump Markov chain Monte Carlo.

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.

Application of Reversible Jump Markov Chain Monte Carlo Algorithms to Elastic and Petrophysical Amplitude-Versus-Angle Inversions

We infer the elastic and petrophysical properties from pre-stack seismic data through a transdimensional Bayesian inversion. In this approach the number of model parameters (i.e. the number of layers) is treated as an unknown, and a reversible jump Markov Chain Monte Carlo (rjMCMC) algorithm is used to sample the variable-dimension model space. This inversion scheme provides a parsimonious solution, and reliably quantifies the uncertainties affecting the estimated model parameters. Parallel tempering, which employs a sequence of interacting Markov chains in which the likelihood function is successively relaxed, is used to improve the efficiency of the probabilistic sampling. In addition, the delayed rejection updating scheme is employed to speed up the convergence of the rjMCMC algorithm to the stationary regime. Both elastic and petrophysical inversions invert the amplitude versus angle responses and employ a convolutional forward modelling based on the exact Zoeppritz equations. First, synthetic tests are used to assess the reliability of the implemented rjMCMC algorithms, then their applicability is demonstrated by inverting field seismic data acquired onshore. In this case the inversion was aimed at inferring the elastic and petrophysical properties around a gas-saturated reservoir hosted in a shale-sand sequence. In this case, the final outcomes provided by the rjMCMC algorithms are also compared with the predictions of linear Bayesian elastic and petrophysical inversions. The synthetic and field data examples demonstrate that the implemented algorithms can successfully estimate model uncertainty, model dimensionality and subsurface parameters with an affordable computational cost.

A fully Bayesian mixture model approach for identifying noncompliance in a regulatory tobacco clinical trial.

Identifying noncompliance in a randomized trial is challenging, but could be improved by leveraging biomarker data to identify participants that did not comply with their assigned treatment. For randomized trials of very low nicotine content (VLNC) cigarettes, the biomarker of total nicotine equivalents (TNE) could be used to identify noncompliance. Compliant participants should have lower levels of TNEs than participants that did not comply and smoked normal nicotine content cigarettes, resulting in a mixture of compliant and noncompliant participants at each dose level. Thresholds of TNE could then be identified from the compliant groups at each dose level and used to determine which study participants were compliant. Furthermore, proposed biological relationships of TNE with nicotine dose could be incorporated into improve the efficiency of estimation, but may introduce bias if misspecified. To account for multiple modeling assumptions across dose levels, we explore model averaging via reversible jump markov chain monte carlo (MCMC) within each dose level to take advantage of improvements in efficiency when the proposed relationship is true and to downweight the biological model when it is misspecified. In simulation studies, we demonstrate that model averaging in the presence of a correct biological relationship results in a decrease in the mean square error (MSE) of up to 85%, but downweights the model in dose levels where the relationship is not appropriate. We apply our approach to data from a randomized trial of VLNC cigarettes to estimate TNE thresholds and probability of compliance curves as a function of TNEs for each nicotine dose used in the trial.

BPEC: An R Package for Bayesian Phylogeographic and Ecological Clustering

BPEC is an R package for Bayesian phylogeographic and ecological clustering which allows geographical, environmental and phenotypic measurements to be combined with deoxyribonucleic acid (DNA) sequences in order to reveal geographic structuring of DNA sequence clusters consistent with migration events. DNA sequences are modelled using a collapsed version of a simplified coalescent model projected onto haplotype trees, which subsequently give rise to constrained clusterings as migrations occur. Within each cluster, a multivariate Gaussian distribution of the covariates (geographical, environmental, phenotypic) is used. Inference follows tailored reversible jump Markov chain Monte Carlo sampling so that the number of clusters (i.e., migrations) does not need to be pre-specified. A number of output plots and visualizations are provided which reflect the posterior distribution of the parameters of interest. BPEC also includes functions that create output files which can be loaded into Google Earth. The package commands are illustrated through an example dataset of the polytypic Near Eastern brown frog Rana macrocnemis analyzed using BPEC.

BASS: An R Package for Fitting and Performing Sensitivity Analysis of Bayesian Adaptive Spline Surfaces

We present the R package BASS as a tool for nonparametric regression. The primary focus of the package is fitting fully Bayesian adaptive spline surface (BASS) models and performing global sensitivity analyses of these models. The BASS framework is similar to that of Bayesian multivariate adaptive regression splines (BMARS) from Denison, Mallick, and Smith (1998), but with many added features. The software is built to efficiently handle significant amounts of data with many continuous or categorical predictors and with functional response. Under our Bayesian framework, most priors are automatic but these can be modified by the user to focus on parsimony and the avoidance of overfitting. If directed to do so, the software uses parallel tempering to improve the reversible jump Markov chain Monte Carlo (RJMCMC) methods used to perform inference. We discuss the implementation of these features and present the performance of BASS in a number of analyses of simulated and real data.

Hierarchical Bayesian Choice of Laplacian ARMA Models Based on Reversible Jump MCMC Computation

An autoregressive moving average (ARMA) is a time series model that is applied in everyday life for pattern recognition and forecasting. The ARMA model contains a noise which is assumed to have a specific distribution. The noise is often considered to have a Gaussian distribution. However in applications, the noise is sometimes found that does not have a Gaussian distribution. The first objective is to develop the ARMA model in which noise has a Laplacian distribution. The second objective is to estimate the parameters of the ARMA model. The ARMA model parameters include ARMA model orders, ARMA model coefficients, and noise variance. The parameter estimation of the ARMA model is carried out in the Bayesian framework. In the Bayesian framework, the ARMA model parameters are treated as a variable that has a prior distribution. The prior distribution for the ARMA model parameters is combined with the likelihood function for the data to get the posterior distribution for the parameter. The posterior distribution for parameters has a complex form so that the Bayes estimator cannot be determined analytically. The reversible jump Markov chain Monte Carlo (MCMC) algorithm was adopted to determine the Bayes estimator. The first result, the ARMA model can be developed by assuming Laplacian distribution noise. The second result, the performance of the algorithm was tested using simulation studies. The simulation shows that the reversible jump MCMC algorithm can estimate the parameters of the ARMA model correctly.

A Conditional Density Estimation Partition Model Using Logistic Gaussian Processes.

Conditional density estimation (density regression) estimates the distribution of a response variable y conditional on covariates x. Utilizing a partition model framework, a conditional density estimation method is proposed using logistic Gaussian processes. The partition is created using a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The Markov chain Monte Carlo algorithm is made possible through a Laplace approximation on the latent variables of the logistic Gaussian process model. This approximation marginalizes the parameters in each partition element, allowing an efficient search of the posterior distribution of the tessellation. The method has desirable consistency properties. In simulation and applications, the model successfully estimates the partition structure and conditional distribution of y.

Sequential Monte Carlo with transformations

This paper examines methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. For this, we use sequential Monte Carlo samplers, introducing the innovation of using deterministic transformations to move particles effectively between target distributions with different dimensions. This approach, combined with adaptive methods, yields an extremely flexible and general algorithm for Bayesian model comparison that is suitable for use in applications where the acceptance rate in reversible jump Markov chain Monte Carlo is low. We use this approach on model comparison for mixture models, and for inferring coalescent trees sequentially, as data arrives.

Hierarchical Bayesian segmentation for piecewise stationary autoregressive model based on reversible jump MCMC

This paper aims to decompose time series data in segments where many segments are unknown. The data in each segment is modeled as a stationary autoregressive where the model order is unknown. The model parameters include the number of segments, the location of segment changes, the order of each segment, and the autoregressive coefficients of each segment. The Bayesian method is used to estimate parameters, but Bayesian estimator cannot be calculated analytically. The Bayesian estimator is calculated using the reversible jump Markov chain Monte Carlo algorithm. The performance of the algorithm is tested using synthesis data. The simulation results show that the algorithm estimates the model parameters well.

Bayesian Multiple Emitter Fitting using Reversible Jump Markov Chain Monte Carlo

In single molecule localization-based super-resolution imaging, high labeling density or the desire for greater data collection speed can lead to clusters of overlapping emitter images in the raw super-resolution image data. We describe a Bayesian inference approach to multiple-emitter fitting that uses Reversible Jump Markov Chain Monte Carlo to identify and localize the emitters in dense regions of data. This formalism can take advantage of any prior information, such as emitter intensity and density. The output is both a posterior probability distribution of emitter locations that includes uncertainty in the number of emitters and the background structure, and a set of coordinates and uncertainties from the most probable model.

Improved estimation of macroevolutionary rates from fossil data using a Bayesian framework

AbstractThe estimation of origination and extinction rates and their temporal variation is central to understanding diversity patterns and the evolutionary history of clades. The fossil record provides the only direct evidence of extinction and biodiversity changes through time and has long been used to infer the dynamics of diversity changes in deep time. The software PyRate implements a Bayesian framework to analyze fossil occurrence data to estimate the rates of preservation, origination, and extinction while incorporating several sources of uncertainty. Building upon this framework, we present a suite of methodological advances including more complex and realistic models of preservation and the first likelihood-based test to compare the fit across different models. Further, we develop a new reversible jump Markov chain Monte Carlo algorithm to estimate origination and extinction rates and their temporal variation, which provides more reliable results and includes an explicit estimation of the number and temporal placement of statistically significant rate changes. Finally, we implement a new C++ library that speeds up the analyses by orders of magnitude, therefore facilitating the application of the PyRate methods to large data sets. We demonstrate the new functionalities through extensive simulations and with the analysis of a large data set of Cenozoic marine mammals. We compare our analytical framework against two widely used alternative methods to infer origination and extinction rates, revealing that PyRate decisively outperforms them across a range of simulated data sets. Our analyses indicate that explicit statistical model testing, which is often neglected in fossil-based macroevolutionary analyses, is crucial to obtain accurate and robust results.

Bayesian Model Averaging Over Tree-based Dependence Structures for Multivariate Extremes

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 which 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. Supplementary materials for this article are available online.

A Hidden Semi-Markov Model for Characterizing Regime Shifts in Ocean Density Variability

Summary Societally important decadal predictions of temperature and precipitation over Europe are largely affected by variability in the North Atlantic Ocean. Within this region, the Labrador Sea is of particular importance because of its link between surface-driven density variability and the Atlantic meridional overturning circulation. Using physical justifications, we propose a statistical model to describe the temporal variability of ocean density in terms of salinity-driven and temperature-driven density. This is a hidden semi-Markov model that allows for either a salinity-driven or a temperature-driven ocean density regime, such that the persistence in each regime is governed probabilistically by a semi-Markov chain. The model is fitted in the Bayesian framework, and a reversible jump Markov chain Monte Carlo algorithm is proposed to deal with a single-regime scenario. The model is first applied to a reanalysis data set, where model checking measures are also proposed. Then it is applied to data from 43 climate models to investigate whether and how ocean density variability differs between them and also the reanalysis data. Parameter estimates relating to the mean holding time for each regime are used to establish a link between regime behaviour and the Atlantic meridional overturning circulation.

Copula Gaussian graphical modelling of biological networks and Bayesian inference of model parameters

Understanding complex biological networks enable us to better understand the systems’ diseases such as cancers and heart attacks, and to produce drug targets which is one of the major research questions under the personalized medicine. But the description of these complexities is challenging since the associated data are very sparse, high dimensional and seriously correlated. The copula Gaussian graphical model (CGGM), which depends on the representation of the multivariate normal distribution via marginals and a copula term, is one of the successful modelling approaches to present such type of datasets. In this study, we apply CGGM in modelling steady-state activations of biological networks and make inference of model parameters under Bayesian settings. We suggest the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to estimate plausible interactions between the systems’ elements which are proteins or genes. We also generate the open-source R codes of RJMCMC for CGGM under different dimensional networks. In the application, we use real datasets and evaluate the accuracy of estimates via F1-score. From the results, we observe that CGGM with RJMCMC is successful in the presentation of real and complex systems with higher accuracy and can be a promising approach to understand biological networks and diseases.

Data Fusion Method and Probabilistic Pairing Approach in Elastic Constants Measurement by Resonance Ultrasound Spectroscopy

Resonant ultrasound spectroscopy (RUS) is a nondestructive technique for measuring the stiffness parameters of solid materials. Trying to achieve an improved automatic, elastic coefficients measurement via RUS, this work proposes a data fusion method based on Bayesian formulation and a probabilistic pairing approach. Several sets of RUS data have been acquired by measuring a novel piezoelectric crystal Ca3NbAl0.5Ga0.5Si2O14 (CNAGS) with a self-designed RUS measurement system. In order to suppress the influence of the phenomenon of frequency shifting, missing, and overlapping, a repeated measurement is executed to achieve the multiple measurement data fusion by using Bayesian formulation, and the posterior distribution of each parameter is estimated by reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm. Besides, an automatic probabilistic pairing method is proposed to solve the problem of frequency crossing so as to facilitate the frequency pairing process. The RUS measuring apparatus, the algorithm principle, and the calculation process are illustrated systematically in this paper. The algorithm is tested and analyzed based on the measured RUS data, and full sets of elastic coefficients of CNAGS specimen has been obtained in this work. Compared to the IEEE standard resonant method, the method proposed in this work can accomplish the characterization within a shorter time, and the relative error of the results is less than 2%.

MARKED POINT PROCESSES FOR THE AUTOMATIC DETECTION OF BOMB CRATERS IN AERIAL WARTIME IMAGES

Abstract. Many countries were the target of air strikes during the Second World War. The aftermath of such attacks is felt until today, as numerous unexploded bombs or duds still exist in the ground. Typically, such areas are documented in so-called impact maps, which are based on detected bomb craters. This paper proposes a stochastic approach to automatically detect bomb craters in aerial wartime images that were taken during World War II. In this work, one aspect we investigate is the type of object model for the crater: we compare circles with ellipses. The respective models are embedded in the probabilistic framework of marked point processes. By means of stochastic sampling the most likely configuration of objects within the scene is determined. Each configuration is evaluated using an energy function which describes the conformity with a predefined model. High gradient magnitudes along the border of the object are favoured and overlapping objects are penalized. In addition, a term that requires the grey values inside the object to be homogeneous is investigated. Reversible Jump Markov Chain Monte Carlo sampling in combination with simulated annealing provides the global optimum of the energy function. Afterwards, a probability map is generated from the automatic detections via kernel density estimation. By setting a threshold, areas around the detections are classified as contaminated or uncontaminated sites, respectively, which results in an impact map. Our results, based on 22 aerial wartime images, show the general potential of the method for the automated detection of bomb craters and the subsequent automatic generation of an impact map.

Input modelling for multimodal data

Multimodal data occurs frequently in discrete-event simulation input analysis, typically arising when an input sample stream comes from different sources. A finite mixture distribution is a simple input model for representing such data, but fitting a mixture distribution is not straightforward as the problem is well-known to be statistically non-standard. Even though much studied, the most common fitting approach, Bayesian reversible jump Markov Chain Monte Carlo (RJMCMC), is not very satisfactory for use in setting up input models. We describe an alternative Bayesian approach, MAPIS, which uses maximum a posteriori estimation with importance sampling, showing it overcomes the main problems encountered with RJMCMC. We demonstrate use of a publicly available implementation of MAPIS, which we have called FineMix, applying it to practical examples coming from finance and manufacturing.