Reversible Jump Markov Chain Monte Research Articles

Generating impact maps from bomb craters automatically detected in aerial wartime images using marked point processes

Even more than 75 years after the Second World War, numerous unexploded bombs (duds) linger in the ground and pose a considerable hazard to society. The areas containing these duds are documented in so-called impact maps, which are based on locations of exploded bombs; these locations can be found in aerial images taken shortly after bombing. To generate impact maps, in this paper we present a novel approach based on marked point processes (MPPs) for the automatic detection of bomb craters in such images, some of which are overlapping. The object model for the craters is represented by circles and is embedded in the MPP-framework. By means of stochastic sampling, the most likely configuration of objects within the scene is determined. Each configuration is evaluated using an energy function that describes the consistency with a predefined object model. High gradient magnitudes along the object borders and homogeneous grey values inside the objects are favoured, while overlaps between objects are penalized. Reversible Jump Markov Chain Monte Carlo sampling, in combination with simulated annealing, provides the global optimum of the energy function. Our procedure allows the combination of individual detection results covering the same location. Afterwards, a probability map for duds is generated from the detections via kernel density estimation and areas around the detections are classified as contaminated, resulting in an impact map. Our results, based on 74 aerial wartime images taken over different areas in Central Europe, show the potential of the method; among other findings, a clear improvement is achieved by using redundant image information. We also compared the MPP method for bomb crater detection with a state-of-of-the-art convolutional neural network (CNN) for generating region proposals; it turned out that the CNN outperforms the MPPs if a sufficient amount of representative training data is available and a threshold for a region to be considered as crater is properly tuned prior to running the experiments. If this is not the case, the MPP approach achieves better results.

Modeling the evolution of competitive market structure via competitive group dynamics

PurposeThis paper aims to examine the evolution of a competitive market structure over time through the lens of competitive group membership dynamics.Design/methodology/approachA new hidden Markov modeling approach is devised that accounts for the three sources of competitive heterogeneity involving managerial strategy, corporate performance and the impact of strategy on performance. In addition, some observed “entry” and “exit” states are considered to model firms’ entry into and exit from the market. The proposed model is illustrated with an investigation of the US banking industry based on a data set created from the COMPUSTAT database. This paper estimated the model within the Bayesian framework and devised a reversible jump Markov chain Monte Carlo estimation procedure to determine the number of latent competitive groups and uncover the characteristics of each group.FindingsThis paper shows that the US banking industry, contrary to the prior findings of having a relatively stable structure, has, in fact, gone through dramatic changes in the past number of decades.Originality/valueContrary to prior work that has primarily focused on managerial strategy to study market evolutions, the competitive groups perspective accounts for all three sources of intra-industry competitive heterogeneity. In addition, unlike prior research, the analysis is not limited to firms remaining in the panel of study for the entire observation period. Such limitation results in missing the various changes that occur in the competitive market structure because of the new entrants or the struggling firms that do not survive in the market.

Bayesian model of time series with multiple change points, censured observations and autoregressive segments of order one (AR(1))

A Bayesian model for a nonstationary time series with an unknown number of change points and censored observations where each piece is assumed to be an autoregressive process of order unknown is considered in this paper. To estimate the number and localizations of the unknown change points the Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm developed by [green95] is used. The censured problem is solved by the method of [jungetal05] by imputing the censured values from a multivariate normal distribution given the observed part.

Exact Bayesian inference of epidemiological parameters from mortality data: application to African swine fever virus.

Pathogens such as African swine fever virus (ASFV) are an increasing threat to global livestock production with implications for economic well-being and food security. Quantification of epidemiological parameters, such as transmission rates and latent and infectious periods, is critical to inform efficient disease control. Parameter estimation for livestock disease systems is often reliant upon transmission experiments, which provide valuable insights in the epidemiology of disease but which may also be unrepresentative of at-risk populations and incur economic and animal welfare costs. Routinely collected mortality data are a potential source of readily available and representative information regarding disease transmission early in outbreaks. We develop methodology to conduct exact Bayesian parameter inference from mortality data using reversible jump Markov chain Monte Carlo incorporating multiple routes of transmission (e.g. within-farm secondary and background transmission from external sources). We use this methodology to infer epidemiological parameters for ASFV using data from outbreaks on nine farms in the Russian Federation. This approach improves inference on transmission rates in comparison with previous methods based on approximate Bayesian computation, allows better estimation of time of introduction and could readily be applied to other outbreaks or pathogens.

Reversible Jump MCMC Algorithm for Transformed Laplacian AR: Application in Modeling CO<sub>2</sub> Emission Data

Autoregressive (AR) model is applied to model various types of data. For confidential data, data confusion is very important to protect the data from being known by other unauthorized parties. This paper aims to find data modeling with transformations in the AR model. In this AR model, the noise has a Laplace distribution. AR model parameters include order, coefficients, and variance of the noise. The estimation of the AR model parameter is proposed in a Bayesian method by using the reversible jump Markov Chain Monte Carlo (MCMC) algorithm. This paper shows that the posterior distribution of AR model parameters has a complicated equation, so the Bayes estimator cannot be determined analytically. Bayes estimators for AR model parameters are calculated using the reversible jump MCMC algorithm. This algorithm was validated through a simulation study. This algorithm can accurately estimate the parameters of the transformed AR model with Laplacian noise. This algorithm produces an AR model that satisfies the stationary conditions. The novelty in this paper is the use of transformations in the Laplacian AR model to secure research data when the research results are published in a scientific journal. As an example application, the Laplacian AR model was used to model CO₂ emission data. The results of this paper can be applied to modeling and forecasting confidential data in various sectors.

A Regional SAR Dark Spot Detection Method Based on GMTRJ Algorithm

Generalized Multiple-Try Reversible Jump (GMTRJ) is a recent algorithm which makes it possible to improve the accurate tuning of the jump proposals in the Reversible Jump Markov Chain Monte Carlo algorithm. In this paper, the GMTRJ algorithm is combined the regular tessellation and the Bayesian paradigm to propose a regional synthetic aperture radar (SAR) dark spot detection method. First, the regular tessellation and the Bayesian paradigm are applied to build a regional SAR dark spot detection model; then the GMTRJ algorithm is designed to simulate from the detection model to obtain the optimal regional detection result. As the blocks may cross the boundaries between dark spot and ocean background regions, a refined operation is designed to improve the detection accuracy of boundaries. We present test results demonstrating the feasibility and advantages of the GMTRJ algorithm on simulating from the detection model, and illustrating the feasibility of the refined SAR dark spot detection operation on improving the detection accuracy of boundaries.

Clustering Point Process Based Network Topology Structure Constrained Urban Road Extraction From Remote Sensing Images

To extract complicated road network from remote sensing images on urban scenes, this article presents a clustering point process (CPP) based network topology structure constrained road extraction algorithm. Firstly, the CPP is constructed to model the feature points, such as endpoints, bends, and crossroads in a road system. Based on that, an initial network topology structure is constructed by connecting the points with lines. Then, according to the network structure characteristic and the spectral characteristic of road, a network topology structure constraining model and a spectral measurement constraining model are constructed, respectively. By combining the models above, a road extraction model is built under the framework of Bayes’ theorem. Finally, to simulate from the road extraction model and extract an optimal road network, a solution strategy, reversible jump Markov Chain Monte Carlo (RJMCMC) simulation algorithm with related transfer operations, is designed according to the CPP and network topology structure. Several high-resolution remote sensing images on urban scenes are tested. According to a buffer evaluation method, and compared with the comparing algorithms, accuracy and extraction rate of results from the proposed algorithm are increased by 10.86% and 8.75% on average, respectively. It is proved that the proposed algorithm can extract the complicated road network effectively.

ParMA: Parallelized Bayesian Model Averaging for Generalized Linear Models

This paper describes the gretl function package ParMA, which provides Bayesian model averaging (BMA) in generalized linear models. In order to overcome the lack of analytical specification for many of the models covered, the package features an implementation of the reversible jump Markov chain Monte Carlo technique, following the original idea by Green (1995), as a flexible tool to model several specifications. Particular attention is devoted to computational aspects such as the automatization of the model building procedure and the parallelization of the sampling scheme.

A Reversible Jump MCMC in Bayesian Blind Deconvolution With a Spherical Prior

Blind deconvolution (BD) is the recovery of a scene of interest convolved with an unknown impulse response function. Within a Bayesian context, prior distributions are assigned to both unknowns to regularize the BD problem. A common approach is to use Gaussian priors. Nonetheless, the latter do not alleviate the so-called scale ambiguity that prevents from efficiently sampling the joint posterior distribution and building appropriate estimators. In this paper, we instead use a Von–Mises prior that removes scale ambiguity and we focus on the design of a sampling scheme of the joint posterior. The latter may exhibit multiple modes. We propose accordingly a reversible jump Markov chain Monte Carlo method that prevents samples from lingering in local modes. Compared to state-of-the-art techniques, the algorithm shows an improved within- and between-mode mixing property with synthetic data. This paves the way for the design of Bayesian estimators naturally deprived of scale ambiguity.

Trans-dimensional imaging of the random inhomogeneity structure in the southern Ryukyu arc, Japan

SUMMARY The seismic velocity structure of the lithosphere shows various inhomogeneities over a wide range of scales, and such inhomogeneity causes complex seismic waves above a few hertz due to multiple scattering. Medium around active volcanoes and large faults tends to show strong random inhomogeneity in relatively small areas. For a more precise understanding of such random velocity inhomogeneities, it is necessary to estimate their detailed spatial variation without smoothing constraints. This study introduces a trans-dimensional approach for the 3-D imaging of random inhomogeneity using the reversible jump Markov chain Monte Carlo (rjMCMC) method, and set the number of structural parameters and their spatial layout as unknown parameters. Since the scale dependence of the random inhomogeneity is related to the frequency dependence of seismic wave scattering, the covariance matrix of the likelihood function was defined to be non-diagonal so that residuals at different frequencies in each ray path are correlated. A synthetic test showed this covariance matrix worked adequately for estimating parameters of a power-law-type spectrum of random inhomogeneity. Analysis of seismic data at the southern Ryukyu arc in the southwest Japan found anomalies with strong and weak inhomogeneities. A strongly inhomogeneous band with a width of 20–30 km was distributed in the Okinawa Trough at depths of 0–20 km. In part of this area, magma intrusions and associated complex structures have been detected by a seismic reflection survey. The scale of the structures discussed in this study is almost the same with that discussed in the reflection survey. The rjMCMC-based analysis made it possible to compare random inhomogeneities with the structural variations estimated by the deterministic seismic reflection survey. Since analyses of scattered seismic waves can examine much greater depths than seismic reflection surveys, further comparisons between the two methods in the shallow crust could provide useful insights for detailed interpretation of complex structures at deeper depth.

Generalized Mixtures of Finite Mixtures and Telescoping Sampling

Within a Bayesian framework, a comprehensive investigation of mixtures of finite mixtures (MFMs), i.e., finite mixtures with a prior on the number of components, is performed. This model class has applications in model-based clustering as well as for semi-parametric density estimation and requires suitable prior specifications and inference methods to exploit its full potential. We contribute by considering a generalized class of MFMs where the hyperparameter γK of a symmetric Dirichlet prior on the weight distribution depends on the number of components. We show that this model class may be regarded as a Bayesian non-parametric mixture outside the class of Gibbs-type priors. We emphasize the distinction between the number of components K of a mixture and the number of clusters K+, i.e., the number of filled components given the data. In the MFM model, K+ is a random variable and its prior depends on the prior on K and on the hyperparameter γK. We employ a flexible prior distribution for the number of components K and derive the corresponding prior on the number of clusters K+ for generalized MFMs. For posterior inference we propose the novel telescoping sampler which allows Bayesian inference for mixtures with arbitrary component distributions without resorting to reversible jump Markov chain Monte Carlo (MCMC) methods. The telescoping sampler explicitly samples the number of components, but otherwise requires only the usual MCMC steps of a finite mixture model. The ease of its application using different component distributions is demonstrated on several data sets.

Transdimensional simultaneous inversion of velocity structure and event locations in downhole microseismic monitoring

In downhole microseismic monitoring, the velocity model plays a vital role in accurate mapping of the hydraulic fracturing image. For velocity model uncertainties in the number of layers or interface depths, the conventional velocity calibration method has been shown to effectively locate the perforation shots; however, it introduces nonnegligible location errors for microseismic events, especially for complex geologic formations with inclinations. To improve the event location accuracy, we have exploited the advantages of the reversible jump Markov chain Monte Carlo approach in generating different dimensions of velocity models and adopted a transdimensional Bayesian simultaneous inversion framework for obtaining the effective velocity structure and event locations simultaneously. The transdimensional inversion changes the number of layers during the inversion process and selects the optimal interface depths and velocity values to improve the event location accuracy. The confidence intervals of the simultaneous inversion event locations estimated by Bayesian inference enable us to evaluate the location uncertainties in the horizontal and vertical directions. Two synthetic examples and a field test are presented to illustrate the performance of our methodology, and the event location accuracy is shown to be higher than that obtained using the conventional methods. With less dependence on prior information, our transdimensional simultaneous inversion method can be used to obtain an effective velocity structure for facilitating highly accurate hydraulic fracturing mapping.

Performance Analysis of Typical Telemetry Modulation Methods Under Downlink Integrated Channel of Hypersonic Vehicles

Due to the severe impact of dynamic plasma sheath on electromagnetic (EM) waves, the communication quality of hypersonic vehicles deteriorates, even resulting in communication blackouts during the reentry process. In this article, the hypersonic vehicle downlink integrated channels that cascade the plasma sheath channel and Rice fading channel, i.e., the downlink telemetry channels, are first established, and then the demodulation method and performance of typical telemetry modulations including the M-ary phase shift keying (MPSK), M-ary amplitude shift keying (MASK), and M-ary frequency shift keying (MFSK) are studied. Considering the high dynamics of the plasma sheath, the pilot signals are used to detect the signal correctly for MPSK, and the non-coherent demodulation is adopted for MASK and MFSK. Especially, an adaptive maximum likelihood (ML) receiver for ASK is proposed based on a reduced reversible jump Markov chain Monte Carlo (RRJ-MCMC) algorithm to estimate the probability density function (pdf) of the received signal. The simulation results show that the communication performance of PSK and ASK is improved with the modulation order $M$ decreasing; the performance of non-coherent FSK is improved with the modulation order $M$ increasing. Meanwhile, the performance follows the order of NC-MFSK (M ≥ 8) > BPSK > NC-4FSK > NC-2FSK > 2ASK. For NC-8FSK, when the electron density peak value ${Ne}_{\mathrm {peak}}$ = {2, 4, 6, 8, 10} $\times 10^{18}\,\,\text{m}^{-3}$ , the signal to noise ratio (SNR) required to reduce the bit error rate (BER) to 10−6 are 17, 18, 19, 21, and 34 dB, respectively.

Forecasting Software Using Laplacian AR Model based on Bootstrap-Reversible Jump MCMC: Application on Stock Price Data

The application of the Bootstrap-Metropolis-Hastings algorithm is limited to fixed dimension models. In various fields, data often has a variable dimension model. The Laplacian autoregressive (AR) model includes a variable dimension model so that the Bootstrap-Metropolis-Hasting algorithm cannot be applied. This article aims to develop a Bootstrap reversible jump Markov Chain Monte Carlo (MCMC) algorithm to estimate the Laplacian AR model. The parameters of the Laplacian AR model were estimated using a Bayesian approach. The posterior distribution has a complex structure so that the Bayesian estimator cannot be calculated analytically. The Bootstrap-reversible jump MCMC algorithm was applied to calculate the Bayes estimator. This study provides a procedure for estimating the parameters of the Laplacian AR model. Algorithm performance was tested using simulation studies. Furthermore, the algorithm is applied to the finance sector to predict stock price on the stock market. In general, this study can be useful for decision makers in predicting future events. The novelty of this study is the triangulation between the bootstrap algorithm and the reversible jump MCMC algorithm. The Bootstrap-reversible jump MCMC algorithm is useful especially when the data is large and the data has a variable dimension model. The study can be extended to the Laplacian Autoregressive Moving Average (ARMA) model.

On the Reversible Jump Markov Chain Monte Carlo (RJMCMC) Algorithm for Extreme Value Mixture Distribution as a Location-Scale Transformation of the Weibull Distribution

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.

Bayesian inference for continuous-time hidden Markov models with an unknown number of states

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.

Real-time agent-based crowd simulation with the Reversible Jump Unscented Kalman Filter

Commonly-used data assimilation methods are being adapted for use with agent-based models with the aim of allowing optimisation in response to new data in real-time. However, existing methods face difficulties working with categorical parameters, which are common in agent-based models. This paper presents a new method, the RJUKF, that combines the Unscented Kalman Filter (UKF) data assimilation algorithm with elements of the Reversible Jump (RJ) Markov chain Monte Carlo method. The proposed method is able to conduct data assimilation on both continuous and categorical parameters simultaneously. Compared to similar techniques for mixed state estimation, the RJUKF has the advantage of being efficient enough for online (i.e. real-time) application. The new method is demonstrated on the simulation of a crowd of people traversing a train station and is able to estimate both their current position (a continuous, Gaussian variable) and their chosen destination (a categorical parameter). This method makes a valuable contribution towards the use of agent-based models as tools for the management of crowds in busy places such as public transport hubs, shopping centres, or high streets.

Reversible Jump MCMC for Deghosting in MSPSR Systems.

This paper deals with bistatic track association and deghosting in the classical frequency modulation (FM)-based multi-static primary surveillance radar (MSPSR). The main contribution of this paper is a novel algorithm for bistatic track association and deghosting. The proposed algorithm is based on a hierarchical model which uses the Indian buffet process (IBP) as the prior probability distribution for the association matrix. The inference of the association matrix is then performed using the classical reversible jump Markov chain Monte Carlo (RJMCMC) algorithm with the usage of a custom set of the moves proposed by the sampler. A detailed description of the moves together with the underlying theory and the whole model is provided. Using the simulated data, the algorithm is compared with the two alternative ones and the results show the significantly better performance of the proposed algorithm in such a simulated setup. The simulated data are also used for the analysis of the properties of Markov chains produced by the sampler, such as the convergence or the posterior distribution. At the end of the paper, further research on the proposed method is outlined.

A Robust Approach to the Interest Rate Term Structure Estimation

This paper estimates the interest rate term structures of Treasury and individual corporate bonds using a robust criterion. The Treasury term structure is estimated with Bayesian regression splines based on nonlinear least absolute deviation. The number and locations of the knots in the regression splines are adaptively chosen using the reversible jump Markov chain Monte Carlo method. Due to the small sample size, the individual corporate term structure is estimated by adding a positive parametric credit spread to the estimated Treasury term structure using a Bayesian approach. We present a case study of U.S. Treasury STRIPS (Separate Trading of Registered Interest and Principal of Securities) and AT&T bonds from April 1994 to December 1996. Compared with several existing term structure estimation approaches, the proposed method is robust to outliers in our case study.

Evolution of initiation rites during the Austronesian dispersal.

As adaptive systems, kinship and its accompanying rules have co-evolved with elements of complex societies, including wealth inheritance, subsistence, and power relations. Here we consider an aspect of kinship evolution in the Austronesian dispersal that began from about 5500 BP in Taiwan, reaching Melanesia about 3200 BP, and dispersing into Micronesia by 1500 BP. Previous, foundational work has used phylogenetic comparative methods and ethnolinguistic information to infer matrilocal residence in proto-Austronesian societies. Here we apply Bayesian phylogenetic analyses to a data set on Austronesian societies that combines existing data on marital residence systems with a new set of ethnographic data, introduced here, on initiation rites. Transition likelihoods between cultural-trait combinations were modeled on an ensemble of 1000 possible Austronesian language trees, using Reversible Jump Markov Chain Monte Carlo (RJ-MCMC) simulations. Compared against a baseline phylogenetic model of independent evolution, a phylogenetic model of correlated evolution between female and male initiation rites is substantially more likely (log Bayes factor: 17.9). This indicates, over the generations of Austronesian dispersal, initiation rites were culturally stable when both female and male rites were in the same state (both present or both absent), yet relatively unstable for female-only rites. The results indicate correlated phylogeographic evolution of cultural initiation rites in the prehistoric dispersal of Austronesian societies across the Pacific. Once acquired, male initiation rites were more resilient than female-only rites among Austronesian societies.