Reversible Jump Research Articles

METODE REVERSIBLE JUMP MARKOV CHAIN MONTE CARLO UNTUK ESTIMASI BAYESIAN DALAM MODEL REGRESI LINEAR PER POTONGAN

The method used to estimate the parameters of piecewise linear regression is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems are proposed the Reversible Jump MCMC Algorithm. Reversible Jump MCMC Algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters of piecewise linear regression models.Bayes estimator for the parameters of piecewise linear regression models obtained by the Markov chain.

PEMILIHAN MODEL DAN ESTIMASI PARAMETER BAYESIAN HIRARKI UNTUK MODEL SUBSET ARMA MENGGUNAKAN ALGORITMA REVERSIBLE JUMP SIMULATED ANNEALING MCMC

If the Subset ARMA models fitted to real data, then the true value of the order and model parameters are often unknown. The purpose of this paper is to find an estimator-estimator for the order and parameters of the model based on the data. In this paper, the identification of order and subset ARMA model parameter estimation is done in a hierarchical Bayesian framework. Within this framework, the order and model parameters are assumed distributed priors. All order information about the characteristics and parameters of the model then expressed in the posterior distribution. Determination of the probability of the order and parameters of the posterior models requires the integration of the resulting posterior distribution, is an operation which is very difficult to do analytically. Here the algorithm Reversible Jump MCMC Simulated Annealing developed to perform the necessary integration through simulated posterior distribution.

Nonparametric Bayesian Attributed Scattering Center Extraction for Synthetic Aperture Radar Targets

As a good way to represent target backscatter measured by high-frequency synthetic aperture radar (SAR) systems, the attributed scattering center (ASC) model is able to provide concise and physically relevant features of a complex target and has played an important role in model-based automatic target recognition (ATR). However, most existing ASC feature extraction methods suffer from imprecise image segmentation or high computational cost, which greatly encumber their practical applications. To tackle this problem, we present a novel ASC feature extraction algorithm for SAR targets based on Levy random fields in a nonparametric Bayesian framework. Specifically, Levy random fields, yielding a natural sparse representation of the unknown ASC model, are introduced to construct prior distributions, which lead to the specification of a joint prior distribution for the number of ASCs and the ASC associated parameters. Meanwhile, the problem may be formulated as a sparse representation problem, with regularization induced through the Levy random field prior. We also develop a reversible jump Markov chain Monte Carlo (RJ-MCMC) method to enable relatively fast posterior inference. Experimental results confirm the effectiveness and efficiency of the proposed algorithm.

Velocity log upscaling based on reversible jump Markov chain Monte Carlo simulated annealing

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.

COUPLING REGULAR TESSELLATION WITH RJMCMC ALGORITHM TO SEGMENT SAR IMAGE WITH UNKNOWN NUMBER OF CLASSES

Abstract. 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.

COUPLING REGULAR TESSELLATION WITH RJMCMC ALGORITHM TO SEGMENT SAR IMAGE WITH UNKNOWN NUMBER OF CLASSES

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.

NETWORK DETECTION IN RASTER DATA USING MARKED POINT PROCESSES

Abstract. We propose a new approach for the automatic detection of network structures in raster data. The model for the network structure is represented by a graph whose nodes and edges correspond to junction-points and to connecting line segments, respectively; nodes and edges are further described by certain parameters. We embed this model in the probabilistic framework of marked point processes and determine the most probable configuration of objects by stochastic sampling. That is, different graph configurations are constructed randomly by modifying the graph entity parameters, by adding and removing nodes and edges to/ from the current graph configuration. Each configuration is then evaluated based on the probabilities of the changes and an energy function describing the conformity with a predefined model. By using the Reversible Jump Markov Chain Monte Carlo sampler, a global optimum of the energy function is determined. We apply our method to the detection of river and tidal channel networks in digital terrain models. In comparison to our previous work, we introduce constraints concerning the flow direction of water into the energy function. Our goal is to analyse the influence of different parameter settings on the results of network detection in both, synthetic and real data. Our results show the general potential of our method for the detection of river networks in different types of terrain.

NETWORK DETECTION IN RASTER DATA USING MARKED POINT PROCESSES

We propose a new approach for the automatic detection of network structures in raster data. The model for the network structure is represented by a graph whose nodes and edges correspond to junction-points and to connecting line segments, respectively; nodes and edges are further described by certain parameters. We embed this model in the probabilistic framework of marked point processes and determine the most probable configuration of objects by stochastic sampling. That is, different graph configurations are constructed randomly by modifying the graph entity parameters, by adding and removing nodes and edges to/ from the current graph configuration. Each configuration is then evaluated based on the probabilities of the changes and an energy function describing the conformity with a predefined model. By using the Reversible Jump Markov Chain Monte Carlo sampler, a global optimum of the energy function is determined. We apply our method to the detection of river and tidal channel networks in digital terrain models. In comparison to our previous work, we introduce constraints concerning the flow direction of water into the energy function. Our goal is to analyse the influence of different parameter settings on the results of network detection in both, synthetic and real data. Our results show the general potential of our method for the detection of river networks in different types of terrain.

SAR IMAGE SEGMENTATION WITH UNKNOWN NUMBER OF CLASSES COMBINED VORONOI TESSELLATION AND RJMCMC ALGORITHM

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 <i>a priori</i>, 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.

SAR IMAGE SEGMENTATION WITH UNKNOWN NUMBER OF CLASSES COMBINED VORONOI TESSELLATION AND RJMCMC ALGORITHM

Abstract. 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.

Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent.

The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation.

Smart pilot points using reversible‐jump Markov‐chain Monte Carlo

AbstractPilot points are typical means for calibration of highly parameterized numerical models. We propose a novel procedure based on estimating not only the pilot point values, but also their number and suitable locations. This is accomplished by a trans‐dimensional Bayesian inversion procedure that also allows for uncertainty quantification. The utilized algorithm, reversible‐jump Markov‐Chain Monte Carlo (RJ‐MCMC), is computationally demanding and this challenges the application for model calibration. We present a solution for fast, approximate simulation through the application of a Bayesian inversion. A fast pathfinding algorithm is used to estimate tracer travel times instead of doing a full transport simulation. This approach extracts the information from measured breakthrough curves, which is crucial for the reconstruction of aquifer heterogeneity. As a result, the “smart pilot points” can be tuned during thousands of rapid model evaluations. This is demonstrated for both a synthetic and a field application. For the selected synthetic layered aquifer, two different hydrofacies are reconstructed. For the field investigation, multiple fluorescent tracers were injected in different well screens in a shallow alluvial aquifer and monitored in a tomographic source‐receiver configuration. With the new inversion procedure, a sand layer was identified and reconstructed with a high spatial resolution in 3‐D. The sand layer was successfully validated through additional slug tests at the site. The promising results encourage further applications in hydrogeological model calibration, especially for cases with simulation of transport.

Prior specification of neighbourhood and interaction structure in binary Markov random fields

We formulate a prior distribution for the energy function of stationary binary Markov random fields (MRFs) defined on a rectangular lattice. In the prior we assign distributions to all parts of the energy function. In particular we define priors for the neighbourhood structure of the MRF, what interactions to include in the model, and for potential values. We define a reversible jump Markov chain Monte Carlo (RJMCMC) procedure to simulate from the corresponding posterior distribution when conditioned to an observed scene. Thereby we are able to learn both the neighbourhood structure and the parametric form of the MRF from the observed scene. We circumvent evaluations of the intractable normalising constant of the MRF when running the RJMCMC 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.

JAM: A Scalable Bayesian Framework for Joint Analysis of Marginal SNP Effects.

ABSTRACTRecently, large scale genome‐wide association study (GWAS) meta‐analyses have boosted the number of known signals for some traits into the tens and hundreds. Typically, however, variants are only analysed one‐at‐a‐time. This complicates the ability of fine‐mapping to identify a small set of SNPs for further functional follow‐up. We describe a new and scalable algorithm, joint analysis of marginal summary statistics (JAM), for the re‐analysis of published marginal summary stactistics under joint multi‐SNP models. The correlation is accounted for according to estimates from a reference dataset, and models and SNPs that best explain the complete joint pattern of marginal effects are highlighted via an integrated Bayesian penalized regression framework. We provide both enumerated and Reversible Jump MCMC implementations of JAM and present some comparisons of performance. In a series of realistic simulation studies, JAM demonstrated identical performance to various alternatives designed for single region settings. In multi‐region settings, where the only multivariate alternative involves stepwise selection, JAM offered greater power and specificity. We also present an application to real published results from MAGIC (meta‐analysis of glucose and insulin related traits consortium) – a GWAS meta‐analysis of more than 15,000 people. We re‐analysed several genomic regions that produced multiple significant signals with glucose levels 2 hr after oral stimulation. Through joint multivariate modelling, JAM was able to formally rule out many SNPs, and for one gene, ADCY5, suggests that an additional SNP, which transpired to be more biologically plausible, should be followed up with equal priority to the reported index.

The Ostomachion Process

Stochastic partition processes for exchangeable graphs produce axis-aligned blocks on a product space. In relational modeling, the resulting blocks uncover the underlying interactions between two sets of entities of the relational data. Although some flexible axis-aligned partition processes, such as the Mondrian process, have been able to capture complex interacting patterns in a hierarchical fashion, they are still in short of capturing dependence between dimensions. To overcome this limitation, we propose the Ostomachion process (OP), which relaxes the cutting direction by allowing for oblique cuts. The partitions generated by an OP are convex polygons that can capture inter-dimensional dependence. The OP also exhibits interesting properties: 1) Along the time line the cutting times can be characterized by a homogeneous Poisson process, and 2) on the partition space the areas of the resulting components comply with a Dirichlet distribution. We can thus control the expected number of cuts and the expected areas of components through hyper-parameters. We adapt the reversible-jump MCMC algorithm for inferring OP partition structures. The experimental results on relational modeling and decision tree classification have validated the merit of the OP.

Bayesian Multiple Change Point Estimation of Poisson Rates in Control Charts

Effectiveness of root cause analysis efforts, following a control chart signal, will be enhanced if there exist more accurate information about the true time of the change in the process. In this study, we consider a Poisson process ex- periencing an unknown multiple number of step changes in the Poisson rate. We formulate the multiple change point scenario using Bayesian hierarchical models. We compute posterior distributions of the change point parameters including number, location and magnitude of changes and also corresponding probabilistic intervals and inferences through Reversible Jump Markov Chain Monte Carlo methods. The performance of the Bayesian estimator is investi- gated over several simulated change point scenarios. Results show that when the proposed Bayesian estimator is used in conjunction with the c-chart, it can provide precise estimates about the underlying change point scenario (number, timing, direction and size of step changes). In comparison with alternatives including Poisson EWMA and CUSUM built-in estimators and a maximum likelihood estimator, our estimator performs satisfactorily over consecutive monotonic and non-monotonic changes. The proposed Bayesian model and computation framework also benefit of probability quantification as well as flexibility which allows us to formulate other process types and change scenarios.

A new online anomaly learning and detection for large-scale service of Internet of Thing

The online anomaly detection has been propounded as the key idea of monitoring fault of large-scale sensor nodes in Internet of Things. Now, the exciting progresses of research have been made in online anomaly detection area. However, the highly dynamic distributing character of Internet of Things makes the anomaly detection scheme difficult to be used in online manner. This paper presents a new online anomaly learning and detection mechanism for large-scale service of Internet of Thing. Firstly, our model uses the reversible-jump MCMC learning to online learn anomaly-free of dynamics network and service data. Next, we perform a structural analysis of IoT-based service topology by network utility maximization theory. The results of experiment demonstrate the method accuracy in forecasting dynamics network and service structures from synthetic data.

A GRAPH BASED MODEL FOR THE DETECTION OF TIDAL CHANNELS USING MARKED POINT PROCESSES

Abstract. 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.

Dynamics of Real Per Capita GDP

This study investigates the dynamics of quarterly real GDP per capita growth rates across four countries, the US, UK, Canada and France. I obtain estimates for ARIMA(p,q) processes for first differences of log quarterly real GDP per capita using Reversible Jump Markov Chain Monte Carlo, allowing me to account for model uncertainty when comparing the implied impulse responses across countries. The results are checked for robustness with respect to the detrending device. The estimated impulse response functions are different in shape. The persistence estimates for the US, France, Canada and Italy are clustered together, while the UK and Japan are clear outliers. Significant posterior uncertainty remains regarding the persistence estimates and the appropriate ARMA models. The results for the UK is sensitive to the time period. An analysis of the components of GDP for the US suggests that the dynamics are mainly driven by consumption.

An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations.

Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient ‘global’ proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently.