Search

We consider the problem of ascertaining daily patterns using passive sensors to establish a baseline for elderly people living alone. The data are whether or not some movement, or human related activity, has occurred in the previous 15 min. We seek to segment the broad patterns within a day, for example, awake/sleep times or potentially more activity around meal-times. To address this problem we use changepoint detection which can segment the day into more/less active times. Traditional changepoint detection methods are inappropriate for these data as they fail to utilize the periodic nature of the data. The traditional assumption of conditional independence of the segments also hampers estimation of the within segment parameters. A new within-period changepoint detection scheme is proposed that instead assumes a circular perspective of the time axis. This permits the pooling of evidence of changepoint events from across multiple days. Inference is performed within the Bayesian framework by utilizing the reversible jump Markov chain Monte Carlo sampler to explore the variable dimension parameter space. Simulations demonstrate that the sampler achieves high accuracy in approximating the posterior while being able to detect small segments. Application to four individuals from our industrial collaborator provides insights to their daily patterns.

Hidden Markov models (HMMs) are widely used to analyze heterogeneous longitudinal data owing to their capability to model dynamic heterogeneity. Early advancements in HMMs have mainly assumed that the number of hidden states is fixed and predetermined based on the knowledge of the subjects or a certain criterion. However, as a limitation, this approach determines the number of hidden states on a pairwise basis, which becomes increasingly tedious when the state space is enlarged. Moreover, criterion-based statistics tend to select complex models with overestimated numbers of components in mixture modeling. A full Bayesian approach is developed to analyze hidden Markov structural equation models with an unknown number of hidden states. An efficient and hybrid algorithm that combines the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm, the forward filtering and backward sampling scheme, and the Metropolis-Hastings algorithm is proposed to simultaneously select the number of hidden states and perform parameter estimation. The simulation study shows the satisfactory performance of the proposed method. Two real datasets collected from the UCLA Drug Abuse Research Center and National Longitudinal Survey of Youth are analyzed.

Our article deals with the detection and model generation of complex objects with curvilinear parts, like trees, with stochastic relaxation. The proposed algorithm can rely on any initial estimation of object parts as a probability map (like those generated by Gaussian mixture models or neural networks) and can model the relation of randomly sampled parts resulting in a structural representation of whole objects. Semantic segmentation by convolutional neural networks or the pose estimation with deep learning of object parts can predict the possible areas or positions of interest, but in many cases, a higher representation of structures is needed for further (e.g., shape or connectivity) analysis. The model validation of such data is straightforward for objects with known structure (like the human body or other rigid things) but tough for such complex objects like trees in forest environments. In our approach, the possible configurations of structures are generated by a marked point process while the optimal state is achieved by a solver based on reversible jump Markov chain Monte Carlo dynamics. The model generator relaxation method itself is unsupervised, no training is required, and our analyses show it has satisfactory stability, regarding detection accuracy, against changing its parameters. Besides giving the theoretical background and algorithmic steps, we present numerical evaluations on three datasets: synthetic trees, another of natural images with different species of trees in various forest environments, and the third is of road maps. The analyzed examples show that our approach, contrary to previous thin line detectors, can handle thin and thick objects.

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.

To address the need for efficient inference for a range of hydrological extreme value problems, spatial pooling of information is the standard approach for marginal tail estimation. We propose the first extreme value spatial clustering methods which account for both the similarity of the marginal tails and the spatial dependence structure of the data to determine the appropriate level of pooling. Spatial dependence is incorporated in two ways: to determine the cluster selection and to account for dependence of the data over sites within a cluster when making the marginal inference. We introduce a statistical model for the pairwise extremal dependence which incorporates distance between sites, and accommodates our belief that sites within the same cluster tend to exhibit a higher degree of dependence than sites in different clusters. We use a Bayesian framework which learns about both the number of clusters and their spatial structure, and that enables the inference of site-specific marginal distributions of extremes to incorporate uncertainty in the clustering allocation. The approach is illustrated using simulations, the analysis of daily precipitation levels in Norway and daily river flow levels in the UK., Comment: 41

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.

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.

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.

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.

Network inference has been attracting increasing attention in several fields, notably systems biology, control engineering and biomedicine. To develop a therapy, it is essential to understand the connectivity of biochemical units and the internal working mechanisms of the target network. A network is mainly characterized by its topology and internal dynamics. In particular, sparse topology and stable system dynamics are fundamental properties of many real-world networks. In recent years, kernel-based methods have been popular in the system identification community. By incorporating empirical Bayes, this framework, which we call KEB, is able to promote system stability and impose sparse network topology. Nevertheless, KEB may not be ideal for topology detection due to local optima and numerical errors. Here, therefore, we propose an alternative, data-driven, method that is designed to greatly improve inference accuracy, compared with KEB. The proposed method uses dynamical structure functions to describe networks so that the information of unmeasurable nodes is encoded in the model. A powerful numerical sampling method, namely reversible jump Markov chain Monte Carlo (RJMCMC), is applied to explore full Bayesian models effectively. Monte Carlo simulations indicate that our approach produces more accurate networks compared with KEB methods. Furthermore, simulations of a synthetic biological network demonstrate that the performance of the proposed method is superior to that of the state-of-the-art method, namely iCheMA. The implication is that the proposed method can be used in a wide range of applications, such as controller design, machinery fault diagnosis and therapy development.

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.

Reversible jump Markov chain Monte Carlo (RJMCMC) is a powerful Bayesian trans-dimensional algorithm for performing model selection while inferring the distribution of model parameters. The present work introduces CU-MSDSp as an open source and fully automated parallel RJMCMC implementation that aims to increase the accessibility of RJMCMC to practitioners. CU-MSDSp begins by independently forming Markov Chains to approximate the posterior distribution of each model’s parameters. These approximations are then used to estimate the posterior distribution of the model space. This embarrassingly parallelizable software eliminates the need of designing a trans-dimensional proposal distribution and Jacobian all while ensuring the same theoretical guarantees as the non-parallel RJMCMC algorithm. Finally, CU-MSDSp enables practitioners to rely on their previous knowledge of fixed dimension MCMC convergence assessment and simulation design.

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.

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.

Summary Ambient-noise surface wave tomography has proven to be an effective tool for 3D crustal imaging. Conventionally, a two-step inversion approach is adopted. That is, a first inversion results in separate, frequency-dependent 2D surface-wave velocity maps, upon which local frequency-to-depth inversions are performed. In our case, phase velocities are used. A one-step 3D non-linear algorithm has recently been proposed in a Bayesian framework using reversible jump Markov chain Monte Carlo which is called transdimensional tomography. This approach has a number of advantages over the two-step approach with the most notable being the fact that the one-step approach preserves spatial correlation information in 3D. The 3D volume is parameterized using a polyhedral Voronoi tessellation. Here, we investigate the feasibility of using this transdimensional algorithm to recover the 3D seismic velocity structure below the Reykjanes peninsula, SW Iceland. To that end, we design synthetic tests using the station configuration of Reykjanes seismic network, which has been recording the field data. We show that the algorithm successfully recovers the 3D velocity structure of the area. This work is a first step towards 3D non-linearized surface-wave tomography using the field data recorded by the stations of the Reykjanes seismic network.

In several scientific fields, like bioinformatics, financial and macro-economics, important theoretical and practical issues exist that involve multimodal data distributions. We propose a Bayesian approach using mixtures distributions to approximate accurately such data distributions. Shape and other features of the mixture approximations are estimated including their uncertainty. For discrete data, we introduce a novel mixture of shifted Poisson distributions with an unknown number of components, which overcomes the equidispersion restriction in the standard Poisson which accomodates a wide range of shapes such as multimodality and long tails. Our simulation-based Bayesian inference treats the density features as random variables and highest credibility regions around features are easily obtained. For discrete data we develop an adapted version of the Reversible Jump Markov Chain Monte Carlo (RJMCMC) method, which allows for an unknown number of components instead of the more restrictive approach of choosing a particular number of mixture components using information criteria. Using simulated data, we show that our approach works successfully for three issues that one encounters during the estimation of mixtures: label switching; mixture complexity and prior information and mode membership versus component membership. The proposed method is applied to three empirical data sets: The count data method yields a novel perspective of the data on DNA tandem repeats in \cite{DNA_leiden}; the bimodal distribution of payment details of clients obtaining a loan from a financial institution in Spain in 1990 gives insight into the repayment ability of individual clients; and the distribution of the modes of real GDP growth data from the PennWorld Tables and their evolution over time explores possible world-wide economic convergence as well as group convergence between the US and European countries. The results of our descriptive analysis may be used as input for forecasting and policy analysis.

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.

Summary Seismic surface wave tomography is an effective tool for 3D crustal imaging. Conventionally, a two-step inversion algorithm is used to recover a three-dimensional model of surface wave velocity. That is, starting from surface wave dispersion data (frequency-dependent phase velocities), an initial inversion resulting in a series of (2D) maps of frequency-dependent surface-wave velocity is followed by a separate (1D) depth inversion. A single-step 3D non-linear algorithm has recently been proposed in a Bayesian framework. The algorithm involves a reversible jump Markov chain Monte Carlo approach and is referred to transdimensional tomography. Here, we investigate the feasibility of this transdimensional algorithm for the purpose of recovering the 3D surface wave velocity structure below the Reykjanes Peninsula, southwest Iceland. In particular, we investigate this for the specific receiver configuration for which we have obtained year-long recordings of ambient seismic noise. To that end, we designed a number of synthetic tests using receiver-receiver travel times associated with that station configuration. We find that the transdimensional algorithm successfully recovers the 3D velocity structure of the area. In particular, the algorithm successfully adapts its resolution to the density of rays and the level of data noise. Moreover, quantified solution uncertainty makes the result better interpretable.

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.

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.

This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del Moral et al., 2006, 2007), making use of the full flexibility of this framework in order that the method is computationally efficient. In particular, we introduce 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 (RJMCMC) is low. We demonstrate this approach on the well-studied problem of model comparison for mixture models, and for the novel application of inferring coalescent trees sequentially, as data arrives.

International audience; We present a novel method for the joint inversion of thermal indicator data (vitrinite reflectance and apatite fission track) and additional data (bottom-hole temperature and porosity) for thermal history reconstruction in basin modeling. A transdimensional and hierarchical Bayesian formulation is implemented with a reversible jump Markov chain Monte Carlo algorithm, with a 1-D transient thermal model. The objective of the inverse problem is to infer the heat flow history below a borehole given the data and a set of geological constraints (e.g., burial histories and physical properties of the sediments). The algorithm incorporates an adaptive, data-driven parametrization of the heat flow history, allows for automatic estimation of the relative importance of each data type and quantification of parameter uncertainties and trade-offs. Our approach deals with uncertainties on the imposed geological constraints in two ways. First, the amount of erosion and timing of an erosional event are treated as independent parameters. Second, uncertainties on compaction parameters and surface temperature history are directly propagated into the final solution. Synthetic tests show that porosity data can be used to reduce uncertainties on the amount of erosion. This work illustrates a truly probabilistic analysis of the trade-off between the magnitude of erosion and variations in heat flow histories which is key in basin modeling. The algorithm is then applied to real data from a well in the Barents Sea. Our algorithm can reconcile estimates of erosion from the thermal indicator and porosity data, which is a difficult and subjective task in basin modeling.

Many countries were the target of air strikes during World War II. Numerous unexploded bombs still exist in the ground. These duds can be tracked down with the help of bomb craters, indicating areas where unexploded bombs may be located. Such areas are documented in so-called impact maps based on detected bomb craters. In this paper, a stochastic approach based on marked point processes (MPPs) for the automatic detection of bomb craters in aerial images taken during World War II is presented. As most areas are covered by multiple images, the influence of redundant image information on the object detection result is investigated: we compare the results generated based on single images with those obtained by our new approach that combines the individual detection results of multiple images covering the same location. The object model for the bomb craters is represented by circles. Our MPP approach determines the most likely configuration of objects within the scene. The goal is reached by minimizing an energy function that describes the conformity with a predefined model by Reversible Jump Markov Chain Monte Carlo sampling in combination with simulated annealing. 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 show a significant improvement with respect to its quality when redundant image information is used.

We develop efficient Bayesian inference for the one-factor copula model with two significant contributions over existing methodologies. First, our approach leads to straightforward inference on dependence parameters and the latent factor; only inference on the former is available under frequentist alternatives. Second, we develop a reversible jump Markov chain Monte Carlo algorithm that averages over models constructed from different bivariate copula building blocks. Our approach accommodates any combination of discrete and continuous margins. Through extensive simulations, we compare the computational and Monte Carlo efficiency of alternative proposed sampling schemes. The preferred algorithm provides reliable inference on parameters, the latent factor, and model space. The potential of the methodology is highlighted in an empirical study of 10 binary measures of socio-economic deprivation collected for 11,463 East Timorese households. The importance of conducting inference on the latent factor i...

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.

Target geometrical reconstruction from multi-dimensional SAR(synthetic aperture radar) images is very important for target recognition and scene understanding. This paper proposes a novel geometric reconstruction method for man-made targets based on scattering primitives, e.g., plate, cylinder, dihedral, trihedral and so on. Non-parametric Bayesian learning is employed to optimize the scatterer parameters into an integral computation. The Bayesian learning can extract scattering primitives of targets via a reversible jump Markov chain Monte Carlo strategy. Experimental results of two models demonstrate good feasibility of the proposed method.

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.

We applied a transdimensional stochastic inversion algorithm, reversible jump Markov chain Monte Carlo (rjMCMC), to angle-stack seismic inversion for characterization of reservoir acoustic and shear impedance with uncertainty quantification. The rjMCMC is able to infer the number of parameters for the model as well as the parameter values. In our case, the number of parameters depends on the number of model layers for a given data set. We also use this method in uncertainty quantification because a transdimensional sampling helps prevent underparameterization or strong overparameterization. An ensemble of models with proper parameterization can improve parameter estimation and uncertainty quantification. Our new results in uncertainty analysis indicate that (1) the uncertainty in seismic inversion, including uncertainty in earth properties and their locations, is related to the discontinuity of property across an interface, and (2) there is a trade-off between property uncertainty and location uncertainty. A stronger discontinuity will induce more property uncertainty but less location uncertainty at the discontinuity interface. Therefore, we further use the inversion uncertainty as a novel seismic attribute to assist in delineation of subsurface discontinuity interfaces and quantify the magnitude of the discontinuities, which further facilitates quantitative interpretation and stratigraphic interpretation.

We present a discrete reversible jump Markov Chain Monte Carlo (rjMCMC) algorithm to build lane accurate maps by solving a partition problem. Our algorithm finds lane middle axes by 2D cubic Hermite splines least squares alignment to trajectory clusters. The steps of the rjMCMC optimization are designed to change the number of clusters and the trajectory assignment. Furthermore, we introduce our tracking approach, which is used to generate our trajectory data base by tracking vehicles in Velodyne LiDAR scans at several junctions in Hannover, Germany. We validate our results by comparing them to a manually generated ground truth map, based on LiDAR mobile mapping data, and a manually generated reference map on base of the trajectory data to evaluate our result by ignoring accuracy errors of the tracking process. Finally, we show the transferability of our approach by applying it to datasets from the map construction data base.

The goal of constructing models from examples has been approached from different perspectives. Statistical methods have been widely used and proved effective in generating accurate models. Finite Gaussian mixture models have been widely used to describe a wide variety of random phenomena and have played a prominent role in many attempts to develop expressive statistical models in machine learning. However, their effectiveness is limited to applications where underlying modeling assumptions (e.g., the per-components densities are Gaussian) are reasonably satisfied. Thus, much research efforts have been devoted to developing better alternatives. In this paper, we focus on constructing statistical models from positive vectors (i.e., vectors whose elements are strictly greater than zero) for which the generalized inverted Dirichlet (GID) mixture has been shown to be a flexible and powerful parametric framework. In particular, we propose a Bayesian density estimation method based upon mixtures of GIDs. The consideration of Bayesian learning is interesting in several respects. It allows to take uncertainty into account by introducing prior information about the parameters, it allows simultaneous parameters estimation and model selection, and it allows to overcome learning problems related to over- or under-fitting. Indeed, we develop a reversible jump Markov Chain Monte Carlo sampler for GID mixtures that we apply for simultaneous clustering and feature selection in the context of some challenging real-world applications concerning scene classification, action recognition, and video forgery detection.

This paper presents a new computer code developed to solve the 1D magnetotelluric (MT) inverse problem using a Bayesian trans-dimensional Markov chain Monte Carlo algorithm. MT data are sensitive to the depth-distribution of rock electric conductivity (or its reciprocal, resistivity). The solution provided is a probability distribution - the so-called posterior probability distribution (PPD) for the conductivity at depth, together with the PPD of the interface depths. The PPD is sampled via a reversible-jump Markov Chain Monte Carlo (rjMcMC) algorithm, using a modified Metropolis-Hastings (MH) rule to accept or discard candidate models along the chains. As the optimal parameterization for the inversion process is generally unknown a trans-dimensional approach is used to allow the dataset itself to indicate the most probable number of parameters needed to sample the PPD. The algorithm is tested against two simulated datasets and a set of MT data acquired in the Clare Basin (County Clare, Ireland). For the simulated datasets the correct number of conductive layers at depth and the associated electrical conductivity values is retrieved, together with reasonable estimates of the uncertainties on the investigated parameters. Results from the inversion of field measurements are compared with results obtained using a deterministic method and with well-log data from a nearby borehole. The PPD is in good agreement with the well-log data, showing as a main structure a high conductive layer associated with the Clare Shale formation. In this study, we demonstrate that our new code go beyond algorithms developend using a linear inversion scheme, as it can be used: (1) to by-pass the subjective choices in the 1D parameterizations, i.e. the number of horizontal layers in the 1D parameterization, and (2) to estimate realistic uncertainties on the retrieved parameters. The algorithm is implemented using a simple MPI approach, where independent chains run on isolated CPU, to take full advantage of parallel computer architectures. In case of a large number of data, a master/slave appoach can be used, where the master CPU samples the parameter space and the slave CPUs compute forward solutions.

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.

Multivariate heterogenous data with latent variables are common in many fields such as biological, medical, behavioral, and social-psychological sciences. Mixture structural equation models are multivariate techniques used to examine heterogeneous interrelationships among latent variables. In the analysis of mixture models, determination of the number of mixture components is always an important and challenging issue. This article aims to develop a full Bayesian approach with the use of reversible jump Markov chain Monte Carlo method to analyze mixture structural equation models with an unknown number of components. The proposed procedure can simultaneously and efficiently select the number of mixture components and conduct parameter estimation. Simulation studies show the satisfactory empirical performance of the method. The proposed method is applied to study risk factors of osteoporotic fractures in older people.