Search Results (11)

To investigate deep Earth information, researchers often utilize geomagnetic observatories and satellite data to obtain the conversion function of geomagnetic sounding, C-response data, and employ traditional inversion techniques to reconstruct subsurface structures. However, the traditional gradient-based inversion produces geophysical models with artificial structure constraint enforced subjectively to guarantee a unique solution. This method typically requires the model parameterization knowledge a priori (e.g., based on personal preference) without uncertainty estimation. In this paper, we apply an efficient trans-dimensional (trans-D) Bayesian algorithm to invert C-response data from observatory and satellite geomagnetic data for the electrical conductivity structure of the Earth’s mantle, with the model parameterization treated as unknown and determined by the data. In trans-D Bayesian inversion, the posterior probability density (PPD) represents a complete inversion solution, based on which useful inversion inferences about the model can be made with the requirement of high-dimensional integration of PPD. This is realized by an efficient reversible-jump Markov-chain Monte Carlo (rjMcMC) sampling algorithm based on the birth/death scheme. Within the trans-D Bayesian algorithm, the model parameter is perturbated in the principal-component parameter space to minimize the effect of inter-parameter correlations and improve the sampling efficiency. A parallel tempering scheme is applied to guarantee the complete sampling of the multiple model space. Firstly, the trans-D Bayesian inversion is applied to invert C-response data from two synthetic models to examine the resolution of the model structure constrained by the data. Then, C-response data from geomagnetic satellites and observatories are inverted to recover the global averaged mantle conductivity structure and the local mantle structure with quantitative uncertainty estimation, which is consistent with the data. Full article

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results. Full article

Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions to the marginal likelihood. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach can be employed to jointly sample models and coefficients, but the effective design of the trans-dimensional jumps of RJMCMC can be challenging, making it hard to implement. Alternatively, the marginal likelihood can be derived conditional on latent variables using a data-augmentation scheme (e.g., Pólya-gamma data augmentation for logistic regression) or using other estimation methods. However, suitable data-augmentation schemes are not available for every generalised linear model and survival model, and estimating the marginal likelihood using a Laplace approximation or a correlated pseudo-marginal method can be computationally expensive. In this paper, three main contributions are presented. Firstly, we present an extended Point-wise implementation of Adaptive Random Neighbourhood Informed proposal (PARNI) to efficiently sample models directly from the marginal posterior distributions of generalised linear models and survival models. Secondly, in light of the recently proposed approximate Laplace approximation, we describe an efficient and accurate estimation method for marginal likelihood that involves adaptive parameters. Additionally, we describe a new method to adapt the algorithmic tuning parameters of the PARNI proposal by replacing Rao-Blackwellised estimates with the combination of a warm-start estimate and the ergodic average. We present numerous numerical results from simulated data and eight high-dimensional genetic mapping data-sets to showcase the efficiency of the novel PARNI proposal compared with the baseline add–delete–swap proposal. Full article

The geometric features of ground objects can reflect the shape, contour, length, width, and pixel distribution of ground objects and have important applications in the process of object detection and recognition. However, the geometric features of objects usually present irregular geometric shapes. In order to fit the irregular geometry accurately, this paper proposes the mark clustering point process. Firstly, the random points in the parent process are used to determine the location of the ground object, and the irregular graph constructed by the clustering points in the sub-process is used as the identification to fit the geometry of the ground object. Secondly, assuming that the spectral measurement values of ground objects obey the independent and unified multivalued Gaussian distribution, the spectral measurement model of remote sensing image data is constructed. Then, the geometric extraction model of the ground object is constructed under the framework of Bayesian theory and combined with the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to simulate the posterior distribution and estimate the parameters. Finally, the optimal object extraction model is solved according to the maximum a posteriori (MAP) probability criterion. This paper experiments on color remote sensing images. The experimental results show that the proposed method can not only determine the position of the object but also fit the geometric features of the object accurately. Full article

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. Full article

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. Full article

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. Full article

This paper presents a regionalized segmentation method for synthetic aperture radar (SAR) intensity images based on tessellation with irregular polygons. In the proposed method, the image domain is partitioned into a collection of irregular polygons, which are constructed using sets of nodes and are used to fit homogeneous regions with arbitrary shapes. Each partitioned polygon is taken as the basic processing unit. Assuming the intensities of the pixels in the polygon follow an independent and identical gamma distribution, the likelihood of the image intensities is modeled. After defining the prior distributions of the tessellation and the parameters for the likelihood model, a posterior probability model can be built based on the Bayes theorem as a segmentation model. To obtain optimal segmentation, a reversible-jump Markov chain Monte Carlo (RJMCMC) algorithm is designed to simulate from the segmentation model, where the move operations include updating the gamma distribution parameter, updating labels, moving nodes, merging polygons, splitting polygons, adding nodes, and deleting nodes. Experiments were carried out on synthetic and real SAR intensity images using the proposed method while the regular and Voronoi tessellation-based methods were also preformed for comparison. Our results show the proposed method overcomes some intrinsic limitations of current segmentation methods and is able to generate good results for homogeneous regions with different shapes. Full article

To extract more structural features, which can contribute to segment a synthetic aperture radar (SAR) image accurately, and explore their roles in the segmentation procedure, this paper presents an energy-based SAR image segmentation method with weighted features. To precisely segment a SAR image, multiple structural features are incorporated into a block- and energy-based segmentation model in weighted way. In this paper, the multiple features of a pixel, involving spectral feature obtained from original SAR image, texture and boundary features extracted by a curvelet transform, form a feature vector. All the pixels’ feature vectors form a feature set of a SAR image. To automatically determine the roles of the multiple features in the segmentation procedure, weight variables are assigned to them. All the weight variables form a weight set. Then the image domain is partitioned into a set of blocks by regular tessellation. Afterwards, an energy function and a non-constrained Gibbs probability distribution are used to combine the feature and weight sets to build a block-based energy segmentation model with feature weighted on the partitioned image domain. Further, a reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm is designed to simulate from the segmentation model. In the RJMCMC algorithm, three move types were designed according to the segmentation model. Finally, the proposed method was tested on the SAR images, and the quantitative and qualitative results demonstrated its effectiveness. Full article

Multi-object tracking (MOT), especially by using a moving monocular camera, is a very challenging task in the field of visual object tracking. To tackle this problem, the traditional tracking-by-detection-based method is heavily dependent on detection results. Occlusion and mis-detections will often lead to tracklets or drifting. In this paper, the tasks of MOT and camera motion estimation are formulated as finding a maximum a posteriori (MAP) solution of joint probability and synchronously solved in a unified framework. To improve performance, we incorporate the three-dimensional (3D) relative-motion model into a sequential Bayesian framework to track multiple objects and the camera’s ego-motion estimation. A 3D relative-motion model that describes spatial relations among objects is exploited for predicting object states robustly and recovering objects when occlusion and mis-detections occur. Reversible jump Markov chain Monte Carlo (RJMCMC) particle filtering is applied to solve the posteriori estimation problem. Both quantitative and qualitative experiments with benchmark datasets and video collected on campus were conducted, which confirms that the proposed method is outperformed in many evaluation metrics. Full article

We describe the use of Bayesian inference techniques, notably Markov chain Monte Carlo (MCMC) and reversible jump MCMC (RJMCMC) methods, to recover forest structural and biochemical parameters from multispectral LiDAR (Light Detection and Ranging) data. We use a variable dimension, multi-layered model to represent a forest canopy or tree, and discuss the recovery of structure and depth profiles that relate to photochemical properties. We first demonstrate how simple vegetation indices such as the Normalized Differential Vegetation Index (NDVI), which relates to canopy biomass and light absorption, and Photochemical Reflectance Index (PRI) which is a measure of vegetation light use efficiency, can be measured from multispectral data. We further describe and demonstrate our layered approach on single wavelength real data, and on simulated multispectral data derived from real, rather than simulated, data sets. This evaluation shows successful recovery of a subset of parameters, as the complete recovery problem is ill-posed with the available data. We conclude that the approach has promise, and suggest future developments to address the current difficulties in parameter inversion. Full article