Structured sparse BAYESIAN hyperspectral compressive sensing using spectral unmixing

Airport air traffic is one of the most important and hardest one among all the airport data forecasts. In this paper, the Markov Chain Monte Carlo (MCMC) method of applied theory of statistics has been introduced into the aviation sector, and the discussion on airport air traffic forecast has been conducted taking Shanghai airport as the application background. MCMC method is designed to solve the problem parameters expectations where some baysian inference can not be directly calculated. This paper conducts the iterative computation using WinBUGS, EViews is used to estimate the initial iteration parameter of the regression model, and it is on this basis that the regression equation under the MCMC method is obtained.

Markov chain Monte Carlo (MCMC) methods offer a rapid parametric approach that can test for linkage throughout the entire genome. It has an advantage similar to nonparametric methods in that the model does not have to be completely specified a priori. However, unlike nonparametric methods, there are no limitations on pedigree size and MCMC methods can also handle relatively complex pedigree structures. In addition MCMC methods can be used to carry segregation analysis in order to answer questions on the genetic components of a disease phenotype. Segregation analysis gave evidence for between two and eight alcoholism susceptibility loci, each having a modest effect on the phenotype. MCMC methods were used to map alcoholism loci using the phenotypes ALDX1 (DSM-III-R and Feighner criteria) and ALDX2 (World Health Organization diagnosis ICD-10 criteria). There was mild evidence for quantitative trait loci on chromosomes 2, 10, and 11.

This paper presents an overview of Markov Chain Monte Carlo (MCMC) methods for statistical inference and applications. The article begins by describing ordinary Monte Carlo methods, which in principle has the same goals as the MCMC but can hardly be implemented in practice. Following that basic Markov Chain Monte Carlo is discussed, which is founded on the Hastings algorithm and includes Metropolis method and the Gibbs sampler as special cases. Finally, various special applications of Markov Chain Monte Carlo methods are briefly mentioned and some recent development of MCMC are covered in final remarks section.KeywordsReal EstateMarkov Chain Monte CarloGibbs SamplerDetailed BalanceMarkov Chain Monte Carlo MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The maximum likelihood and Bayesian approaches for parameter estimations and prediction of future record values have been considered for the two-parameter Burr Type XII distribution based on record values with the number of trials following the record values (inter-record times). Firstly, the Bayes estimates are obtained based on a joint bivariate prior for the shape parameters. In this case, the Bayes estimates of the parameters have been developed by using Lindley's approximation and the Markov Chain Monte Carlo (MCMC) method due to the lack of explicit forms under the squared error and the linear-exponential loss functions. The MCMC method has been also used to construct the highest posterior density credible intervals. Secondly, the Bayes estimates are obtained with respect to a discrete prior for the first shape parameter and a conjugate prior for other shape parameter. The Bayes and the maximum likelihood estimates are compared in terms of the estimated risk by the Monte Carlo simulations. We further consider the non-Bayesian and Bayesian prediction for future lower record arising from the Burr Type XII distribution based on record data. The comparison of the derived predictors is carried out by using Monte Carlo simulations. A real data are analysed for illustration purposes.

PurposeThe application of statistical inversion theory provides a powerful approach for solving estimation problems including the ability for uncertainty quantification (UQ) by means of Markov chain Monte Carlo (MCMC) methods and Monte Carlo integration. This paper aims to analyze the application of a state reduction technique within different MCMC techniques to improve the computational efficiency and the tuning process of these algorithms.Design/methodology/approachA reduced state representation is constructed from a general prior distribution. For sampling the Metropolis Hastings (MH) Algorithm and the Gibbs sampler are used. Efficient proposal generation techniques and techniques for conditional sampling are proposed and evaluated for an exemplary inverse problem.FindingsFor the MH-algorithm, high acceptance rates can be obtained with a simple proposal kernel. For the Gibbs sampler, an efficient technique for conditional sampling was found. The state reduction scheme stabilizes the ill-posed inverse problem, allowing a solution without a dedicated prior distribution. The state reduction is suitable to represent general material distributions.Practical implicationsThe state reduction scheme and the MCMC techniques can be applied in different imaging problems. The stabilizing nature of the state reduction improves the solution of ill-posed problems. The tuning of the MCMC methods is simplified.Originality/valueThe paper presents a method to improve the solution process of inverse problems within the Bayesian framework. The stabilization of the inverse problem due to the state reduction improves the solution. The approach simplifies the tuning of MCMC methods.

To meet the goal of tenfold increase in spectral efficiency, interference cancellation and multiuser detection are expected to be important tasks of fifth-generation (5G) radio access systems. Both tasks can be realized by joint detection algorithms. However, joint detection algorithms such as maximum likelihood (ML) detection have a high computational complexity. Previous works have shown that joint detectors based on Markov chain Monte Carlo (MCMC) methods can achieve similar results compared to ML detection with a large reduction in the computational complexity for systems with a large number of streams or users. The purpose of this work is to present a MIMO joint detector based on MCMC methods and evaluate it within the constraints of LTE Advanced (LTE-A), namely, using at most 8 transmit antennas and 64-QAM modulation. The evaluation is done separately from the channel decoder. Moreover, the complexity of the presented algorithm is compared to the one of an ML detector. The results show that the proposed MIMO detector offers a similar detection error rate compared to an ML detector. Furthermore, it was observed that the complexity reduction is significant for systems with more than six transmit antennas.

When a Markov Chain Monte Carlo (MCMC) method is applied to solve signal-processing problems, it is commonly implemented using Gibbs sampler. The implementation of Gibbs sampler requires the availability of full conditional probability density functions (pdfs) of all the parameters of interest of a problem. For some problems, however, the full conditional pdfs of all the parameters of interest are not readily available. In such cases, Metropolis-Hastings method can be incorporated within a Gibbs sampler to draw samples from the parameters whose full conditional pdf cannot be analytically determined. This paper demonstrates the application of such an algorithm, known as Metropolis-Hastings-within Gibbs, by considering the problem of joint data detection and channel estimation of a single-hop relay-based communication system. By formulating the signal model of the transmission process in alternative ways, we develop two algorithms for the problem. Moreover, simulation results of the two algorithms are provided to illustrate their effectiveness.

This paper presents a novel approach for characterizing wideband (CDMA) multiple dimensional channels for the wireless environment in arbitrarily coloured additive Gaussian noise. This characterization is sufficient for the specification of optimal multichannel space-time receivers. The proposed solution is defined in the Bayesian framework and uses the reversible jump Markov chain Monte Carlo (MCMC) method to obtain estimates of the number of scatterers, their directions of arrival and their times of arrival. The developed method is applied to simulated and real measured data to verify the performance of the approach.

Hyperspectral images (HSI) have high spectral and low spatial resolutions. However, multispectral images (MSI) usually have low spectral and high spatial resolutions. In various applications HSI with high spectral and spatial resolutions are required. In this paper, a new method for spatial resolution enhancement of HSI using high resolution MSI based on sparse coding and linear spectral unmixing (SCLSU) is introduced. In the proposed method (SCLSU), high spectral resolution features of HSI and high spatial resolution features of MSI are fused. In this case, the sparse representation of some high resolution MSI and linear spectral unmixing (LSU) model of HSI and MSI is simultaneously used in order to construct high resolution HSI (HRHSI). The fusion process of HSI and MSI is formulated as an ill-posed inverse problem. It is solved by the Split Augmented Lagrangian Shrinkage Algorithm (SALSA) and an orthogonal matching pursuit (OMP) algorithm. Finally, the proposed algorithm is applied to the Hyperion and ALI datasets. Compared with the other state-of-the-art algorithms such as Coupled Nonnegative Matrix Factorization (CNMF) and local spectral unmixing, the SCLSU has significantly increased the spatial resolution and in addition the spectral content of HSI is well maintained.

Bayesian model updating provides a rigorous framework to account for uncertainty induced by lack of knowledge about engineering systems in their respective mathematical models through updates of the joint probability density function (PDF), the so-called posterior PDF, of the unknown model parameters. The Markov chain Monte Carlo (MCMC) methods are currently the most popular approaches for generating samples from the posterior PDF. However, these methods often found wanting when sampling from difficult distributions (e.g., high-dimensional PDFs, PDFs with flat manifolds, multimodal PDFs, and very peaked PDFs). This paper introduces a new multi-level sampling approach for Bayesian model updating, called Sequential Gauss-Newton algorithm, which is inspired by the Transitional Markov chain Monte Carlo (TMCMC) algorithm. The Sequential Gauss-Newton algorithm improves two aspects of TMCMC to make an efficient and effective MCMC algorithm for drawing samples from difficult posterior PDFs. First, the statistical efficiency of the algorithm is enhanced by use of the systematic resampling scheme. Second, a new MCMC algorithm, called Gauss-Newton MCMC algorithm, is proposed which is essentially an M-H algorithm with a Gaussian proposal PDF tailored to the posterior PDF using the gradient and Hessian information of the negative log posterior. The effectiveness of the proposed algorithm for solving the Bayesian model updating problem is illustrated using three examples with irregularly shaped posterior PDFs.

In this paper, we discuss the problem of constant-stress accelerated life test when the failure data are progressive type-I interval censored. Both classical and Bayesian inferential approaches of the distribution parameters and reliability characteristics are discussed. In the classical scenario, the maximum likelihood estimates are approximated using the EM algorithm and the mid-point approximation method. Furthermore, the model's parameters are estimated by method of moments. Next in the Bayesian framework, the point estimates of unknown parameters are obtained using Tierney-Kadane's technique and Markov Chain Monte Carlo (MCMC) method. In addition, both approximate and credible confidence intervals (CIs) of the estimators are constructed. For illustration purpose, a Monte Carlo simulation is conducted to investigate the performance of the proposed estimators and a real data set is analysed.

Traditional full-waveform inversion (FWI) methods only render a “best-fit” model that cannot account for uncertainties of the ill-posed inverse problem. Additionally, local optimization-based FWI methods cannot always converge to a geologically meaningful solution unless the inversion starts with an accurate background model. We seek the solution for FWI in the Bayesian inference framework to address those two issues. In Bayesian inference, the model space is directly probed by sampling methods such that we obtain a reliable uncertainty appraisal, determine optimal models, and avoid entrapment in a small local region of the model space. The solution of such a statistical inverse method is completely described by the posterior distribution, which quantifies the distributions for parameters and inversion uncertainties. To efficiently sample the posterior distribution, we introduce a sampling algorithm in which the proposal distribution is constructed by the local gradient and the diagonal approximate Hessian of the local log posterior. Our algorithm is called the gradient-based Markov chain Monte Carlo (GMCMC) method. The GMCMC FWI method can quantify inversion uncertainties with estimated posterior distribution given sufficiently long Markov chains. By directly sampling the posterior distribution, we obtain a global view of the model space. Theoretically speaking, statistical assessments do not depend on starting models. Our method is applied to the 2D Marmousi model with the frequency-domain FWI setting. Numerical results suggest that our method can be readily applied to 2D cases with affordable computational efforts.

In this work, a technique is presented for the fusion of multi-spectral (MS) and hyperspectral (HS) images to enhance the spatial resolution of the latter. The technique works in the wavelet domain, and is based on a Bayesian estimation of the HS image, assuming a joint normal model for the images, and an additive noise imaging model for the HS image. An appropriate estimation strategy is also proposed. The technique is compared to its counterpart in the spatial domain, and validated for noisy conditions. Further, its performance is compared to several state-of-the-art pansharpening techniques, in the case where the MS image becomes a panchromatic image, and to some MS and HS image fusion techniques from the literature.

As alluded to in the chapter “Linkage Analysis of Qualitative Traits”, neither the Elston–Steward algorithm nor the Lander–Green approach is amenable to genetic data from large complex pedigrees and a large number of markers. In such cases, Monte Carlo estimation methods provide a viable alternative to the exact solutions. Two types of Monte Carlo methods have been developed for linkage analysis, haplotype inference, and other kinds of genetic analysis. They are Markov chain Monte Carlo (MCMC) methods and Monte Carlo methods that are based on independent samples. Approaches based on Markov chain Monte Carlo methods are more widely applicable; there is practically no limit on the size or complexity of the pedigrees, nor on the number of markers to be considered simultaneously. In this chapter, we will review the basic principles of MCMC methods for multipoint linkage analysis with extended pedigrees. Both simulations and application to data from the Framingham study will be used to compare and contrast three MCMC software packages: LOKI, MORGAN, and SIMWALK.

A reliability analysis procedure is proposed based on a Bayesian framework, which can address the uncertainty in the input variables and the metamodel uncertainty of the response function in an integrated manner. The input uncertainty includes the statistical uncertainty due to the lack of knowledge or insufficient data, which is often the case in the design practice. A method of posterior prediction is used to evaluate the influence of this uncertainty. The metamodel uncertainty is accounted for, which arises due to the surrogate approximation to reduce the costly computation of the response function. Gaussian process model, also known as Kriging model, is employed to assess the associated uncertainty in the form of prediction band. Posterior distributions are obtained by Markov Chain Monte Carlo (MCMC) method, which is an efficient simulation method to draw random sequence of parameters that samples the given distribution. Mathematical and engineering examples are used to demonstrate the proposed method.