Applying Metropolis-Hastings-within-Gibbs algorithms for data detection in relay-based communication systems

In this paper, we develop a novel statistical detection algorithm following similar principles to that of expectation maximization (EM) algorithm. Our goal is to develop an iterative algorithm for joint channel estimation and data detection in channels that have a long memory and are fast varying in time. At each iteration, starting with an estimate of the channel, we combine a Markov Chain Monte Carlo (MCMC) algorithm for data detection, and an adaptive algorithm for channel tracking, to develop a statistical search procedure that finds joint important samples of possible transmitted data and channel impulse responses. The result of this step, which may be thought as E-step of the proposed algorithm, is used in an M-step that refines the channel estimate, for the next iteration. Excellent behavior of the proposed algorithm is presented by examining it on real data from underwater acoustic communication channels

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.

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.

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.

Markov chain Monte Carlo methods, in particular, the Gibbs sampler, are widely used algorithms both in application and theoretical works in the classical and Bayesian paradigms. However, these algorithms are often computer intensive. Samawi et al. [Steady-state ranked Gibbs sampler. J. Stat. Comput. Simul. 2012;82(8), 1223–1238. doi:10.1080/00949655.2011.575378] demonstrate through theory and simulation that the dependent steady-state Gibbs sampler is more efficient and accurate in model parameter estimation than the original Gibbs sampler. This paper proposes the independent steady-state Gibbs sampler (ISSGS) approach to improve the original Gibbs sampler in multidimensional problems. It is demonstrated that ISSGS provides accuracy with unbiased estimation and improves the performance and convergence of the Gibbs sampler in multidimensional problems.

As themany examples in this book illustrate,Markov chainMonte Carlo (MCMC)methods have revolutionized Bayesian statistical analyses. Rather than using off-the-shelf models and methods, we can use MCMC to fit application-specific models that are designed to account for the particular complexities of a problem. These complex multilevel models are becoming more prevalent throughout the natural, social, and engineering sciences largely because of the ease of using standard MCMC methods such as the Gibbs and MetropolisHastings (MH) samplers. Indeed, the ability to easily fit statistical models that directly represent the complexity of a data-generationmechanismhas arguably lead to the increased popularity of Bayesian methods in many scientific disciplines. Although simple standard methods work surprisingly well in many problems, neitherthe Gibbs nor theMH sampler can directly handle problemswith very high posterior correlations among theparameters. Themarginal distribution of a givenparameter ismuchmore variable than the corresponding full conditional distribution in this case, causing the Gibbs sampler to take small steps. With MH a proposal distribution that does not account for the posterior correlation either has far toomuchmass in regions of low posterior probability or has such smallmarginal variances that only small steps are proposed, causing high rejection rates and/or high autocorrelations in the resultingMarkov chains. Unfortunately, accounting for the posterior correlation requires more information about the posterior distribution than is typically available when the proposal distribution is constructed. Much work has been devoted to developing computational methods that extend theusefulness of these standard tools in the presence of high correlations. For Gibbs sampling, for example, it is nowwell known that blocking or grouping steps (Liu et al., 1994), nesting steps (van Dyk, 2000), collapsing or marginalizing parameters (Liu et al., 1994; Meng and vanDyk, 1999), incorporatingauxiliaryvariables (BesagandGreen, 1993), certainparameter transformations (Gelfand et al., 1995; Yu and Meng, 2011), and parameter expansion (Liu andWu,1999) canall beused to improve the convergenceof certain samplers.Byembedding an MH sampler within the Gibbs sampler and updating one parameter at a time (i.e. the well-known Metropolis-within-Gibbs sampler in the terminology of Gilks et al., 1995), the same strategies can be used to improve MH samplers.

ATM: An open-source tool for asteroid thermal modeling and its application to NEOWISE data

Osteoporosis (OP) is a common metabolic bone disease with high incidence, and is recognized as a major public health problem worldwide. It is essential to clarify the pathogenesis of the disease for improving the diagnosis, prevention and treatment of OP. The aim of this study was to clarify the pivotal pathways and hub genes in OP using Gibbs sampling. The gene expression profile datasets were obtained from Gene Expression Omnibus (GEO) database. The pathways were enriched by Kyoto Encyclopedia of Genes and Genomes (KEGG) with genes intersection ≥5 based on gene expression profile data. Then, the acquired pathways were converted into Markov chains (MC). Gibbs sampling was conducted to obtain a new MC. In addition, the average probabilities of each pathway in two states containing human mesenchymal stem cells (hMSC) _middle-aged and hMSC_elderly were calculated through Markov chain Monte Carlo (MCMC) algorithm. Moreover, gene expression variation was taken into account to adjust the probability. Pivotal pathways were identified under adjusted posterior value >0.8. Then, Gibbs sampling was implemented to find hub genes from pathways. There were 280 pathways determined by the gene intersection ≥5. Gibbs sampling identified two disturbed pathways (pathways in cancer and influenza A) and two hub genes (cyclin A1 and WNT2) under the adjusted probability >0.8. Gene expression analysis showed that all the disturbed pathways and hub genes had increased expression levels in hMSC_middle-aged samples compared with hMSC_elderly samples. We identified two pivotal pathways and two hub genes in OP using Gibbs sampling. The results contribute to the understanding of underlying pathogenesis and could be considered as potential biomarkers for the therapy of OP.

Markov chain Monte Carlo (MCMC) is a statistical innovation that allows researchers to fit far more com- plex models to data than is feasible using conventional methods. Despite its widespread use in a variety of scien- tific fields, MCMC appears to be underutilized in wildlife applications. This may be due to a misconception that MCMC requires the adoption of a subjective Bayesian analysis, or perhaps simply to its lack of familiarity among wildlife researchers. We introduce the basic ideas of MCMC and software BUGS (Bayesian inference using Gibbs sampling), stressing that a simple and satisfactory intuition for MCMC does not require extraordinary mathemat- ical sophistication. We illustrate the use of MCMC with an analysis of the association between latent factors gov- erning individual heterogeneity in breeding and survival rates of kittiwakes (Rissa tridactyla). We conclude with a discussion of the importance of individual heterogeneity for understanding population dynamics and designing management plans.

The epidemic of COVID-19 has been effectively controlled in China, which provides an empirical basis for intervention analysis. An extended SIR transmission model with heterogeneous force of infectiousness is presented including three fractals sub-models of Wuhan, Hubei and China. The model is built upon the data from January 20 to March 23, 2020. The Markov chain Monte Carlo (MCMC) Gibbs sampling and machine learning of Gaussian process regression are applied to solve the parameters estimation and the sensitivity analysis is used in various scenarios. The model has a breakthrough in parameter setting and accuracy optimization. It is found that contact reduction is the most effective core lever to control the epidemic, with 3.5 times or more sensitivity as much as other levers. The asymmetric marginal effect in strong and weak scenarios proves that Chinese controlling strategy is close to the Pareto Optimality. The intervention effectiveness of COVID-19 in China is evaluated by simulation analysis. The result provides valuable reference for China and other countries to judge the epidemic risk, control the intervention pace, and formulate prevention strategies in the future.

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.

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.

To reduce huge consumption of processing hyperspectral images(HSI), a novel Bayesian unmixing compressive sensing framework is proposed to compress and reconstruct HSI effectively, called structured sparse Bayesian umixing compressive sensing(SSBUCS). SSBUCS unites compressive sensing and hyperspectral linear mixed model in Bayesian framework. An HSI is decomposed as a linear combination of endmembers and abundance matrix. The abundance matrix is transformed to a structured sparse signal in the wavelet domain. Then, compressive sensing is employed on this sparse signal to produce a more compact result. To recover the HSI, a Markov chain Monte Carlo(MCMC) method based on Gibbs sampling is proposed, imposing structured sparse prior on abundance matrix. Experimental results verify the superiority of the proposed method over several state-of-art methods.

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.

This article is a review article on the optimal Markov chain Monte Carlo (MCMC) sampling. The focus is on homogeneous Markov chains. This article first reviews the problem of finding the optimal transition matrix, which is defined to minimize the asymptotic variance of MCMC estimators. The article later reviews the locally optimal sampler (LOS), an MCMC sampling that performs local updates based on the optimal transition matrix. We conducted a simulation study to compare the LOS with the Metropolis–Hastings and the Gibbs Sampler. The LOS was shown to provide an improved rate of convergence over these two most popular sampling schemes. The implementation of the LOS requires only minor modifications in existing Gibbs sampling code. WIREs Comput Stat 2013. doi: 10.1002/wics.1265This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)