Sequential stratified regeneration: MCMC for large state spaces with an application to subgraph count estimation

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.

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.

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.

The conventional Markov chain Monte Carlo (MCMC) method is limited to the selected shape and size of proposal distribution and is not easy to start when the initial proposal distribution is far away from the target distribution. To overcome these drawbacks of the conventional MCMC method, two useful improvements in MCMC method, adaptive Metropolis (AM) algorithm and delayed rejection (DR) algorithm, are attempted to be combined. The AM algorithm aims at adapting the proposal distribution by using the generated estimators, and the DR algorithm aims at enhancing the efficiency of the improved MCMC method. Based on the improved MCMC method, a Bayesian amplitude versus offset (AVO) inversion method on the basis of the exact Zoeppritz equation has been developed, with which the P- and S-wave velocities and the density can be obtained directly, and the uncertainty of AVO inversion results has been estimated as well. The study based on the logging data and the seismic data demonstrates the feasibility and robustness of the method and shows that all three parameters are well retrieved. So the exact Zoeppritz-based nonlinear inversion method by using the improved MCMC is not only suitable for reservoirs with strong-contrast interfaces and long-offset ranges but also it is more stable, accurate and anti-noise.

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.

Building an accurate and reasonable time-series model of wind power is of great significance for the power system operation and planning. This paper proposes a Markov chain Monte Carlo (MCMC) method to simulate the time series of the wind power. Taking into account the nonstationarity and stochastics of the wind power, this model constructs Markov chain for time series of the wind power to keep the stochastics and utilize the Gibbs sampling to realize the probability transition matrix. A numerical case study with one-year real measurement of the wind power from one large wind farm in Gansu province of China is applied to illustrate the validity the proposed model: the simulated wind-power time series of arbitrary length that accurately reproduce the statistical behavior of the original series.

Subgraph counts in random graphs using incomplete u-statistics methods

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.

Parameter estimation and uncertainty analysis for a watershed model

Comparing the performance of different multiple imputation strategies for missing binary outcomes in cluster randomized trials: a simulation study Jinhui Ma,1–3 Parminder Raina,1,2 Joseph Beyene,1 Lehana Thabane1,3–51Department of Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, ON, Canada; 2McMaster University Evidence-based Practice Center, Hamilton, ON, Canada; 3Biostatistics Unit, St Joseph's Healthcare Hamilton, Hamilton, ON, Canada; 4Centre for Evaluation of Medicines, St Joseph's Healthcare Hamilton, Hamilton, ON, Canada; 5Population Health Research Institute, Hamilton Health Sciences, Hamilton, ON, CanadaIntroduction: Although researchers have proposed various strategies to handle missing outcomes in cluster randomized trials (CRTs), limited attention has been paid to the performance of these strategies. Under the assumption of covariate-dependent missingness, the objective of this simulation study is to compare the performance of various strategies in handling missing binary outcomes in CRTs under different design settings.Methods: There are six missing data strategies investigated in this paper, which include complete case analysis, standard multiple imputation (MI) strategies using either logistic regression or Markov chain Monte Carlo (MCMC) method, within-cluster MI strategies using either logistic regression or MCMC method, and MI using logistic regression with cluster as a fixed effect. The performance of these strategies is evaluated through bias, empirical standard error, root mean squared error, and coverage probability.Results: Under the assumption of covariate-dependent missingness and applying the generalized estimating equations approach for fitting the logistic regression, it was shown that complete case analysis yields valid inferences when the percentage of missing outcomes is not large (<20%) for all the designs of CRTs considered in this paper. Standard MI strategies can be adopted when the design effect is small (variance inflation factor [VIF] ≤ 3); however, they tend to underestimate the standard error of treatment effect when the design effect is large. Within-cluster MI strategy using logistic regression is valid for imputation of missing data from CRTs, especially when the cluster size is large (>50) and the design effect is large (VIF > 3). In contrast, within-cluster MI strategy using MCMC method may yield biased estimates of treatment effect for CRTs with small cluster size (≤50). MI using logistic regression with cluster as a fixed effect may substantially overestimate the standard error of the estimated treatment effect when the intracluster correlation coefficient is small. It may also lead to biased estimated treatment effect.Conclusion: Findings from this simulation study provide researchers with quantitative evidence to guide selection of an appropriate strategy to deal with missing binary outcomes.Keywords: missing data, design effect, variance inflation factor

Clustering is a fundamental problem in statistics and machine learning, whose solution is commonly computed by the Expectation-Maximization (EM) method, which finds a locally optimal solution for an objective function called log-likelihood. Since the surface of the log-likelihood function is non convex, a stochastic search with Markov Chain Monte Carlo (MCMC) methods can help escaping locally optimal solutions. In this article, we tackle two fundamental conflicting goals: Finding higher quality solutions and achieving faster convergence. With that motivation in mind, we introduce an efficient algorithm that combines elements of the EM and MCMC methods to find clustering solutions that are qualitatively better than those found by the standard EM method. Moreover, our hybrid algorithm allows tuning model parameters and understanding the uncertainty in their estimation. The main issue with MCMC methods is that they generally require a very large number of iterations to explore the posterior of each model parameter. Convergence is accelerated by several algorithmic improvements which include sufficient statistics, simplified model parameter priors, fixing covariance matrices and iterative sampling from small blocks of the data set. A brief experimental evaluation shows promising results.

Article Free Access Share on Exact sampling and approximate counting techniques Author: Mark Huber School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NYView Profile Authors Info & Claims STOC '98: Proceedings of the thirtieth annual ACM symposium on Theory of computingMay 1998 Pages 31–40https://doi.org/10.1145/276698.276709Published:23 May 1998Publication History 25citation666DownloadsMetricsTotal Citations25Total Downloads666Last 12 Months66Last 6 weeks15 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

In many applications of Bayesian clustering, posterior sampling on the discrete state space of cluster allocations is achieved via Markov chain Monte Carlo (MCMC) techniques. As it is typically challenging to design transition kernels to explore this state space efficiently, MCMC convergence diagnostics for clustering applications are especially important. Here we propose a diagnostic tool for discrete‐space MCMC, focusing on Bayesian clustering applications where the model parameters have been integrated out. We construct a Hotelling‐type statistic on the highest probability states, and use regenerative sampling theory to derive its equilibrium distribution. By leveraging information from the unnormalized posterior, our diagnostic offers added protection against seemingly convergent chains in which the relative frequency of visited states is incorrect. The methodology is illustrated with a Bayesian clustering analysis of genetic mutants of the flowering plantArabidopsis thaliana.This article is categorized under:Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and ClassificationStatistical Learning and Exploratory Methods of the Data Sciences > Knowledge DiscoveryStatistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo

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.

An Introduction to Markov Chain Monte Carlo