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Author: Efthymios G. Tsionas Publisher: ISBN: Category : Languages : en Pages : 41
Book Description
In this paper we take up Bayesian inference in general, multivariate stable distributions. We use approximate Bayesian computation (ABC) along with carefully crafted proposal distributions for the implementation of MCMC. The problem of selecting summary statistics in ABC is resolved through the use of the characteristic function. Two important problems in multivariate stable distributions are: (i) the selection of an optimal con guration of the grid points where the empirical and theoretical characteristic functions are compared, and (ii) the estimation of the spectral measure through which the distributions are de ned in Rd. The problems are resolved successfully and certain new approximations to the spectral measure are proposed and implemented. E fficient proposal/importance distributions are constructed, and tested thoroughly, to ensure good performance in connection with ABC. The new techniques are applied to exchange rate and stock return data and are supplemented by Monte Carlo simulations. In addition, critical values are provided for a closeness statistic between the empirical and theoretical characteristic functions, resolving successfully another major problem in ABC-related inference.
Author: Efthymios G. Tsionas Publisher: ISBN: Category : Languages : en Pages : 41
Book Description
In this paper we take up Bayesian inference in general, multivariate stable distributions. We use approximate Bayesian computation (ABC) along with carefully crafted proposal distributions for the implementation of MCMC. The problem of selecting summary statistics in ABC is resolved through the use of the characteristic function. Two important problems in multivariate stable distributions are: (i) the selection of an optimal con guration of the grid points where the empirical and theoretical characteristic functions are compared, and (ii) the estimation of the spectral measure through which the distributions are de ned in Rd. The problems are resolved successfully and certain new approximations to the spectral measure are proposed and implemented. E fficient proposal/importance distributions are constructed, and tested thoroughly, to ensure good performance in connection with ABC. The new techniques are applied to exchange rate and stock return data and are supplemented by Monte Carlo simulations. In addition, critical values are provided for a closeness statistic between the empirical and theoretical characteristic functions, resolving successfully another major problem in ABC-related inference.
Author: Efthymios G. Tsionas Publisher: ISBN: Category : Languages : en Pages : 40
Book Description
In this paper we take up Bayesian inference in general multivariate stable distributions. We exploit the representation of Matsui and Takemura (2009) for univariate projections, and the representation of the distributions in terms of their spectral measure. We present e cient MCMC schemes to perform the computations when the spectral measure is approximated discretely or, as we propose, by a normal distribution. Appropriate latent variables are introduced to implement MCMC. In relation to the discrete approximation, we propose e cient computational schemes based on the characteristic function.
Author: S. James Press Publisher: Courier Corporation ISBN: 0486139387 Category : Mathematics Languages : en Pages : 706
Book Description
Geared toward upper-level undergraduates and graduate students, this two-part treatment deals with the foundations of multivariate analysis as well as related models and applications. Starting with a look at practical elements of matrix theory, the text proceeds to discussions of continuous multivariate distributions, the normal distribution, and Bayesian inference; multivariate large sample distributions and approximations; the Wishart and other continuous multivariate distributions; and basic multivariate statistics in the normal distribution. The second half of the text moves from defining the basics to explaining models. Topics include regression and the analysis of variance; principal components; factor analysis and latent structure analysis; canonical correlations; stable portfolio analysis; classifications and discrimination models; control in the multivariate linear model; and structuring multivariate populations, with particular focus on multidimensional scaling and clustering. In addition to its value to professional statisticians, this volume may also prove helpful to teachers and researchers in those areas of behavioral and social sciences where multivariate statistics is heavily applied. This new edition features an appendix of answers to the exercises.
Author: Efthymios G. Tsionas Publisher: ISBN: Category : Languages : en Pages : 12
Book Description
In this paper we take up Bayesian inference in multivariate stable distributions through innovative multivariate stable copulae. The problem that the characteristic function is defined through a difficult object, the spectral measure is completely bypassed by our approach. The new methods are applied to major exchange rates with encouraging results. The copula-based technique is based on non-parametric margins (both data-estimated as well as Dirichlet process priors) and we compare with a multivariate stable copula whose margins can be normal, Student-t or univariate stable.
Author: Daniel B. Rowe Publisher: CRC Press ISBN: 1420035266 Category : Mathematics Languages : en Pages : 350
Book Description
Of the two primary approaches to the classic source separation problem, only one does not impose potentially unreasonable model and likelihood constraints: the Bayesian statistical approach. Bayesian methods incorporate the available information regarding the model parameters and not only allow estimation of the sources and mixing coefficients, but
Author: George E. P. Box Publisher: John Wiley & Sons ISBN: 111803144X Category : Mathematics Languages : en Pages : 610
Book Description
Its main objective is to examine the application and relevance of Bayes' theorem to problems that arise in scientific investigation in which inferences must be made regarding parameter values about which little is known a priori. Begins with a discussion of some important general aspects of the Bayesian approach such as the choice of prior distribution, particularly noninformative prior distribution, the problem of nuisance parameters and the role of sufficient statistics, followed by many standard problems concerned with the comparison of location and scale parameters. The main thrust is an investigation of questions with appropriate analysis of mathematical results which are illustrated with numerical examples, providing evidence of the value of the Bayesian approach.
Author: Gudmund R. Iversen Publisher: SAGE ISBN: 9780803923287 Category : Mathematics Languages : en Pages : 88
Book Description
Statisticians now generally acknowledge the theorectical importance of Bayesian inference, if not its practical validity. According to Gudmund R. Iversen, one reason for the lag in applications is that empirical researchers have lacked a grounding in the methodology. His volume provides this introduction and serves as a companion to #4, Tests of Significance.
Author: LYLE D. BROEMELING Publisher: CRC Press ISBN: 9780367572433 Category : Bayesian statistical decision theory Languages : en Pages : 432
Book Description
The book aims to introduce Bayesian inference methods for stochastic processes. The Bayesian approach has advantages compared to non-Bayesian, among which is the optimal use of prior information via data from previous similar experiments. Examples from biology, economics, and astronomy reinforce the basic concepts of the subject. R a
Author: Jeff Gill Publisher: CRC Press ISBN: 1584885629 Category : Mathematics Languages : en Pages : 696
Book Description
The first edition of Bayesian Methods: A Social and Behavioral Sciences Approach helped pave the way for Bayesian approaches to become more prominent in social science methodology. While the focus remains on practical modeling and basic theory as well as on intuitive explanations and derivations without skipping steps, this second edition incorporates the latest methodology and recent changes in software offerings. New to the Second Edition Two chapters on Markov chain Monte Carlo (MCMC) that cover ergodicity, convergence, mixing, simulated annealing, reversible jump MCMC, and coupling Expanded coverage of Bayesian linear and hierarchical models More technical and philosophical details on prior distributions A dedicated R package (BaM) with data and code for the examples as well as a set of functions for practical purposes such as calculating highest posterior density (HPD) intervals Requiring only a basic working knowledge of linear algebra and calculus, this text is one of the few to offer a graduate-level introduction to Bayesian statistics for social scientists. It first introduces Bayesian statistics and inference, before moving on to assess model quality and fit. Subsequent chapters examine hierarchical models within a Bayesian context and explore MCMC techniques and other numerical methods. Concentrating on practical computing issues, the author includes specific details for Bayesian model building and testing and uses the R and BUGS software for examples and exercises.
Author: Efthymios G. Tsionas
Author: Efthymios G. Tsionas
Author: Efthymios G. Tsionas
Author: Liangwei Wang
Author: S. James Press
Author: Efthymios G. Tsionas
Author: Daniel B. Rowe
Author: George E. P. Box
Author: Gudmund R. Iversen
Author: LYLE D. BROEMELING
Author: Jeff Gill