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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: 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: 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: 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: Roberto Casarin Publisher: ISBN: Category : Languages : en Pages : 50
Book Description
In many different fields such as hydrology, telecommunications, physics of condensed matter and finance, the gaussian model results unsatisfactory and reveals difficulties in fitting data with skewness, heavy tails and multimodality. The use of stable distributions allows for modelling skewness and heavy tails but gives rise to inferential problems related to the estimation of the stable distributions' parameters. Some recent works have proposed characteristic function based estimation method and MCMC simulation based estimation techniques like the MCMC-EM method and the Gibbs sampling method in a full Bayesian approach. The aim of this work is to generalise the stable distribution framework by introducing a model that accounts also for multimodality. In particular we introduce a stable mixture model and a suitable reparametrisation of the mixture, which allow us to make inference on the mixture parameters. We use a full Bayesian approach and MCMC simulation techniques for the estimation of the posterior distribution. Finally we propose some applications of stable mixtures to financial data.
Author: Ole E Barndorff-Nielsen Publisher: Springer Science & Business Media ISBN: 1461201977 Category : Mathematics Languages : en Pages : 414
Book Description
A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.
Author: Efthymios G. Tsionas
Author: Efthymios G. Tsionas
Author: Efthymios G. Tsionas
Author: Efthymios G. Tsionas
Author: Liangwei Wang
Author: S. James Press
Author: Daniel B. Rowe
Author: George E. P. Box
Author: Zuqiang Qiou
Author: Roberto Casarin
Author: Ole E Barndorff-Nielsen