Convergence Diagnostics for MCMC Methods in the Bayesian Analysis of Volatility Models PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Convergence Diagnostics for MCMC Methods in the Bayesian Analysis of Volatility Models PDF full book. Access full book title Convergence Diagnostics for MCMC Methods in the Bayesian Analysis of Volatility Models by P. Giudici. Download full books in PDF and EPUB format.
Author: P. Giudici
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
Get Book Here
Book Description
Author: P. Giudici
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
Get Book Here
Book Description
Author: Christian P. Robert
Publisher: Springer Science & Business Media
ISBN: 1461217164
Category : Mathematics
Languages : en
Pages : 201
Get Book Here
Book Description
The exponential increase in the use of MCMC methods and the corre sponding applications in domains of even higher complexity have caused a growing concern about the available convergence assessment methods and the realization that some of these methods were not reliable enough for all-purpose analyses. Some researchers have mainly focussed on the con vergence to stationarity and the estimation of rates of convergence, in rela tion with the eigenvalues of the transition kernel. This monograph adopts a different perspective by developing (supposedly) practical devices to assess the mixing behaviour of the chain under study and, more particularly, it proposes methods based on finite (state space) Markov chains which are obtained either through a discretization of the original Markov chain or through a duality principle relating a continuous state space Markov chain to another finite Markov chain, as in missing data or latent variable models. The motivation for the choice of finite state spaces is that, although the resulting control is cruder, in the sense that it can often monitor con vergence for the discretized version alone, it is also much stricter than alternative methods, since the tools available for finite Markov chains are universal and the resulting transition matrix can be estimated more accu rately. Moreover, while some setups impose a fixed finite state space, other allow for possible refinements in the discretization level and for consecutive improvements in the convergence monitoring.
Author: Dani Gamerman
Publisher: CRC Press
ISBN: 9781584885870
Category : Mathematics
Languages : en
Pages : 352
Get Book Here
Book Description
While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition presents a concise, accessible, and comprehensive introduction to the methods of this valuable simulation technique. The second edition includes access to an internet site that provides the code, written in R and WinBUGS, used in many of the previously existing and new examples and exercises. More importantly, the self-explanatory nature of the codes will enable modification of the inputs to the codes and variation on many directions will be available for further exploration. Major changes from the previous edition: · More examples with discussion of computational details in chapters on Gibbs sampling and Metropolis-Hastings algorithms · Recent developments in MCMC, including reversible jump, slice sampling, bridge sampling, path sampling, multiple-try, and delayed rejection · Discussion of computation using both R and WinBUGS · Additional exercises and selected solutions within the text, with all data sets and software available for download from the Web · Sections on spatial models and model adequacy The self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. The book will appeal to everyone working with MCMC techniques, especially research and graduate statisticians and biostatisticians, and scientists handling data and formulating models. The book has been substantially reinforced as a first reading of material on MCMC and, consequently, as a textbook for modern Bayesian computation and Bayesian inference courses.
Author: Maximilian Richter
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Markov Chain Monte Carlo (MCMC) methods are a Bayesian approach to tackle one of the main obstacles encountered in the estimation of modern-day stochastic volatility models: the curse of dimensionality induced by the increasing number of latent variables. This thesis strives to study the performance of affine jump-diffusion models in comparison to state-of-the-art Lévy-based return dynamics. Thus MCMC methods are applied to a novel dataset of S & P500 returns that comprises different periods of economic turmoil, such as the subprime crisis. The subordinate research goal is to address difficulties in the implementation of the MCMC methodology. In line with previous studies, the results indicate that jump components are indeed crucial for capturing complex patterns like skewness and excess kurtosis of the return distributions. Moreover, infinite-activity Lévy jumps prove to be superior to discrete compound Poisson jumps.
Author: Zhongxian Men
Publisher:
ISBN:
Category :
Languages : en
Pages : 163
Get Book Here
Book Description
Stochastic volatility (SV) models provide a natural framework for a representation of time series for financial asset returns. As a result, they have become increasingly popular in the finance literature, although they have also been applied in other fields such as signal processing, telecommunications, engineering, biology, and other areas. In working with the SV models, an important issue arises as how to estimate their parameters efficiently and to assess how well they fit real data. In the literature, commonly used estimation methods for the SV models include general methods of moments, simulated maximum likelihood methods, quasi Maximum likelihood method, and Markov Chain Monte Carlo (MCMC) methods. Among these approaches, MCMC methods are most flexible in dealing with complicated structure of the models. However, due to the difficulty in the selection of the proposal distribution for Metropolis-Hastings methods, in general they are not easy to implement and in some cases we may also encounter convergence problems in the implementation stage. In the light of these concerns, we propose in this thesis new estimation methods for univariate and multivariate SV models.
Author: Christian Robert
Publisher: Springer Science & Business Media
ISBN: 1441915753
Category : Computers
Languages : en
Pages : 297
Get Book Here
Book Description
This book covers the main tools used in statistical simulation from a programmer’s point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison.
Author: Michael S. Johannes
Publisher:
ISBN:
Category :
Languages : en
Pages : 96
Get Book Here
Book Description
This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuous-time asset pricing models. The Bayesian solution to the inference problem is the distribution of parameters and latent variables conditional on observed data, and MCMC methods provide a tool for exploring these high-dimensional, complex distributions. We first provide a description of the foundations and mechanics of MCMC algorithms. This includes a discussion of the Clifford-Hammersley theorem, the Gibbs sampler, the Metropolis-Hastings algorithm, and theoretical convergence properties of MCMC algorithms. We next provide a tutorial on building MCMC algorithms for a range of continuous-time asset pricing models. We include detailed examples for equity price models, option pricing models, term structure models, and regime-switching models. Finally, we discuss the issue of sequential Bayesian inference, both for parameters and state variables.
Author: Brandon David Butcher
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Bayesian Additive Regression Trees (BART) is a relatively new model within the domain of statistical/machine learning. BART has seen rapid development in recent years, having been extended and adapted to new application areas. Given that BART is a fully Bayesian model, care should be taken to justify that samples drawn via Markov Chain Monte Carlo (MCMC) from BART's posterior distribution can be regarded as from a stationary posterior distribution. Presently, no formal method exists for conducting such diagnostic checks. As such, a formal convergence criterion is developed for BART called the Posterior Tree Deviance (PTD). This method for assessing convergence of BART's MCMC sampler is implemented in a novel software package, BART.jl, written in the Julia programming language. Working with BART presents an onerous software burden. BART.jl contains a much smaller codebase than implementations in other programming languages and provides user-friendly functionality for working with BART's ensemble of decision trees. Lastly, BART is adapted to two novel application areas: (1) variable selection in the presence of mandatory and optional covariates (2) correcting for bias resulting from a predictor measured with error.
Author: J. M. Bernardo
Publisher: Oxford University Press
ISBN: 9780198504856
Category : Mathematics
Languages : en
Pages : 886
Get Book Here
Book Description
Bayesian statistics is a dynamic and fast-growing area of statistical research and the Valencia International Meetings provide the main forum for discussion. These resulting proceedings form an up-to-date collection of research.
Author: Michael Johnson
Publisher:
ISBN:
Category :
Languages : en
Pages : 59
Get Book Here
Book Description
Stochastic volatility models (SVM) are commonly used to model time series data. They have many applications in finance and are useful tools to describe the evolution of asset returns. The motivation for this project is to determine if stochastic volatility models can be used to model Bitcoin exchange rates in a way that can contribute to an effective trading strategy. We consider a basic SVM and several extensions that include fat tails, leverage, and covariate effects. The Bayesian approach with the particle Markov chain Monte Carlo (PMCMC) method is employed to estimate the model parameters. We assess the goodness of the estimated model using the deviance information criterion (DIC). Simulation studies are conducted to assess the performance of particle MCMC and to compare with the traditional MCMC approach. We then apply the proposed method to the Bitcoin exchange rate data and compare the effectiveness of each type of SVM.
