8,124 research outputs found
Monte Carlo Methods in Statistics
Monte Carlo methods are now an essential part of the statistician's toolbox,
to the point of being more familiar to graduate students than the measure
theoretic notions upon which they are based! We recall in this note some of the
advances made in the design of Monte Carlo techniques towards their use in
Statistics, referring to Robert and Casella (2004,2010) for an in-depth
coverage.Comment: Entry submitted to the International Handbook of Statistical Method
On computational tools for Bayesian data analysis
While Robert and Rousseau (2010) addressed the foundational aspects of
Bayesian analysis, the current chapter details its practical aspects through a
review of the computational methods available for approximating Bayesian
procedures. Recent innovations like Monte Carlo Markov chain, sequential Monte
Carlo methods and more recently Approximate Bayesian Computation techniques
have considerably increased the potential for Bayesian applications and they
have also opened new avenues for Bayesian inference, first and foremost
Bayesian model choice.Comment: This is a chapter for the book "Bayesian Methods and Expert
Elicitation" edited by Klaus Bocker, 23 pages, 9 figure
Bayesian Poisson Log-Bilinear Mortality Projections
Mortality projections are major concerns for public policy, social security and private insurance. This paper implements a Bayesian log-bilinear Poisson regression model to forecast mortality. Computations are carried out using Markov Chain Monte Carlo methods in which the degree of smoothing is learnt from the data. Comparisons are made with the approach proposed by Brouhns, Denuit & Vermunt (2002a,b), as well as with the original model of Lee & Carter (1992)
Pseudo-Marginal Bayesian Inference for Gaussian Processes
The main challenges that arise when adopting Gaussian Process priors in
probabilistic modeling are how to carry out exact Bayesian inference and how to
account for uncertainty on model parameters when making model-based predictions
on out-of-sample data. Using probit regression as an illustrative working
example, this paper presents a general and effective methodology based on the
pseudo-marginal approach to Markov chain Monte Carlo that efficiently addresses
both of these issues. The results presented in this paper show improvements
over existing sampling methods to simulate from the posterior distribution over
the parameters defining the covariance function of the Gaussian Process prior.
This is particularly important as it offers a powerful tool to carry out full
Bayesian inference of Gaussian Process based hierarchic statistical models in
general. The results also demonstrate that Monte Carlo based integration of all
model parameters is actually feasible in this class of models providing a
superior quantification of uncertainty in predictions. Extensive comparisons
with respect to state-of-the-art probabilistic classifiers confirm this
assertion.Comment: 14 pages double colum
Simulation in Statistics
Simulation has become a standard tool in statistics because it may be the
only tool available for analysing some classes of probabilistic models. We
review in this paper simulation tools that have been specifically derived to
address statistical challenges and, in particular, recent advances in the areas
of adaptive Markov chain Monte Carlo (MCMC) algorithms, and approximate
Bayesian calculation (ABC) algorithms.Comment: Draft of an advanced tutorial paper for the Proceedings of the 2011
Winter Simulation Conferenc
Bayesian Estimation of Inequalities with Non-Rectangular Censored Survey Data
Synthetic indices are used in Economics to measure various aspects of
monetary inequalities. These scalar indices take as input the distribution over
a finite population, for example the population of a specific country. In this
article we consider the case of the French 2004 Wealth survey. We have at hand
a partial measurement on the distribution of interest consisting of bracketed
and sometimes missing data, over a subsample of the population of interest. We
present in this article the statistical methodology used to obtain point and
interval estimates taking into account the various uncertainties. The
inequality indices being nonlinear in the input distribution, we rely on a
simulation based approach where the model for the wealth per household is
multivariate. Using the survey data as well as matched auxiliary tax
declarations data, we have at hand a quite intricate non-rectangle
multidimensional censoring. For practical issues we use a Bayesian approach.
Inference using Monte-Carlo approximations relies on a Monte-Carlo Markov chain
algorithm namely the Gibbs sampler. The quantities interesting to the decision
maker are taken to be the various inequality indices for the French population.
Their distribution conditional on the data of the subsample are assumed to be
normal centered on the design-based estimates with variance computed through
linearization and taking into account the sample design and total nonresponse.
Exogeneous selection of the subsample, in particular the nonresponse mechanism,
is assumed and we condition on the adequate covariates
Bayesian computational methods
In this chapter, we will first present the most standard computational
challenges met in Bayesian Statistics, focussing primarily on mixture
estimation and on model choice issues, and then relate these problems with
computational solutions. Of course, this chapter is only a terse introduction
to the problems and solutions related to Bayesian computations. For more
complete references, see Robert and Casella (2004, 2009), or Marin and Robert
(2007), among others. We also restrain from providing an introduction to
Bayesian Statistics per se and for comprehensive coverage, address the reader
to Robert (2007), (again) among others.Comment: This is a revised version of a chapter written for the Handbook of
Computational Statistics, edited by J. Gentle, W. Hardle and Y. Mori in 2003,
in preparation for the second editio
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