77,067 research outputs found
Particle Efficient Importance Sampling
The efficient importance sampling (EIS) method is a general principle for the
numerical evaluation of high-dimensional integrals that uses the sequential
structure of target integrands to build variance minimising importance
samplers. Despite a number of successful applications in high dimensions, it is
well known that importance sampling strategies are subject to an exponential
growth in variance as the dimension of the integration increases. We solve this
problem by recognising that the EIS framework has an offline sequential Monte
Carlo interpretation. The particle EIS method is based on non-standard
resampling weights that take into account the look-ahead construction of the
importance sampler. We apply the method for a range of univariate and bivariate
stochastic volatility specifications. We also develop a new application of the
EIS approach to state space models with Student's t state innovations. Our
results show that the particle EIS method strongly outperforms both the
standard EIS method and particle filters for likelihood evaluation in high
dimensions. Moreover, the ratio between the variances of the particle EIS and
particle filter methods remains stable as the time series dimension increases.
We illustrate the efficiency of the method for Bayesian inference using the
particle marginal Metropolis-Hastings and importance sampling squared
algorithms
An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration
While statisticians are well-accustomed to performing exploratory analysis in
the modeling stage of an analysis, the notion of conducting preliminary
general-purpose exploratory analysis in the Monte Carlo stage (or more
generally, the model-fitting stage) of an analysis is an area which we feel
deserves much further attention. Towards this aim, this paper proposes a
general-purpose algorithm for automatic density exploration. The proposed
exploration algorithm combines and expands upon components from various
adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at
its heart. Additionally, the algorithm is run on interacting parallel chains --
a feature which both decreases computational cost as well as stabilizes the
algorithm, improving its ability to explore the density. Performance is studied
in several applications. Through a Bayesian variable selection example, the
authors demonstrate the convergence gains obtained with interacting chains. The
ability of the algorithm's adaptive proposal to induce mode-jumping is
illustrated through a trimodal density and a Bayesian mixture modeling
application. Lastly, through a 2D Ising model, the authors demonstrate the
ability of the algorithm to overcome the high correlations encountered in
spatial models.Comment: 33 pages, 20 figures (the supplementary materials are included as
appendices
Bayesian Inference on Dynamic Models with Latent Factors
In time series analysis, latent factors are often introduced to model the heterogeneous time evolution of the observed processes. The presence of unobserved components makes the maximum likelihood estimation method more difficult to apply. A Bayesian approach can sometimes be preferable since it permits to treat general state space models and makes easier the simulation based approach to parameters estimation and latent factors filtering. The paper examines economic time series models in a Bayesian perspective focusing, through some examples, on the extraction of the business cycle components. We briefly review some general univariate Bayesian dynamic models and discuss the simulation based techniques, such as Gibbs sampling, adaptive importance sampling and finally suggest the use of the particle filter, for parameter estimation and latent factor extraction.Bayesian Dynamic Models, Simulation Based Inference, Particle Filters, Latent Factors, Business Cycle
Lookahead Strategies for Sequential Monte Carlo
Based on the principles of importance sampling and resampling, sequential
Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with
complex stochastic dynamic systems. Many of these systems possess strong
memory, with which future information can help sharpen the inference about the
current state. By providing theoretical justification of several existing
algorithms and introducing several new ones, we study systematically how to
construct efficient SMC algorithms to take advantage of the "future"
information without creating a substantially high computational burden. The
main idea is to allow for lookahead in the Monte Carlo process so that future
information can be utilized in weighting and generating Monte Carlo samples, or
resampling from samples of the current state.Comment: Published in at http://dx.doi.org/10.1214/12-STS401 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Free energy Sequential Monte Carlo, application to mixture modelling
We introduce a new class of Sequential Monte Carlo (SMC) methods, which we
call free energy SMC. This class is inspired by free energy methods, which
originate from Physics, and where one samples from a biased distribution such
that a given function of the state is forced to be
uniformly distributed over a given interval. From an initial sequence of
distributions of interest, and a particular choice of ,
a free energy SMC sampler computes sequentially a sequence of biased
distributions with the following properties: (a) the
marginal distribution of with respect to is
approximatively uniform over a specified interval, and (b)
and have the same conditional distribution with respect to . We
apply our methodology to mixture posterior distributions, which are highly
multimodal. In the mixture context, forcing certain hyper-parameters to higher
values greatly faciliates mode swapping, and makes it possible to recover a
symetric output. We illustrate our approach with univariate and bivariate
Gaussian mixtures and two real-world datasets.Comment: presented at "Bayesian Statistics 9" (Valencia meetings, 4-8 June
2010, Benidorm
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