23,606 research outputs found
Decoding the H-likelihood
Discussion of "Likelihood Inference for Models with Unobservables: Another
View" by Youngjo Lee and John A. Nelder [arXiv:1010.0303]Comment: Published in at http://dx.doi.org/10.1214/09-STS277C the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Multiprocess parallel antithetic coupling for backward and forward Markov Chain Monte Carlo
Antithetic coupling is a general stratification strategy for reducing Monte
Carlo variance without increasing the simulation size. The use of the
antithetic principle in the Monte Carlo literature typically employs two strata
via antithetic quantile coupling. We demonstrate here that further
stratification, obtained by using k>2 (e.g., k=3-10) antithetically coupled
variates, can offer substantial additional gain in Monte Carlo efficiency, in
terms of both variance and bias. The reason for reduced bias is that
antithetically coupled chains can provide a more dispersed search of the state
space than multiple independent chains. The emerging area of perfect simulation
provides a perfect setting for implementing the k-process parallel antithetic
coupling for MCMC because, without antithetic coupling, this class of methods
delivers genuine independent draws. Furthermore, antithetic backward coupling
provides a very convenient theoretical tool for investigating antithetic
forward coupling. However, the generation of k>2 antithetic variates that are
negatively associated, that is, they preserve negative correlation under
monotone transformations, and extremely antithetic, that is, they are as
negatively correlated as possible, is more complicated compared to the case
with k=2. In this paper, we establish a theoretical framework for investigating
such issues. Among the generating methods that we compare, Latin hypercube
sampling and its iterative extension appear to be general-purpose choices,
making another direct link between Monte Carlo and quasi Monte Carlo.Comment: Published at http://dx.doi.org/10.1214/009053604000001075 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Cross-Fertilizing Strategies for Better EM Mountain Climbing and DA Field Exploration: A Graphical Guide Book
In recent years, a variety of extensions and refinements have been developed
for data augmentation based model fitting routines. These developments aim to
extend the application, improve the speed and/or simplify the implementation of
data augmentation methods, such as the deterministic EM algorithm for mode
finding and stochastic Gibbs sampler and other auxiliary-variable based methods
for posterior sampling. In this overview article we graphically illustrate and
compare a number of these extensions, all of which aim to maintain the
simplicity and computation stability of their predecessors. We particularly
emphasize the usefulness of identifying similarities between the deterministic
and stochastic counterparts as we seek more efficient computational strategies.
We also demonstrate the applicability of data augmentation methods for handling
complex models with highly hierarchical structure, using a high-energy
high-resolution spectral imaging model for data from satellite telescopes, such
as the Chandra X-ray Observatory.Comment: Published in at http://dx.doi.org/10.1214/09-STS309 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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