61 research outputs found
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
Bayesian methods to overcome the winner's curse in genetic studies
Parameter estimates for associated genetic variants, report ed in the initial
discovery samples, are often grossly inflated compared to the values observed
in the follow-up replication samples. This type of bias is a consequence of the
sequential procedure in which the estimated effect of an associated genetic
marker must first pass a stringent significance threshold. We propose a
hierarchical Bayes method in which a spike-and-slab prior is used to account
for the possibility that the significant test result may be due to chance. We
examine the robustness of the method using different priors corresponding to
different degrees of confidence in the testing results and propose a Bayesian
model averaging procedure to combine estimates produced by different models.
The Bayesian estimators yield smaller variance compared to the conditional
likelihood estimator and outperform the latter in studies with low power. We
investigate the performance of the method with simulations and applications to
four real data examples.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS373 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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