22,951 research outputs found

    Decoding the H-likelihood

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    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

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    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

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    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