138 research outputs found
Discussion of "EQUI-energy sampler" by Kou, Zhou and Wong
Discussion of ``EQUI-energy sampler'' by Kou, Zhou and Wong [math.ST/0507080]Comment: Published at http://dx.doi.org/10.1214/009053606000000506 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Metropolized Randomized Maximum Likelihood for sampling from multimodal distributions
This article describes a method for using optimization to derive efficient
independent transition functions for Markov chain Monte Carlo simulations. Our
interest is in sampling from a posterior density for problems in which
the dimension of the model space is large, is multimodal with regions
of low probability separating the modes, and evaluation of the likelihood is
expensive. We restrict our attention to the special case for which the target
density is the product of a multivariate Gaussian prior and a likelihood
function for which the errors in observations are additive and Gaussian
Bayesian meta-analysis for identifying periodically expressed genes in fission yeast cell cycle
The effort to identify genes with periodic expression during the cell cycle
from genome-wide microarray time series data has been ongoing for a decade.
However, the lack of rigorous modeling of periodic expression as well as the
lack of a comprehensive model for integrating information across genes and
experiments has impaired the effort for the accurate identification of
periodically expressed genes. To address the problem, we introduce a Bayesian
model to integrate multiple independent microarray data sets from three recent
genome-wide cell cycle studies on fission yeast. A hierarchical model was used
for data integration. In order to facilitate an efficient Monte Carlo sampling
from the joint posterior distribution, we develop a novel Metropolis--Hastings
group move. A surprising finding from our integrated analysis is that more than
40% of the genes in fission yeast are significantly periodically expressed,
greatly enhancing the reported 10--15% of the genes in the current literature.
It calls for a reconsideration of the periodically expressed gene detection
problem.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS300 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Semi-independent resampling for particle filtering
Among Sequential Monte Carlo (SMC) methods,Sampling Importance Resampling
(SIR) algorithms are based on Importance Sampling (IS) and on some
resampling-based)rejuvenation algorithm which aims at fighting against weight
degeneracy. However %whichever the resampling technique used this mechanism
tends to be insufficient when applied to informative or high-dimensional
models. In this paper we revisit the rejuvenation mechanism and propose a class
of parameterized SIR-based solutions which enable to adjust the tradeoff
between computational cost and statistical performances
Parallel resampling in the particle filter
Modern parallel computing devices, such as the graphics processing unit
(GPU), have gained significant traction in scientific and statistical
computing. They are particularly well-suited to data-parallel algorithms such
as the particle filter, or more generally Sequential Monte Carlo (SMC), which
are increasingly used in statistical inference. SMC methods carry a set of
weighted particles through repeated propagation, weighting and resampling
steps. The propagation and weighting steps are straightforward to parallelise,
as they require only independent operations on each particle. The resampling
step is more difficult, as standard schemes require a collective operation,
such as a sum, across particle weights. Focusing on this resampling step, we
analyse two alternative schemes that do not involve a collective operation
(Metropolis and rejection resamplers), and compare them to standard schemes
(multinomial, stratified and systematic resamplers). We find that, in certain
circumstances, the alternative resamplers can perform significantly faster on a
GPU, and to a lesser extent on a CPU, than the standard approaches. Moreover,
in single precision, the standard approaches are numerically biased for upwards
of hundreds of thousands of particles, while the alternatives are not. This is
particularly important given greater single- than double-precision throughput
on modern devices, and the consequent temptation to use single precision with a
greater number of particles. Finally, we provide auxiliary functions useful for
implementation, such as for the permutation of ancestry vectors to enable
in-place propagation.Comment: 21 pages, 6 figure
- …