55,611 research outputs found
An assessment of empirical Bayes and composite estimators for small areas
We compare a set of empirical Bayes and composite estimators of the population means of the districts (small areas) of a country, and show that the natural modelling strategy of searching for a well fitting empirical Bayes model and using it for estimation of the area-level means can be inefficient.Composite estimator, empirical Bayes models, mean squared error, small-area estimation
A Nonparametric Bayesian Approach to Uncovering Rat Hippocampal Population Codes During Spatial Navigation
Rodent hippocampal population codes represent important spatial information
about the environment during navigation. Several computational methods have
been developed to uncover the neural representation of spatial topology
embedded in rodent hippocampal ensemble spike activity. Here we extend our
previous work and propose a nonparametric Bayesian approach to infer rat
hippocampal population codes during spatial navigation. To tackle the model
selection problem, we leverage a nonparametric Bayesian model. Specifically, to
analyze rat hippocampal ensemble spiking activity, we apply a hierarchical
Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference
methods, one based on Markov chain Monte Carlo (MCMC) and the other based on
variational Bayes (VB). We demonstrate the effectiveness of our Bayesian
approaches on recordings from a freely-behaving rat navigating in an open field
environment. We find that MCMC-based inference with Hamiltonian Monte Carlo
(HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and
MCMC approaches with hyperparameters set by empirical Bayes
Improving population-specific allele frequency estimates by adapting supplemental data: an empirical Bayes approach
Estimation of the allele frequency at genetic markers is a key ingredient in
biological and biomedical research, such as studies of human genetic variation
or of the genetic etiology of heritable traits. As genetic data becomes
increasingly available, investigators face a dilemma: when should data from
other studies and population subgroups be pooled with the primary data? Pooling
additional samples will generally reduce the variance of the frequency
estimates; however, used inappropriately, pooled estimates can be severely
biased due to population stratification. Because of this potential bias, most
investigators avoid pooling, even for samples with the same ethnic background
and residing on the same continent. Here, we propose an empirical Bayes
approach for estimating allele frequencies of single nucleotide polymorphisms.
This procedure adaptively incorporates genotypes from related samples, so that
more similar samples have a greater influence on the estimates. In every
example we have considered, our estimator achieves a mean squared error (MSE)
that is smaller than either pooling or not, and sometimes substantially
improves over both extremes. The bias introduced is small, as is shown by a
simulation study that is carefully matched to a real data example. Our method
is particularly useful when small groups of individuals are genotyped at a
large number of markers, a situation we are likely to encounter in a
genome-wide association study.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS121 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Computing analytic Bayes factors from summary statistics in repeated-measures designs
Bayes factors are an increasingly popular tool for indexing evidence from
experiments. For two competing population models, the Bayes factor reflects the
relative likelihood of observing some data under one model compared to the
other. In general, computing a Bayes factor is difficult, because computing the
marginal likelihood of each model requires integrating the product of the
likelihood and a prior distribution on the population parameter(s). In this
paper, we develop a new analytic formula for computing Bayes factors directly
from minimal summary statistics in repeated-measures designs. This work is an
improvement on previous methods for computing Bayes factors from summary
statistics (e.g., the BIC method), which produce Bayes factors that violate the
Sellke upper bound of evidence for smaller sample sizes. The new approach taken
in this paper extends requires knowing only the -statistic and degrees of
freedom, both of which are commonly reported in most empirical work. In
addition to providing computational examples, we report a simulation study that
benchmarks the new formula against other methods for computing Bayes factors in
repeated-measures designs. Our new method provides an easy way for researchers
to compute Bayes factors directly from a minimal set of summary statistics,
allowing users to index the evidential value of their own data, as well as data
reported in published studies
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