Results 1  10
of
1,565
Empirical Bayes Analysis of a Microarray Experiment
 Journal of the American Statistical Association
, 2001
"... Microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels. A typical microarray experiment can produce millions of data points, raising serious problems of data reduction, and simultaneous inference. We consider one such experiment in whi ..."
Abstract

Cited by 492 (20 self)
 Add to MetaCart
in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on seven thousand human genes. A simple nonparametric empirical Bayes model is introduced, which is used to guide the ef � cient reduction of the data to a single summary statistic per gene, and also to make
Linear models and empirical bayes methods for assessing differential expression in microarray experiments.
 Stat. Appl. Genet. Mol. Biol.
, 2004
"... Abstract The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated twocolor experiment using a simple hierarchical parametric model. ..."
Abstract

Cited by 1321 (24 self)
 Add to MetaCart
from spot filtering or spot quality weights. The posterior odds statistic is reformulated in terms of a moderated tstatistic in which posterior residual standard deviations are used in place of ordinary standard deviations. The empirical Bayes approach is equivalent to shrinkage of the estimated
An empirical Bayes approach to statistics
 Proc Third Berkeley Symp Math Statist Probab
, 1956
"... Let X be a random variable which for simplicity we shall assume to have discrete values x and which has a probability distribution depending in a known way on an unknown real parameter A, (1) p (xIX) =Pr [X = xIA =X], Aitself being a random variable with a priori distribution function (2) G (X) =P ..."
Abstract

Cited by 139 (0 self)
 Add to MetaCart
Let X be a random variable which for simplicity we shall assume to have discrete values x and which has a probability distribution depending in a known way on an unknown real parameter A, (1) p (xIX) =Pr [X = xIA =X], Aitself being a random variable with a priori distribution function (2) G (X) =Pr [A< X. The unconditional probability distribution of X is then given by
Microarrays, Empirical Bayes Methods, and False Discovery Rates
 Genet. Epidemiol
, 2001
"... In a classic twosample problem one might use Wilcoxon's statistic to test for a dierence between Treatment and Control subjects. The analogous microarray experiment yields thousands of Wilcoxon statistics, one for each gene on the array, and confronts the statistician with a dicult simultan ..."
Abstract

Cited by 217 (14 self)
 Add to MetaCart
simultaneous inference situation. We will discuss two inferential approaches to this problem: an empirical Bayes method that requires very little a priori Bayesian modeling, and the frequentist method of \False Discovery Rates" proposed by Benjamini and Hochberg in 1995. It turns out that the two
Calibration and Empirical Bayes Variable Selection
 Biometrika
, 1997
"... this paper, is that with F =2logp. This choice was proposed by Foster &G eorge (1994) where it was called the Risk Inflation Criterion (RIC) because it asymptotically minimises the maximum predictive risk inflation due to selection when X is orthogonal. This choice and its minimax property were ..."
Abstract

Cited by 192 (20 self)
 Add to MetaCart
this paper, is that with F =2logp. This choice was proposed by Foster &G eorge (1994) where it was called the Risk Inflation Criterion (RIC) because it asymptotically minimises the maximum predictive risk inflation due to selection when X is orthogonal. This choice and its minimax property were also discovered independently by Donoho & Johnstone (1994) in the wavelet regression context, where they refer to it as the universal hard thresholding rule
Empirical Bayes for Learning to Learn
 Proceedings of ICML
, 2000
"... We present a new model for studying multitask learning, linking theoretical results to practical simulations. In our model all tasks are combined in a single feedforward neural network. Learning is implemented in a Bayesian fashion. In this Bayesian framework the hiddentooutput weights, bein ..."
Abstract

Cited by 34 (1 self)
 Add to MetaCart
is that the probability of these hyperparameters given the data can be computed explicitely and only depends on a set of sufficient statistics. None of these statistics scales with the number of tasks or patterns, which makes empirical Bayes for multitask learning a relatively straightforward optimization problem
EMPIRICAL BAYES SELECTION OF WAVELET THRESHOLDS
, 2005
"... This paper explores a class of empirical Bayes methods for leveldependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavytailed density. The mixing weight, or sparsity parameter, for each level of ..."
Abstract

Cited by 117 (5 self)
 Add to MetaCart
This paper explores a class of empirical Bayes methods for leveldependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavytailed density. The mixing weight, or sparsity parameter, for each level
Empirical Bayes density regression
 Statistica Sinica
, 2007
"... Abstract: In Bayesian hierarchical modeling, it is often appealing to allow the conditional density of an (observable or unobservable) random variable Y to change flexibly with categorical and continuous predictors X. A mixture of regression models is proposed, with the mixture distribution varying ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
with X. Treating the smoothing parameters and number of mixture components as unknown, the MLE does not exist, motivating an empirical Bayes approach. The proposed method shrinks the spatiallyadaptive mixture distributions to a common baseline, while penalizing rapid changes and large numbers
Results 1  10
of
1,565