165,581 research outputs found
On Flexible finite polygenic models for multiple-trait evaluation
Finite polygenic models (FPM) might be an alternative to the infinitesimal model (TIM) for the genetic evaluation of pedigreed multiple-generation populations for multiple quantitative traits. I present a general flexible Bayesian method that includes the number of genes in the FPM as an additional random variable. Markov-chain Monte Carlo techniques such as Gibbs sampling and the reversible jump sampler are used for implementation. Sampling of genotypes of all genes in the FPM is done via the use of segregation indicators. A broad range of FPM models, some combined with TIM, are empirically tested for the estimation of variance components and the number of genes in the FPM. Four simulation scenarios were studied, including genetic models with 5 or 50 additive independent diallelic genes affecting the traits, and random selection or selection on one of the traits was performed. The results in this study were based on ten replicates per simulation scenario. In the case of random selection, uniform priors on additive gene effects led to posterior mean estimates of genetic variance that were positively correlated with the number of genes fitted in the FPM. In the case of trait selection, assuming normal priors on gene effects also led to genetic variance estimates for the selected trait that were negatively correlated with the number of genes in the FPM. This negative correlation was not observed for the unselected trait. Treating the number of genes in the FPM as random revealed a positive correlation between prior and posterior mean estimates of this number, but the prior hardly affected the posterior estimates of genetic variance. Posterior inferences about the number of genes should be considered to be indicative where trait selection seems to improve the power of distinguishing between TIM and FPM. Based on the results of this study, I suggest not replacing TIM by the FPM, but combining TIM and FPM with the number of genes treated as random, to facilitate a highly flexible and thereby robust method for variance component estimation in pedigreed populations. Further study is required to explore the full potential of these models under different genetic model assumption
An Information-Theoretic Analysis of Thompson Sampling
We provide an information-theoretic analysis of Thompson sampling that
applies across a broad range of online optimization problems in which a
decision-maker must learn from partial feedback. This analysis inherits the
simplicity and elegance of information theory and leads to regret bounds that
scale with the entropy of the optimal-action distribution. This strengthens
preexisting results and yields new insight into how information improves
performance
On weighted local fitting and its relation to the Horvitz-Thompson estimator
Weighting is a largely used concept in many fields of statistics and has frequently caused controversies on its justification and profit. In this paper, we analyze a weighted version of the well-known local polynomial regression estimators, derive their asymptotic bias and variance, and find that the conflict between the asymptotically optimal weighting scheme and the practical requirements has a surprising counterpart in sampling theory, leading us back to the discussion on Basu's (1971) elephants
Conditional inference with a complex sampling: exact computations and Monte Carlo estimations
In survey statistics, the usual technique for estimating a population total
consists in summing appropriately weighted variable values for the units in the
sample. Different weighting systems exit: sampling weights, GREG weights or
calibration weights for example. In this article, we propose to use the inverse
of conditional inclusion probabilities as weighting system. We study examples
where an auxiliary information enables to perform an a posteriori
stratification of the population. We show that, in these cases, exact
computations of the conditional weights are possible. When the auxiliary
information consists in the knowledge of a quantitative variable for all the
units of the population, then we show that the conditional weights can be
estimated via Monte-Carlo simulations. This method is applied to outlier and
strata-Jumper adjustments
Scalable Bayesian model averaging through local information propagation
We show that a probabilistic version of the classical forward-stepwise
variable inclusion procedure can serve as a general data-augmentation scheme
for model space distributions in (generalized) linear models. This latent
variable representation takes the form of a Markov process, thereby allowing
information propagation algorithms to be applied for sampling from model space
posteriors. In particular, we propose a sequential Monte Carlo method for
achieving effective unbiased Bayesian model averaging in high-dimensional
problems, utilizing proposal distributions constructed using local information
propagation. We illustrate our method---called LIPS for local information
propagation based sampling---through real and simulated examples with
dimensionality ranging from 15 to 1,000, and compare its performance in
estimating posterior inclusion probabilities and in out-of-sample prediction to
those of several other methods---namely, MCMC, BAS, iBMA, and LASSO. In
addition, we show that the latent variable representation can also serve as a
modeling tool for specifying model space priors that account for knowledge
regarding model complexity and conditional inclusion relationships
A Conditional Empirical Likelihood Based Method for Model Parameter Estimation from Complex survey Datasets
We consider an empirical likelihood framework for inference for a statistical
model based on an informative sampling design. Covariate information is
incorporated both through the weights and the estimating equations. The
estimator is based on conditional weights. We show that under usual conditions,
with population size increasing unbounded, the estimates are strongly
consistent, asymptotically unbiased and normally distributed. Our framework
provides additional justification for inverse probability weighted score
estimators in terms of conditional empirical likelihood. In doing so, it
bridges the gap between design-based and model-based modes of inference in
survey sampling settings. We illustrate these ideas with an application to an
electoral survey
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