ترغب بنشر مسار تعليمي؟ اضغط هنا

Bayesian Variable Selection for Skewed Heteroscedastic Response

133   0   0.0 ( 0 )
 نشر من قبل Libo Wang
 تاريخ النشر 2016
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

In this article, we propose new Bayesian methods for selecting and estimating a sparse coefficient vector for skewed heteroscedastic response. Our novel Bayesian procedures effectively estimate the median and other quantile functions, accommodate non-local prior for regression effects without compromising ease of implementation via sampling based tools, and asymptotically select the true set of predictors even when the number of covariates increases in the same order of the sample size. We also extend our method to deal with some observations with very large errors. Via simulation studies and a re-analysis of a medical cost study with large number of potential predictors, we illustrate the ease of implementation and other practical advantages of our approach compared to existing methods for such studies.

قيم البحث

اقرأ أيضاً

We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of regression coeffic ients which obviates the need to specify a prior on the rank, and shrinks the regression matrix towards low-rank and row-sparse structures. We provide theoretical support to the proposed methodology by proving minimax optimality of the posterior mean under the prediction risk in ultra-high dimensional settings where the number of predictors can grow sub-exponentially relative to the sample size. A one-step post-processing scheme induced by group lasso penalties on the rows of the estimated coefficient matrix is proposed for variable selection, with default choices of tuning parameters. We additionally provide an estimate of the rank using a novel optimization function achieving dimension reduction in the covariate space. We exhibit the performance of the proposed methodology in an extensive simulation study and a real data example.
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear seemingly unrelated regression framework. We propose a joint predictor and graph selection model and develop an efficient collapsed Gibbs sampler algorithm to search the joint model space. Furthermore, we investigate its theoretical variable selection properties. We demonstrate our method on a variety of simulated data, concluding with a real data set from the TCPA project.
The issue of determining not only an adequate dose but also a dosing frequency of a drug arises frequently in Phase II clinical trials. This results in the comparison of models which have some parameters in common. Planning such studies based on Baye sian optimal designs offers robustness to our conclusions since these designs, unlike locally optimal designs, are efficient even if the parameters are misspecified. In this paper we develop approximate design theory for Bayesian $D$-optimality for nonlinear regression models with common parameters and investigate the cases of common location or common location and scale parameters separately. Analytical characterisations of saturated Bayesian $D$-optimal designs are derived for frequently used dose-response models and the advantages of our results are illustrated via a numerical investigation.
349 - Lu Zhang , Junwei Lu 2021
Variable selection on the large-scale networks has been extensively studied in the literature. While most of the existing methods are limited to the local functionals especially the graph edges, this paper focuses on selecting the discrete hub struct ures of the networks. Specifically, we propose an inferential method, called StarTrek filter, to select the hub nodes with degrees larger than a certain thresholding level in the high dimensional graphical models and control the false discovery rate (FDR). Discovering hub nodes in the networks is challenging: there is no straightforward statistic for testing the degree of a node due to the combinatorial structures; complicated dependence in the multiple testing problem is hard to characterize and control. In methodology, the StarTrek filter overcomes this by constructing p-values based on the maximum test statistics via the Gaussian multiplier bootstrap. In theory, we show that the StarTrek filter can control the FDR by providing accurate bounds on the approximation errors of the quantile estimation and addressing the dependence structures among the maximal statistics. To this end, we establish novel Cramer-type comparison bounds for the high dimensional Gaussian random vectors. Comparing to the Gaussian comparison bound via the Kolmogorov distance established by citet{chernozhukov2014anti}, our Cramer-type comparison bounds establish the relative difference between the distribution functions of two high dimensional Gaussian random vectors. We illustrate the validity of the StarTrek filter in a series of numerical experiments and apply it to the genotype-tissue expression dataset to discover central regulator genes.
Bayesian methods - either based on Bayes Factors or BIC - are now widely used for model selection. One property that might reasonably be demanded of any model selection method is that if a model ${M}_{1}$ is preferred to a model ${M}_{0}$, when these two models are expressed as members of one model class $mathbb{M}$, this preference is preserved when they are embedded in a different class $mathbb{M}$. However, we illustrate in this paper that with the usual implementation of these common Bayesian procedures this property does not hold true even approximately. We therefore contend that to use these methods it is first necessary for there to exist a natural embedding class. We argue that in any context like the one illustrated in our running example of Bayesian model selection of binary phylogenetic trees there is no such embedding.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا