Model-averaged ℓ1 regularization using Markov chain Monte Carlo model composition

Bayesian model averaging (BMA) is an effective technique for addressing model uncertainty in variable selection problems. However, current BMA approaches have computational difficulty dealing with data in which there are many more measurements (variables) than samples. This paper presents a method for combining ?₁ regularization and Markov chain Monte Carlo model composition techniques for BMA. By treating the ?₁ regularization path as a model space, we propose a method to resolve the model uncertainty issues arising in model averaging from solution path point selection. We show that this method is computationally and empirically effective for regression and classification in high-dimensional data sets. We apply our technique in simulations, as well as to some applications that arise in genomics.     

Transient Analysis of Averaged Queue Length in Markovian Queues

Abstract

We consider a Markovian queue and its associated exponentially averaged length. The set of partial differential equations satisfied by the joint distribution of the queue and the averaged queue length is given. We obtain a recursive expression for the moments of the averaged queue length, and develop a stable algorithm to compute them. These results are illustrated through numerical examples.     

Analysis of ordered categorical data with score averaging: with applications to case-control genetic associations

The trend test is often used for the analysis of 2×K ordered categorical data, in which K pre-specified increasing scores are used. There have been discussions on how to assign these scores and the impact of the outcomes on different scores. The scores are often assigned based on the data-generating model. When this model is unknown, using the trend test is not robust. We discuss the weighted average of a trend test over all scientifically plausible choices of scores or models. This approach is more computationally efficient than a commonly used robust test MAX when K is large. Our discussion is for any ordered 2×K table, but simulation and applications to real data are focused on case-control genetic association studies. Although there is no single test optimal for all choices of scores, our numerical results show that some score averaging tests can achieve the performance of MAX.     

Estimation of a Benchmark Dose in the Presence or Absence of Hormesis Using Posterior Averaging

U.S. Environment Protection Agency benchmark doses for dichotomous cancer responses are often estimated using a multistage model based on a monotonic dose‐response assumption. To account for model uncertainty in the estimation process, several model averaging methods have been proposed for risk assessment. In this article, we extend the usual parameter space in the multistage model for monotonicity to allow for the possibility of a hormetic dose‐response relationship. Bayesian model averaging is used to estimate the benchmark dose and to provide posterior probabilities for monotonicity versus hormesis. Simulation studies show that the newly proposed method provides robust point and interval estimation of a benchmark dose in the presence or absence of hormesis. We also apply the method to two data sets on carcinogenic response of rats to 2,3,7,8‐tetrachlorodibenzo‐p‐dioxin.     

中国经济TFP增长的影响因素——基于BACE方法的综合分析

生产率增长是宏观经济研究的一个重要议题。采用经典估计贝叶斯平均(BACE)方法,引入模型的不确定性,在上万次回归的基础上,对众多影响生产率的解释变量按其重要性进行分类和排序。研究发现:在事先列出的16个可能的解释变量中,FDI进入程度、进口依存度、出口依存度、专科以上学历人数占从业人数的比率、相邻地区的生产率(空间邻居变量)以及市场化程度对TFP增长的解释能力最强,并且都具有良好的稳健性。FDI金额、进口额、出口额以及前一期研发投入等四个变量对TFP增长也有一定的解释能力。但各变量在我国东、中、西部地区的影响力存在显著差异。     

Editorial note: referees

Abstract

This study investigates three methods to handle dependency among effect size estimates in meta-analysis arising from studies reporting multiple outcome measures taken on the same sample. The three-level approach is compared with the method of robust variance estimation, and with averaging effects within studies. A simulation study is performed, and the fixed and random effect estimates of the three methods are compared with each other. Both the robust variance estimation and three-level approach result in unbiased estimates of the fixed effects, corresponding standard errors and variances. Averaging effect sizes results in overestimated standard errors when the effect sizes within studies are truly independent. Although the robust variance and three-level approach are more complicated to use, they have the advantage that they do not require an estimate of the correlation between outcomes, and they still result in unbiased parameter estimates.     

A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models

Just as frequentist hypothesis tests have been developed to check model assumptions, prior predictive p-values and other Bayesian p-values check prior distributions as well as other model assumptions. These model checks not only suffer from the usual threshold dependence of p-values, but also from the suppression of model uncertainty in subsequent inference. One solution is to transform Bayesian and frequentist p-values for model assessment into a fiducial distribution across the models. Averaging the Bayesian or frequentist posterior distributions with respect to the fiducial distribution can reproduce results from Bayesian model averaging or classical fiducial inference.     

On-line expectation–maximization algorithm for latent data models

Summary.  We propose a generic on-line (also sometimes called adaptive or recursive) version of the expectation–maximization (EM) algorithm applicable to latent variable models of independent observations. Compared with the algorithm of Titterington, this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete-data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to the stationary points of the Kullback–Leibler divergence between the marginal distribution of the observation and the model distribution at the optimal rate, i.e. that of the maximum likelihood estimator. In addition, the approach proposed is also suitable for conditional (or regression) models, as illustrated in the case of the mixture of linear regressions model.     

Accounting for uncertainty in health economic decision models by using model averaging

Summary.  Health economic decision models are subject to considerable uncertainty, much of which arises from choices between several plausible model structures, e.g. choices of covariates in a regression model. Such structural uncertainty is rarely accounted for formally in decision models but can be addressed by model averaging. We discuss the most common methods of averaging models and the principles underlying them. We apply them to a comparison of two surgical techniques for repairing abdominal aortic aneurysms. In model averaging, competing models are usually either weighted by using an asymptotically consistent model assessment criterion, such as the Bayesian information criterion, or a measure of predictive ability, such as Akaike's information criterion. We argue that the predictive approach is more suitable when modelling the complex underlying processes of interest in health economics, such as individual disease progression and response to treatment.     

Performance of localized regression tree splitting criteria on data with discontinuities

Properties of the localized regression tree splitting criterion, described in Bremner & Taplin (2002) and referred to as the BT method, are explored in this paper and compared to those of Clark & Pregibon's (1992) criterion (the CP method). These properties indicate why the BT method can result in superior trees. This paper shows that the BT method exhibits a weak bias towards edge splits, and the CP method exhibits a strong bias towards central splits in the presence of main effects. A third criterion, called the SM method, that exhibits no bias towards a particular split position is introduced. The SM method is a modification of the BT method that uses more symmetric local means. The BT and SM methods are more likely to split at a discontinuity than the CP method because of their relatively low bias towards particular split positions. The paper shows that the BT and SM methods can be used to discover discontinuities in the data, and that they offer a way of producing a variety of different trees for examination or for tree averaging methods.