A tutorial on adaptive MCMC

We review adaptive Markov chain Monte Carlo algorithms (MCMC) as a mean to optimise their performance. Using simple toy examples we review their theoretical underpinnings, and in particular show why adaptive MCMC algorithms might fail when some fundamental properties are not satisfied. This leads to guidelines concerning the design of correct algorithms. We then review criteria and the useful framework of stochastic approximation, which allows one to systematically optimise generally used criteria, but also analyse the properties of adaptive MCMC algorithms. We then propose a series of novel adaptive algorithms which prove to be robust and reliable in practice. These algorithms are applied to artificial and high dimensional scenarios, but also to the classic mine disaster dataset inference problem.     

General Sparse Boosting: Improving Feature Selection of L2 Boosting by Correlation-Based Penalty Family

In high-dimensional setting, componentwise L₂boosting has been used to construct sparse model that performs well, but it tends to select many ineffective variables. Several sparse boosting methods, such as, SparseL₂Boosting and Twin Boosting, have been proposed to improve the variable selection of L₂boosting algorithm. In this article, we propose a new general sparse boosting method (GSBoosting). The relations are established between GSBoosting and other well known regularized variable selection methods in the orthogonal linear model, such as adaptive Lasso, hard thresholds, etc. Simulation results show that GSBoosting has good performance in both prediction and variable selection.     

Sample Size Calculation and Blinded Sample Size Recalculation in Clinical Trials Where the Treatment Effect is Measured by the Relative Risk

In clinical trials with binary endpoints, the required sample size does not depend only on the specified type I error rate, the desired power and the treatment effect but also on the overall event rate which, however, is usually uncertain. The internal pilot study design has been proposed to overcome this difficulty. Here, nuisance parameters required for sample size calculation are re-estimated during the ongoing trial and the sample size is recalculated accordingly. We performed extensive simulation studies to investigate the characteristics of the internal pilot study design for two-group superiority trials where the treatment effect is captured by the relative risk. As the performance of the sample size recalculation procedure crucially depends on the accuracy of the applied sample size formula, we firstly explored the precision of three approximate sample size formulae proposed in the literature for this situation. It turned out that the unequal variance asymptotic normal formula outperforms the other two, especially in case of unbalanced sample size allocation. Using this formula for sample size recalculation in the internal pilot study design assures that the desired power is achieved even if the overall rate is mis-specified in the planning phase. The maximum inflation of the type I error rate observed for the internal pilot study design is small and lies below the maximum excess that occurred for the fixed sample size design.     

An adaptive sampling scheme guided by BART—with an application to predict processor performance

The evaluation of new processor designs is an important issue in electrical and computer engineering. Architects use simulations to evaluate designs and to understand trade‐offs and interactions among design parameters. However, due to the lengthy simulation time and limited resources, it is often practically impossible to simulate a full factorial design space. Effective sampling methods and predictive models are required. In this paper, the authors propose an automated performance predictive approach which employs an adaptive sampling scheme that interactively works with the predictive model to select samples for simulation. These samples are then used to build Bayesian additive regression trees, which in turn are used to predict the whole design space. Both real data analysis and simulation studies show that the method is effective in that, though sampling at very few design points, it generates highly accurate predictions on the unsampled points. Furthermore, the proposed model provides quantitative interpretation tools with which investigators can efficiently tune design parameters in order to improve processor performance. The Canadian Journal of Statistics 38: 136–152; 2010 © 2010 Statistical Society of Canada     

Using adaptive weighted least squares to reduce the lengths of confidence intervals

The author proposes an adaptive method which produces confidence intervals that are often narrower than those obtained by the traditional procedures. The proposed methods use both a weighted least squares approach to reduce the length of the confidence interval and a permutation technique to insure that its coverage probability is near the nominal level. The author reports simulations comparing the adaptive intervals to the traditional ones for the difference between two population means, for the slope in a simple linear regression, and for the slope in a multiple linear regression having two correlated exogenous variables. He is led to recommend adaptive intervals for sample sizes superior to 40 when the error distribution is not known to be Gaussian.     

Adaptive weights smoothing with applications to image restoration

We propose a new method of nonparametric estimation which is based on locally constant smoothing with an adaptive choice of weights for every pair of data points. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on some simulated univariate and bivariate examples and compare it with other nonparametric methods. Finally we discuss applications of this procedure to magnetic resonance and satellite imaging.     

Adaptive sampling without replacement of clusters

In a common form of adaptive cluster sampling, an initial sample of units is selected by random sampling without replacement and, whenever the observed value of the unit is sufficiently high, its neighboring units are added to the sample, with the process of adding neighbors repeated if any of the added units are also high valued. In this way, an initial selection of a high-valued unit results in the addition of the entire network of surrounding high-valued units and some low-valued “edge” units where sampling stops. Repeat selections can occur when more than one initially selected unit is in the same network or when an edge unit is shared by more than one added network. Adaptive sampling without replacement of networks avoids some of this repeat selection by sequentially selecting initial sample units only from the part of the population not already in any selected network. The design proposed in this paper carries this step further by selecting initial units only from the population, exclusive of any previously selected networks or edge units.     

以热流率作为补偿的智能PID控制

本文以电加热流动热力系统为例，提出了一种以静态模型为基础．以热流率作为补偿的智能ＰＩＤ控制处理动态模型的方法．较好地解决了由于热流率的变化而引起的温度波动，在应用中得到了满意的结果．     

A note on the adaptive control of false discovery rates

Summary.  The use of a fixed rejection region for multiple hypothesis testing has been shown to outperform standard fixed error rate approaches when applied to control of the false discovery rate. In this work it is demonstrated that, if the original step-up procedure of Benjamini and Hochberg is modified to exercise adaptive control of the false discovery rate, its performance is virtually identical to that of the fixed rejection region approach. In addition, the dependence of both methods on the proportion of true null hypotheses is explored, with a focus on the difficulties that are involved in the estimation of this quantity.     

A tolerance interval approach for assessment of agreement in method comparison studies with repeated measurements

This paper generalizes the tolerance interval approach for assessing agreement between two methods of continuous measurement for repeated measurement data—a common scenario in applications. The repeated measurements may be longitudinal or they may be replicates of the same underlying measurement. Our approach is to first model the data using a mixed model and then construct a relevant asymptotic tolerance interval (or band) for the distribution of appropriately defined differences. We present the methodology in the general context of a mixed model that can incorporate covariates, heteroscedasticity and serial correlation in the errors. Simulation for the no-covariate case shows good small-sample performance of the proposed methodology. For the longitudinal data, we also describe an extension for the case when the observed time profiles are modelled nonparametrically through penalized splines. Two real data applications are presented.