Conditional properties of unconditional parametric bootstrap procedures for inference in exponential families

Higher-order inference about a scalar parameter in the presenceof nuisance parameters can be achieved by bootstrapping, incircumstances where the parameter of interest is a componentof the canonical parameter in a full exponential family. Theoptimal test, which is approximated, is a conditional one basedon conditioning on the sufficient statistic for the nuisanceparameter. A bootstrap procedure that ignores the conditioningis shown to have desirable conditional properties in providingthird-order relative accuracy in approximation of p-values associatedwith the optimal test, in both continuous and discrete models.The bootstrap approach is equivalent to third-order analyticalapproaches, and is demonstrated in a number of examples to givevery accurate approximations even for very small sample sizes.     

Higher order inference for the consensus mean in inter-laboratory studies

In inter-laboratory studies, a fundamental problem of interest is inference concerning the consensus mean, when the measurements are made by several laboratories which may exhibit different within-laboratory variances, apart from the between laboratory variability. A heteroscedastic one-way random model is very often used to model this scenario. Under such a model, a modified signed log-likelihood ratio procedure is developed for the interval estimation of the common mean. Furthermore, simulation results are presented to show the accuracy of the proposed confidence interval, especially for small samples. The results are illustrated using an example on the determination of selenium in non-fat milk powder by combining the results of four methods. Here, the sample size is small, and the confidence limits for the common mean obtained by different methods produce very different results. The confidence interval based on the modified signed log-likelihood ratio procedure appears to be quite satisfactory.     

Statistical inference for stochastic simulation models--theory and application

Statistical models are the traditional choice to test scientific theories when observations, processes or boundary conditions are subject to stochasticity. Many important systems in ecology and biology, however, are difficult to capture with statistical models. Stochastic simulation models offer an alternative, but they were hitherto associated with a major disadvantage: their likelihood functions can usually not be calculated explicitly, and thus it is difficult to couple them to well-established statistical theory such as maximum likelihood and Bayesian statistics. A number of new methods, among them Approximate Bayesian Computing and Pattern-Oriented Modelling, bypass this limitation. These methods share three main principles: aggregation of simulated and observed data via summary statistics, likelihood approximation based on the summary statistics, and efficient sampling. We discuss principles as well as advantages and caveats of these methods, and demonstrate their potential for integrating stochastic simulation models into a unified framework for statistical modelling.     

最大似然法和贝叶斯推论与似然比检验探讨泽泻目系统发育关系

应用最大似然法(ML)、贝叶斯推论(BI)、邻接法(NJ)和似然比检验(hLRTs)进行泽泻目分子系统学研究。所用的rbcL基因序列代表了泽泻目14科46属以及作为外类群的6相关属。研究结果表明,*等级制似然比检验表明泽泻目rbcL序列最适合的DNA进化模型为GTR+I+G,最大似然法、贝叶斯法和邻接法构建的系统发育树拓扑结构相似,没有显著的差异,但贝叶斯树支持率较高;泽泻目为一单系类群,由两个主要谱系分支构成,深层分布格局由5个主要分支构成。基于分子系统发育树,文中对泽泻目科间、水鳖科+茨藻科、泽泻科+花蔺科+黄花蔺科、和Cymodoeaceae complex的系统发育关系进行了讨论。研究结果还表明,泽泻目系统发育关系可能还需要更多的证据进一步的澄清。     

Bayesian and influence function-based empirical likelihoods for inference of sensitivity to the early diseased stage in diagnostic tests

In practice, a disease process might involve three ordinal diagnostic stages: the normal healthy stage, the early stage of the disease, and the stage of full development of the disease. Early detection is critical for some diseases since it often means an optimal time window for therapeutic treatments of the diseases. In this study, we propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to construct confidence/credible intervals for the sensitivity of a test to patients in the early diseased stage given a specificity and a sensitivity of the test to patients in the fully diseased stage. Numerical studies are performed to compare the finite sample performances of the proposed approaches with existing methods. The proposed methods are shown to outperform existing methods in terms of coverage probability. A real dataset from the Alzheimer's Disease Neuroimaging Initiative (ANDI) is used to illustrate the proposed methods.     

Generalized conjugate priors for Bayesian analysis of risk and survival regressions

Conjugate priors for Bayesian analyses of relative risks can be quite restrictive, because their shape depends on their location. By introducing a separate location parameter, however, these priors generalize to allow modeling of a broad range of prior opinions, while still preserving the computational simplicity of conjugate analyses. The present article illustrates the resulting generalized conjugate analyses using examples from case-control studies of the association of residential wire codes and magnetic fields with childhood leukemia.     

The likelihood node density effect and consequences for evolutionary studies of molecular rates

Many molecular phylogenies show longer root-to-tip path lengths in species-rich groups, encouraging hypotheses linking cladogenesis with accelerated molecular evolution. However, the pattern can also be caused by an artifact called the node density effect (NDE): this effect occurs when the method used to reconstruct a tree underestimates multiple hits that would have been revealed by extra nodes, leading to longer root-to-tip path lengths in clades with more terminal taxa. Here we use a twofold approach to demonstrate that maximum likelihood and Bayesian methods also suffer from the NDE known to affect parsimony. First, simulations deliberately mismatching the simulation and reconstruction models show that the greater the model disparity, the greater the gap between actual and reconstructed tree lengths, and the greater the NDE. Second, taxon sampling manipulation with empirical data shows that NDE can still be present when using optimized models: across 12 datasets, 70 out of 109 sister path comparisons showed significant evidence of NDE. Unless the model fairly accurately reconstructs the real tree length-and given the complexity of real sequence evolution this may be uncommon -- it will consistently produce a node density artifact. At commonly encountered divergence levels, a 10% underestimation of tree length results in > or = 80% of simulated phylogenies showing a positive NDE. Bayesian trees have a slight but consistently stronger effect. This pervasive methodological artifact increases apparent rate heterogeneity, and can compromise investigations of factors influencing molecular evolutionary rate that use path lengths in topologically asymmetric trees.     

Resampling-based empirical Bayes multiple testing procedures for controlling generalized tail probability and expected value error rates: focus on the false discovery rate and simulation study

This article proposes resampling-based empirical Bayes multiple testing procedures for controlling a broad class of Type I error rates, defined as generalized tail probability (gTP) error rates, gTP (q,g) = Pr(g (V(n),S(n)) > q), and generalized expected value (gEV) error rates, gEV (g) = E [g (V(n),S(n))], for arbitrary functions g (V(n),S(n)) of the numbers of false positives V(n) and true positives S(n). Of particular interest are error rates based on the proportion g (V(n),S(n)) = V(n) /(V(n) + S(n)) of Type I errors among the rejected hypotheses, such as the false discovery rate (FDR), FDR = E [V(n) /(V(n) + S(n))]. The proposed procedures offer several advantages over existing methods. They provide Type I error control for general data generating distributions, with arbitrary dependence structures among variables. Gains in power are achieved by deriving rejection regions based on guessed sets of true null hypotheses and null test statistics randomly sampled from joint distributions that account for the dependence structure of the data. The Type I error and power properties of an FDR-controlling version of the resampling-based empirical Bayes approach are investigated and compared to those of widely-used FDR-controlling linear step-up procedures in a simulation study. The Type I error and power trade-off achieved by the empirical Bayes procedures under a variety of testing scenarios allows this approach to be competitive with or outperform the Storey and Tibshirani (2003) linear step-up procedure, as an alternative to the classical Benjamini and Hochberg (1995) procedure.