Model fitting and evaluation in climate reconstruction of tree-ring data: A comment on Steinschneider et al. (2017): Hierarchical regression models for dendroclimatic standardization and climate reconstruction

Steinschneider et al. (2017) investigate model choices made in the hierarchical climate reconstruction approach of Schofield et al. (2016). We identify two flaws in their approach. The first is the use of an unusual approximation to Bayesian inference that unnecessarily discards important information. The second is that they mischaracterize the robustness of their reconstructions due to overlooking important features of the out-of-sample predictions. We demonstrate how full Bayesian inference can be conducted with no additional effort, providing R/JAGS code. We also show how graphical visualization of the out-of-sample predictions can lead to better understanding and comparison of the models fitted.     

恶性卵巢肿瘤的Bayes预测

文献〔1〕通过逐步回归确定了与卵巢肿瘤有关的五个主要因素:年龄(X_1)、生育关系(x_2)、肿瘤大小(x_3)、肿瘤硬度(X_4)、并发症(X_5),并将这五个主要因素的指标分级如表1,给出最大似然诊断法。本文在此基础上,根据延边医学院1981年1月至1985年12月底经手术治疗的237例肿瘤病人的统计数据,对〔1〕的结果进一步研究与改进,给出了恶性卵巢肿瘤的Bayes诊     

Bayesian Estimation Using Ranked Set Sampling

Bayesian Estimation of the parameter of a distribution is considered using Ranked set sampling (RSS). It is shown that for at least one RSS plan, the Bayes estimator has smaller Bayes risk than the Bayes estimator using simple random sampling (SRS). Furthermore, for exponential family with conjugate prior, the Bayes estimator of the mean using balanced RSS dominates, in terms of its Bayes risk, the Bayes estimator of the mean using SRS. This procedure is used to estimate the average Milk yield of four hundreds and two sheep. The empirical efficiency supports the theoretical findings.     

Accounting for multiplicity in the evaluation of "signals" obtained by data mining from spontaneous report adverse event databases

Surveillance of drug products in the marketplace continues after approval, to identify rare potential toxicities that are unlikely to have been observed in the clinical trials carried out before approval. This surveillance accumulates large numbers of spontaneous reports of adverse events along with other information in spontaneous report databases. Recently developed empirical Bayes and Bayes methods provide a way to summarize the data in these databases, including a quantitative measure of the strength of the reporting association between the drugs and the events. Determining which of the particular drug-event associations, of which there may be many tens of thousands, are real reporting associations and which random noise presents a substantial problem of multiplicity because the resources available for medical and epidemiologic followup are limited. The issues are similar to those encountered with the evaluation of microarrays, but there are important differences. This report compares the application of a standard empirical Bayes approach with micorarray-inspired methods for controlling the False Discovery Rate, and a new Bayesian method for the resolution of the multiplicity problem to a relatively small database containing about 48,000 reports. The Bayesian approach appears to have attractive diagnostic properties in addition to being easy to interpret and implement computationally.     

Extrapolation in Risk Assessment: Improving the Quantification of Uncertainty,and Improving Information to Reduce the Uncertainty

Risk assessments inevitably extrapolate from the known to the unknown. The resulting calculation of risk involves two fundamental kinds of uncertainty: uncertainty owing to intrinsically unpredictable (random) components of the future events, and uncertainty owing to imperfect prediction formulas (parameter uncertainty and error in model structure) that are used to predict the component that we think is predictable. Both types of uncertainty weigh heavily both in health and ecological risk assessments. Our first responsibility in conducting risk assessments is to ensure that the reported risks correctly reflect our actual level of uncertainty (of both types). The statistical methods that lend themselves to correct quantification of the uncertainty are also effective for combining different sources of information. One way to reduce uncertainty is to use all the available data. To further sharpen future risk assessments, it is useful to partition the uncertainty between the random component and the component due to parameter uncertainty, so that we can quantify the expected reduction in uncertainty that can be achieved by investing in a given amount of future data. An example is developed to illustrate the potential for use of comparative data, from toxicity testing on other species or other chemicals, to improve the estimates of low-effect concentration in a particular case with sparse case-specific data.     

The role of game management in wildlife populations: uncertainty analysis of expert knowledge

Uncertainties about future states of wildlife populations make it difficult to pre-adapt to possible threats and ensure sustainability of resources and harvesting over the long term. This uncertainty is partly due to the unknown impact and future states of many factors that explain population sizes and variation. In this paper, the effect of local game management activities on the uncertainty of future population sizes of groups of Finnish wildlife species (ungulates, forest grouse, large predators, small predators and mountain hare) was analysed using expert knowledge and the Bayesian belief networks (BBNs) modelling techniques. As a result, the current knowledge and agreement of the relationships between wildlife population sizes and the game management activities explaining their variation as well as trends are evaluated. Information given to hunters and the number of hunters were seen as the most effective factors for the management of game populations. However, there were great uncertainties in the expectations regarding future trends in the management activities, especially in feeding, and there was disagreement in the direction of the trend in the length of the hunting season. The trends in the size of forest grouse populations were viewed as the most uncertain trend among species groups. At the same time, forest grouse were seen as the most regulated species group by local game management. Among interest variables, experts were very uncertain and they disagreed about the direction of the trend in the recreational value of hunting.     

Where is the light? Bayesian perceptual priors for lighting direction

Perception of shaded three-dimensional figures is inherently ambiguous, but this ambiguity can be resolved if the brain assumes that figures are lit from a specific direction. Under the Bayesian framework, the visual system assigns a weighting to each possible direction, and these weightings define a prior probability distribution for light-source direction. Here, we describe a non-parametric maximum-likelihood estimation method for finding the prior distribution for lighting direction. Our results suggest that each observer has a distinct prior distribution, with non-zero values in all directions, but with a peak which indicates observers are biased to expect light to come from above left. The implications of these results for estimating general perceptual priors are discussed.     

Cryptic diversity,pathogenicity, and evolutionary species boundaries in Cercospora populations associated with Cercospora leaf spot of Beta vulgaris

The taxonomy and evolutionary species boundaries in a global collection of Cercospora isolates from Beta vulgaris was investigated based on sequences of six loci. Species boundaries were assessed using concatenated multi-locus phylogenies, Generalized Mixed Yule Coalescent (GMYC), Poisson Tree Processes (PTP), and Bayes factor delimitation (BFD) framework. Cercospora beticola was confirmed as the primary cause of Cercospora leaf spot (CLS) on B. vulgaris. Cercospora apii, C. cf. flagellaris, Cercospora sp. G, and C. zebrina were also identified in association with CLS on B. vulgaris. Cercospora apii and C. cf. flagellaris were pathogenic to table beet but Cercospora sp. G and C. zebrina did not cause disease. Genealogical concordance phylogenetic species recognition, GMYC and PTP methods failed to differentiate C. apii and C. beticola as separate species. On the other hand, multi-species coalescent analysis based on BFD supported separation of C. apii and C. beticola into distinct species; and provided evidence of evolutionary independent lineages within C. beticola. Extensive intra- and intergenic recombination, incomplete lineage sorting and dominance of clonal reproduction complicate evolutionary species recognition in the genus Cercospora. The results warrant morphological and phylogenetic studies to disentangle cryptic speciation within C. beticola.     

Hierarchical Bayes models for cDNA microarray gene expression

cDNA microarrays are used in many contexts to compare mRNA levels between samples of cells. Microarray experiments typically give us expression measurements on 1000-20 000 genes, but with few replicates for each gene. Traditional methods using means and standard deviations to detect differential expression are not satisfactory in this context. A handful of alternative statistics have been developed, including several empirical Bayes methods. In the present paper we present two full hierarchical Bayes models for detecting gene expression, of which one (D) describes our microarray data very well. We also compare the full Bayes and empirical Bayes approaches with respect to model assumptions, false discovery rates and computer running time. The proposed models are compared to existing empirical Bayes models in a simulation study and for a set of data (Yuen et al., 2002), where 27 genes have been categorized by quantitative real-time PCR. It turns out that the existing empirical Bayes methods have at least as good performance as the full Bayes ones.     

A Bayesian Decision Procedure for Selecting Prognostic Variables Associated with Survival for Data in which Censoring is Prevalent

A Bayesian procedure is developed for the selection of concomitant variables in survival models. The variables are selected in a step-up procedure according to the criterion of maximum expected likelihood, where the expectation is over the prior parameter space. Prior knowledge of the influence of these covariates on patient prognosis is incorporated into the analysis. The step-up procedure is stopped when the Bayes factor in favor of omitting the variable selected in a particular step exceeds a specified value. The resulting model with the selected variables is fitted using Bayes estimates of the coefficients. This technique is applied to Hodgkin's disease data from a large Cooperative Clinical Trial Group and the results are compared to the results from the classical likelihood selection procedure.     

Topology-Bayes versus Clade-Bayes in phylogenetic analysis

Several features of currently used Bayesian methods in phylogenetic analysis are discussed. The distinction between Clade-Bayes and Topology-Bayes is presented and illustrated with an empirical example. Three problems with Bayesian phylogenetic methods--exaggerated clade support, inconsistently biased priors, and the impossibility of hypothesis testing of cladograms--are shown to be the result of using a Clade-based Bayesian approach. Topology-based Bayesian methods do not share these shortcomings.