Modeling tails for collinear data with outliers in the English Longitudinal Study of Ageing: Quantile profile regression

Research has shown that high blood glucose levels are important predictors of incident diabetes. However, they are also strongly associated with other cardiometabolic risk factors such as high blood pressure, adiposity, and cholesterol, which are also highly correlated with one another. The aim of this analysis was to ascertain how these highly correlated cardiometabolic risk factors might be associated with high levels of blood glucose in older adults aged 50 or older from wave 2 of the English Longitudinal Study of Ageing (ELSA). Due to the high collinearity of predictor variables and our interest in extreme values of blood glucose we proposed a new method, called quantile profile regression, to answer this question. Profile regression, a Bayesian nonparametric model for clustering responses and covariates simultaneously, is a powerful tool to model the relationship between a response variable and covariates, but the standard approach of using a mixture of Gaussian distributions for the response model will not identify the underlying clusters correctly, particularly with outliers in the data or heavy tail distribution of the response. Therefore, we propose quantile profile regression to model the response variable with an asymmetric Laplace distribution, allowing us to model more accurately clusters that are asymmetric and predict more accurately for extreme values of the response variable and/or outliers. Our new method performs more accurately in simulations when compared to Normal profile regression approach as well as robustly when outliers are present in the data. We conclude with an analysis of the ELSA.     

Bayesian nonparametric analysis for the detection of spikes in noisy calcium imaging data

Recent advancements in miniaturized fluorescence microscopy have made it possible to investigate neuronal responses to external stimuli in awake behaving animals through the analysis of intracellular calcium signals. An ongoing challenge is deconvolving the temporal signals to extract the spike trains from the noisy calcium signals' time series. In this article, we propose a nested Bayesian finite mixture specification that allows the estimation of spiking activity and, simultaneously, reconstructing the distributions of the calcium transient spikes' amplitudes under different experimental conditions. The proposed model leverages two nested layers of random discrete mixture priors to borrow information between experiments and discover similarities in the distributional patterns of neuronal responses to different stimuli. Furthermore, the spikes' intensity values are also clustered within and between experimental conditions to determine the existence of common (recurring) response amplitudes. Simulation studies and the analysis of a dataset from the Allen Brain Observatory show the effectiveness of the method in clustering and detecting neuronal activities.     

Bayesian semiparametric modeling for matched case-control studies with multiple disease states

We present a Bayesian approach to analyze matched "case-control" data with multiple disease states. The probability of disease development is described by a multinomial logistic regression model. The exposure distribution depends on the disease state and could vary across strata. In such a model, the number of stratum effect parameters grows in direct proportion to the sample size leading to inconsistent MLEs for the parameters of interest even when one uses a retrospective conditional likelihood. We adopt a semiparametric Bayesian framework instead, assuming a Dirichlet process prior with a mixing normal distribution on the distribution of the stratum effects. We also account for possible missingness in the exposure variable in our model. The actual estimation is carried out through a Markov chain Monte Carlo numerical integration scheme. The proposed methodology is illustrated through simulation and an example of a matched study on low birth weight of newborns (Hosmer, D. A. and Lemeshow, S., 2000, Applied Logistic Regression) with two possible disease groups matched with a control group.     

Nonparametric bayesian estimation of positive false discovery rates

We propose a Dirichlet process mixture model (DPMM) for the P-value distribution in a multiple testing problem. The DPMM allows us to obtain posterior estimates of quantities such as the proportion of true null hypothesis and the probability of rejection of a single hypothesis. We describe a Markov chain Monte Carlo algorithm for computing the posterior and the posterior estimates. We propose an estimator of the positive false discovery rate based on these posterior estimates and investigate the performance of the proposed estimator via simulation. We also apply our methodology to analyze a leukemia data set.     

A Bayesian nonparametric testing procedure for paired samples

We propose a Bayesian hypothesis testing procedure for comparing the distributions of paired samples. The procedure is based on a flexible model for the joint distribution of both samples. The flexibility is given by a mixture of Dirichlet processes. Our proposal uses a spike-slab prior specification for the base measure of the Dirichlet process and a particular parametrization for the kernel of the mixture in order to facilitate comparisons and posterior inference. The joint model allows us to derive the marginal distributions and test whether they differ or not. The procedure exploits the correlation between samples, relaxes the parametric assumptions, and detects possible differences throughout the entire distributions. A Monte Carlo simulation study comparing the performance of this strategy to other traditional alternatives is provided. Finally, we apply the proposed approach to spirometry data collected in the United States to investigate changes in pulmonary function in children and adolescents in response to air polluting factors.     

Bayesian semiparametric analysis of developmental toxicology data

Modeling of developmental toxicity studies often requires simple parametric analyses of the dose-response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure. This article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations. We approach our analysis using a Bayesian semiparametric model that we tailored specifically to developmental toxicology studies. It combines parametric dose-response relationships with a flexible nonparametric specification of the distribution of the response, obtained via a product of Dirichlet process mixtures approach (PDPM). Our formulation achieves three goals: (1) the distribution of the response is modeled in a general way, (2) the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data, and (3) the marginal posterior distribution of the parameters of interest is available in closed form. The logistic regression model, as well as many of its extensions such as the beta-binomial model and finite mixture models, are special cases. In the context of the two motivating examples and a simulated example, we provide model comparisons, illustrate overdispersion diagnostics that can assist model specification, show how to derive posterior distributions of the effective dose parameters and predictive distributions of response, and discuss the sensitivity of the results to the choice of the prior distribution.     

Bayesian Hierarchical Modeling and Selection of Differentially Expressed Genes for the EST Data

Summary Expressed sequence tag (EST) sequencing is a one‐pass sequencing reading of cloned cDNAs derived from a certain tissue. The frequency of unique tags among different unbiased cDNA libraries is used to infer the relative expression level of each tag. In this article, we propose a hierarchical multinomial model with a nonlinear Dirichlet prior for the EST data with multiple libraries and multiple types of tissues. A novel hierarchical prior is developed and the properties of the proposed prior are examined. An efficient Markov chain Monte Carlo algorithm is developed for carrying out the posterior computation. We also propose a new selection criterion for detecting which genes are differentially expressed between two tissue types. Our new method with the new gene selection criterion is demonstrated via several simulations to have low false negative and false positive rates. A real EST data set is used to motivate and illustrate the proposed method.     

Bayesian nonparametric analysis of restricted mean survival time

The restricted mean survival time (RMST) evaluates the expectation of survival time truncated by a prespecified time point, because the mean survival time in the presence of censoring is typically not estimable. The frequentist inference procedure for RMST has been widely advocated for comparison of two survival curves, while research from the Bayesian perspective is rather limited. For the RMST of both right- and interval-censored data, we propose Bayesian nonparametric estimation and inference procedures. By assigning a mixture of Dirichlet processes (MDP) prior to the distribution function, we can estimate the posterior distribution of RMST. We also explore another Bayesian nonparametric approach using the Dirichlet process mixture model and make comparisons with the frequentist nonparametric method. Simulation studies demonstrate that the Bayesian nonparametric RMST under diffuse MDP priors leads to robust estimation and under informative priors it can incorporate prior knowledge into the nonparametric estimator. Analysis of real trial examples demonstrates the flexibility and interpretability of the Bayesian nonparametric RMST for both right- and interval-censored data.     

随机漂移亚群体等位基因频率分布的假定及在DNA指纹数据中的应用

研究影响计算两ＤＮＡ指纹偶然匹配率的亚群体结构,首次提出随机漂移各亚群体单个位点等位基因频率服朋参数为（ｐ１（１－θ）／θ,ｐ２（１－θ）／θ,…ｐｍ（１－θ）／θ）的Ｄｉｒｉｃｈｌｅｔ分布的假定（ｐ１,ｐ２,…,ｐｍ为随机漂移初始频率,θ为近交系数）,证明依分布产生亚群体,其结构、性质与群体遗传理论、样本理论一致;将该分布应用于ＤＮＡ指纹数据,得到了其它方法的类似结论。     

Bayes optimal informer sets for early-stage drug discovery

An important experimental design problem in early-stage drug discovery is how to prioritize available compounds for testing when very little is known about the target protein. Informer-based ranking (IBR) methods address the prioritization problem when the compounds have provided bioactivity data on other potentially relevant targets. An IBR method selects an informer set of compounds, and then prioritizes the remaining compounds on the basis of new bioactivity experiments performed with the informer set on the target. We formalize the problem as a two-stage decision problem and introduce the Bayes Optimal Informer SEt (BOISE) method for its solution. BOISE leverages a flexible model of the initial bioactivity data, a relevant loss function, and effective computational schemes to resolve the two-step design problem. We evaluate BOISE and compare it to other IBR strategies in two retrospective studies, one on protein-kinase inhibition and the other on anticancer drug sensitivity. In both empirical settings BOISE exhibits better predictive performance than available methods. It also behaves well with missing data, where methods that use matrix completion show worse predictive performance.     

Scalable Empirical Mixture Models That Account for Across-Site Compositional Heterogeneity

Biochemical demands constrain the range of amino acids acceptable at specific sites resulting in across-site compositional heterogeneity of the amino acid replacement process. Phylogenetic models that disregard this heterogeneity are prone to systematic errors, which can lead to severe long-branch attraction artifacts. State-of-the-art models accounting for across-site compositional heterogeneity include the CAT model, which is computationally expensive, and empirical distribution mixture models estimated via maximum likelihood (C10–C60 models). Here, we present a new, scalable method EDCluster for finding empirical distribution mixture models involving a simple cluster analysis. The cluster analysis utilizes specific coordinate transformations which allow the detection of specialized amino acid distributions either from curated databases or from the alignment at hand. We apply EDCluster to the HOGENOM and HSSP databases in order to provide universal distribution mixture (UDM) models comprising up to 4,096 components. Detailed analyses of the UDM models demonstrate the removal of various long-branch attraction artifacts and improved performance compared with the C10–C60 models. Ready-to-use implementations of the UDM models are provided for three established software packages (IQ-TREE, Phylobayes, and RevBayes).