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.     

Robust estimation of local genetic ancestry in admixed populations using a nonparametric bayesian approach

We present a new haplotype-based approach for inferring local genetic ancestry of individuals in an admixed population. Most existing approaches for local ancestry estimation ignore the latent genetic relatedness between ancestral populations and treat them as independent. In this article, we exploit such information by building an inheritance model that describes both the ancestral populations and the admixed population jointly in a unified framework. Based on an assumption that the common hypothetical founder haplotypes give rise to both the ancestral and the admixed population haplotypes, we employ an infinite hidden Markov model to characterize each ancestral population and further extend it to generate the admixed population. Through an effective utilization of the population structural information under a principled nonparametric Bayesian framework, the resulting model is significantly less sensitive to the choice and the amount of training data for ancestral populations than state-of-the-art algorithms. We also improve the robustness under deviation from common modeling assumptions by incorporating population-specific scale parameters that allow variable recombination rates in different populations. Our method is applicable to an admixed population from an arbitrary number of ancestral populations and also performs competitively in terms of spurious ancestry proportions under a general multiway admixture assumption. We validate the proposed method by simulation under various admixing scenarios and present empirical analysis results from a worldwide-distributed dataset from the Human Genome Diversity Project.     

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.     

Statistical Assessment of Jointly Observed Screening Tests

In this article, Lindley and Novick criteria of screening usefulness is applied to the statistical assessment of jointly observed screening test. Posterior probabilities comparing screening sensitivities and specificities, and posterior probability bounds to comparing screening predictive values are obtained.     

Discussion on “Predictively consistent prior effective sample sizes,” by Beat Neuenschwander,Sebastian Weber,Heinz Schmidli,and Anthony O'Hagan

We extend the approach of finding effective sample size for a typical phase II clinical trial having efficacy and toxicity as two components of the response vector. The case of binary efficacy and binary toxicity is illustrated under Dirichlet and multivariate T priors.     

Thiessen polygons as a model for animal territory estimation

Thiessen polygons are often used to model territory characteristics. However, information about the quality of Thiessen polygon‐based estimates is currently lacking. We used published data to investigate the match between Thiessen polygons and mapped bird territories regarding territory size, shape and neighbourhood. Although territory sizes and the number of neighbours were strongly correlated between these two methods, both parameters were overestimated by the Thiessen polygons. Therefore, caution is required when Thiessen polygons are used as a model for absolute values and when the assumptions of Thiessen polygons, such as formation of discrete territories and a contiguous study area, are not met.     

Semiparametric analysis of two-level bivariate binary data

In medical studies, paired binary responses are often observed for each study subject over timepoints or clusters. A primary interest is to investigate how the bivariate association and marginal univariate risks are affected by repeated measurements on each subject. To achieve this we propose a very general class of semiparametric bivariate binary models. The subject-specific effects involved in the bivariate log odds ratio and the univariate logit components are assumed to follow a nonparametric Dirichlet process (DP). We propose a hybrid method to draw model-based inferences. In the framework of the proposed hybrid method, estimation of parameters is done by implementing the Monte Carlo expectation-maximization algorithm. The proposed methodology is illustrated through a study on the effectiveness of tibolone for reducing menopausal problems experienced by Indian women. A simulation study is also conducted to evaluate the efficiency of the new methodology.     

Bayesian Nonparametric Nonproportional Hazards Survival Modeling

Summary .  We develop a dependent Dirichlet process model for survival analysis data. A major feature of the proposed approach is that there is no necessity for resulting survival curve estimates to satisfy the ubiquitous proportional hazards assumption. An illustration based on a cancer clinical trial is given, where survival probabilities for times early in the study are estimated to be lower for those on a high-dose treatment regimen than for those on the low dose treatment, while the reverse is true for later times, possibly due to the toxic effect of the high dose for those who are not as healthy at the beginning of the study.     

A Bayesian semiparametric joint hierarchical model for longitudinal and survival data

This article proposes a new semiparametric Bayesian hierarchical model for the joint modeling of longitudinal and survival data. We relax the distributional assumptions for the longitudinal model using Dirichlet process priors on the parameters defining the longitudinal model. The resulting posterior distribution of the longitudinal parameters is free of parametric constraints, resulting in more robust estimates. This type of approach is becoming increasingly essential in many applications, such as HIV and cancer vaccine trials, where patients' responses are highly diverse and may not be easily modeled with known distributions. An example will be presented from a clinical trial of a cancer vaccine where the survival outcome is time to recurrence of a tumor. Immunologic measures believed to be predictive of tumor recurrence were taken repeatedly during follow-up. We will present an analysis of this data using our new semiparametric Bayesian hierarchical joint modeling methodology to determine the association of these longitudinal immunologic measures with time to tumor recurrence.     

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.     

Bayesian monitoring of clinical trials with failure-time endpoints

This article presents an aid for monitoring clinical trials with failure-time endpoints based on the Bayesian nonparametric analyses of the data. The posterior distribution is a mixture of Dirichlet processes in the presence of censoring if one assumes a Dirichlet process prior for the survival distribution. Using Gibbs sampling, one can generate random samples from the posterior distribution. With samples from the posterior distributions of treatment-specific survival curves, one can evaluate the current evidence in favor of stopping or continuing the trial based on summary statistics of these survival curves. Because the method is nonparametric, it can easily be used, for example, in situations where hazards cross or are suspected to cross and where relevant clinical decisions might be based on estimating when the integral between the curves might be expected to become positive and in favor of the new but toxic therapy. An example based on an actual trial illustrates the method.     

Positive solutions of an elliptic system arising from a model in evolutionary ecology

We give sufficient and almost necessary conditions for the existence of positive solutions to an elliptic system satisfying various Dirichlet boundary conditions. The elliptic system consists of the steady-state equations of a parabolic system used to model the growth and spread of a particular gene and population living in a bounded region. The model takes into account the fact that the fitness of the individuals in the population may depend on the population size. Some non-existence results are also included.Research partially supported by NSF grant no. DMS-8801968     

Semiparametric bayesian inference for multilevel repeated measurement data

We discuss inference for data with repeated measurements at multiple levels. The motivating example is data with blood counts from cancer patients undergoing multiple cycles of chemotherapy, with days nested within cycles. Some inference questions relate to repeated measurements over days within cycle, while other questions are concerned with the dependence across cycles. When the desired inference relates to both levels of repetition, it becomes important to reflect the data structure in the model. We develop a semiparametric Bayesian modeling approach, restricting attention to two levels of repeated measurements. For the top-level longitudinal sampling model we use random effects to introduce the desired dependence across repeated measurements. We use a nonparametric prior for the random effects distribution. Inference about dependence across second-level repetition is implemented by the clustering implied in the nonparametric random effects model. Practical use of the model requires that the posterior distribution on the latent random effects be reasonably precise.     

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。