Cancer radiomics is an emerging discipline promising to elucidate lesion phenotypes and tumor heterogeneity through patterns of enhancement, texture, morphology, and shape. The prevailing technique for image texture analysis relies on the construction and synthesis of Gray-Level Co-occurrence Matrices (GLCM). Practice currently reduces the structured count data of a GLCM to reductive and redundant summary statistics for which analysis requires variable selection and multiple comparisons for each application, thus limiting reproducibility. In this article, we develop a Bayesian multivariate probabilistic framework for the analysis and unsupervised clustering of a sample of GLCM objects. By appropriately accounting for skewness and zero-inflation of the observed counts and simultaneously adjusting for existing spatial autocorrelation at nearby cells, the methodology facilitates estimation of texture pattern distributions within the GLCM lattice itself. The techniques are applied to cluster images of adrenal lesions obtained from CT scans with and without administration of contrast. We further assess whether the resultant subtypes are clinically oriented by investigating their correspondence with pathological diagnoses. Additionally, we compare performance to a class of machine-learning approaches currently used in cancer radiomics with simulation studies.
This paper is motivated by a Eurobarometer survey on science knowledge. As part of the survey, respondents were asked to rank sources of science information in order of importance. The official statistical analysis of these data however failed to use the complete ranking information. We instead propose a method which treats ranked data as a set of paired comparisons which places the problem in the standard framework of generalized linear models and also allows respondent covariates to be incorporated. An extension is proposed to allow for heterogeneity in the ranked responses. The resulting mo…
We propose a novel nonparametric Bayesian IRT model in this paper by introducing the clustering effect at question level and further assume heterogeneity at examinee level under each question cluster, characterized by the mixture of Binomial distributions. The main contribution of this work is threefold: (1) We demonstrate that the model is identifiable. (2) The clustering effect can be captured asymptotically and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a root n rate (up to a log term). (3) We present a tractable sam…
A nonparametric approach to the modeling of social networks using degree-corrected stochastic blockmodels is proposed. The model for static network consists of a stochastic blockmodel using a probit regression formulation and popularity parameters are incorporated to account for degree heterogeneity. Dirichlet processes are used to detect community structure as well as induce clustering in the popularity parameters. This approach is flexible yet parsimonious as it allows the appropriate number of communities and popularity clusters to be determined automatically by the data. We further discuss…
We consider comparisons of statistical learning algorithms using multiple data sets, via leave-one-in cross-study validation: each of the algorithms is trained on one data set; the resulting model is then validated on each remaining data set. This poses two statistical challenges that need to be addressed simultaneously. The first is the assessment of study heterogeneity, with the aim of identifying a subset of studies within which algorithm comparisons can be reliably carried out. The second is the comparison of algorithms using the ensemble of data sets. We address both problems by integrati…
Modeling Nonlinear Ability Trajectories and Learner Heterogeneity in Online Learning: A Bayesian Nonparametric Dynamic IRT Framework
Shenzhen University（深圳大学）；University of California, Los Angeles（加州大学洛杉矶分校）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Michigan State University（密歇根州立大学）
Intensity estimation is a common problem in statistical analysis of spatial point pattern data. This paper proposes a nonparametric Bayesian method for estimating the spatial point process intensity based on mixture of finite mixture (MFM) model. MFM approach leads to a consistent estimate of the intensity of spatial point patterns in different areas while considering heterogeneity. An efficient Markov chain Monte Carlo (MCMC) algorithm is proposed for our method. Extensive simulation studies are carried out to examine empirical performance of the proposed method. The usage of our proposed met…
Item response theory (IRT) is a popular modeling paradigm for measuring subject latent traits and item properties according to discrete responses in tests or questionnaires. There are very limited discussions on heterogeneity pattern detection for both items and individuals. In this paper, we introduce a nonparametric Bayesian approach for clustering items and individuals simultaneously under the Rasch model. Specifically, our proposed method is based on the mixture of finite mixtures (MFM) model. MFM obtains the number of clusters and the clustering configurations for both items and individua…
Percutaneous coronary interventions (PCIs) are nonsurgical procedures to open blocked blood vessels to the heart, frequently using a catheter to place a stent. The catheter can be inserted into the blood vessels using an artery in the groin or an artery in the wrist. Because clinical trials have indicated that access via the wrist may result in fewer post procedure complications, shortening the length of stay, and ultimately cost less than groin access, adoption of access via the wrist has been encouraged. However, patients treated in usual care are likely to differ from those participating in…
The advent of single-cell sequencing opens new avenues for personalized treatment. In this paper, we address a two-level clustering problem of simultaneous subject subgroup discovery (subject level) and cell type detection (cell level) for single-cell expression data from multiple subjects. However, current statistical approaches either cluster cells without considering the subject heterogeneity or group subjects without using the single-cell information. To bridge the gap between cell clustering and subject grouping, we develop a nonparametric Bayesian model, Subject and Cell clustering for S…
We propose a multidimensional tensor clustering approach for studying how professional basketball players' shooting patterns vary over court locations and game time. Unlike most existing methods that only study continuous-valued tensors or have to assume the same cluster structure along different tensor directions, we propose a Bayesian nonparametric model that deals with count-valued tensors and projects the heterogeneity among players onto tensor dimensions while allowing cluster structures to be different over directions. Our method is fully probabilistic; hence allows simultaneous inferenc…
In this dissertation, we develop nonparametric Bayesian models for biomedical data analysis. In particular, we focus on inference for tumor heterogeneity and inference for missing data. First, we present a Bayesian feature allocation model for tumor subclone reconstruction using mutation pairs. The key innovation lies in the use of short reads mapped to pairs of proximal single nucleotide variants (SNVs). In contrast, most existing methods use only marginal reads for unpaired SNVs. In the same context of using mutation pairs, in order to recover the phylogenetic relationship of subclones, we t…
Cost-effectiveness analyses (CEAs) are at the center of health economic decision making. While these analyses help policy analysts and economists determine coverage, inform policy, and guide resource allocation, they are statistically challenging for several reasons. Cost and effectiveness are correlated and follow complex joint distributions which are difficult to capture parametrically. Effectiveness (often measured as increased survival time) and accumulated cost tends to be right-censored in many applications. Moreover, CEAs are often conducted using observational data with non-random trea…
We develop a dependent Dirichlet process (DDP) model for repeated measures multiple membership (MM) data. This data structure arises in studies under which an intervention is delivered to each client through a sequence of elements which overlap with those of other clients on different occasions. Our interest concentrates on study designs for which the overlaps of sequences occur for clients who receive an intervention in a shared or grouped fashion whose memberships may change over multiple treatment events. Our motivating application focuses on evaluation of the effectiveness of a group thera…
The use of high-dimensional data for targeted therapeutic interventions requires new ways to characterize the heterogeneity observed across subgroups of a specific population. In particular, models for partially exchangeable data are needed for inference on nested datasets, where the observations are assumed to be organized in different units and some sharing of information is required to learn distinctive features of the units. In this manuscript, we propose a nested Common Atoms Model (CAM) that is particularly suited for the analysis of nested datasets where the distributions of the units a…
The stratified proportional hazards model represents a simple solution to account for heterogeneity within the data while keeping the multiplicative effect on the hazard function. Strata are typically defined a priori by resorting to the values taken by a categorical covariate. A general framework is proposed, which allows for the stratification of a generic accelerated life time model, including as a special case the Weibull proportional hazard model. The stratification is determined a posteriori by taking into account that strata might be characterized by different baseline survivals as well…
In recent years, conditional copulas, that allow dependence between variables to vary according to the values of one or more covariates, have attracted increasing attention. In high dimension, vine copulas offer greater flexibility compared to multivariate copulas, since they are constructed using bivariate copulas as building blocks. In this paper we present a novel inferential approach for multivariate distributions, which combines the flexibility of vine constructions with the advantages of Bayesian nonparametrics, not requiring the specification of parametric families for each pair copula.…
In many biomedical problems, data are often heterogeneous, with samples spanning multiple patient subgroups, where different subgroups may have different disease subtypes, stages, or other medical contexts. These subgroups may be related, but they are also expected to have differences with respect to the underlying biology. The heterogeneous data presents a precious opportunity to explore the heterogeneities and commonalities between related subgroups. Unfortunately, effective statistical analysis methods are still lacking. Recently, several novel methods based on integrative analysis have bee…
Longitudinal study designs are indispensable for studying disease progression. Inferring covariate effects from longitudinal data, however, requires interpretable methods that can model complicated covariance structures and detect nonlinear effects of both categorical and continuous covariates, as well as their interactions. Detecting disease effects is hindered by the fact that they often occur rapidly near the disease initiation time, and this time point cannot be exactly observed. An additional challenge is that the effect magnitude can be heterogeneous over the subjects. We present lgpr, a…
Spatial point pattern data are routinely encountered. A flexible regression model for the underlying intensity is essential to characterizing the spatial point pattern and understanding the impacts of potential risk factors on such pattern. We propose a Bayesian semiparametric regression model where the observed spatial points follow a spatial Poisson process with an intensity function which adjusts a nonparametric baseline intensity with multiplicative covariate effects. The baseline intensity is piecewise constant, approached with a powered Chinese restaurant process prior which prevents an …
This study proposes a mixed logit model with multivariate nonparametric finite mixture distributions. The support of the distribution is specified as a high-dimensional grid over the coefficient space, with equal or unequal intervals between successive points along the same dimension; the location of each point on the grid and the probability mass at that point are model parameters that need to be estimated. The framework does not require the analyst to specify the shape of the distribution prior to model estimation, but can approximate any multivariate probability distribution function to any…
Precision medicine is an emerging field that takes into account individual heterogeneity to inform better clinical practice. In clinical trials, the evaluation of treatment effect heterogeneity is an important component, and recently, many statistical methods have been proposed for stratifying patients into different subgroups based on such heterogeneity. However, the majority of existing methods developed for this purpose focus on the case with a dichotomous treatment and are not directly applicable to multi-arm trials. In this paper, we consider the problem of patient stratification in multi…
Although combination antiretroviral therapy (ART) is highly effective in suppressing viral load for people with HIV (PWH), many ART agents may exacerbate central nervous system (CNS)-related adverse effects including depression. Therefore, understanding the effects of ART drugs on the CNS function, especially mental health, can help clinicians personalize medicine with less adverse effects for PWH and prevent them from discontinuing their ART to avoid undesirable health outcomes and increased likelihood of HIV transmission. The emergence of electronic health records offers researchers unpreced…
Converging evidence indicates that the heterogeneity of cognitive profiles may arise through detectable alternations in brain functions. Particularly, brain functional connectivity, measured under resting and cognitive states, characterizes the unique neuronal interconnections across large-scale brain networks. Despite an unprecedented opportunity to uncover neurobiological subtypes through clustering or subtyping analyses on multi-state functional connectivity, few existing approaches are applicable here to accommodate the network topology and unique biological architecture of functional conn…
We propose a Bayesian nonparametric matrix clustering approach to analyze the latent heterogeneity structure in the shot selection data collected from professional basketball players in the National Basketball Association (NBA). The proposed method adopts a mixture of finite mixtures framework and fully utilizes the spatial information via a mixture of matrix normal distribution representation. We propose an efficient Markov chain Monte Carlo algorithm for posterior sampling that allows simultaneous inference on both the number of clusters and the cluster configurations. We also establish larg…
Virginia Polytechnic Institute and State University（弗吉尼亚理工学院暨州立大学）；U.S. Army Research Laboratory（美国陆军研究实验室）
Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In this work, we seek to overcome these issues through (i) employing variational free energy approximations of GPs operating in tandem with online expectation propagation steps; and (ii) introducing a local splitting step which instantiates a new GP whenever the posterior distribution changes significantly as quantified by the Wasserstein metric over posterior…
In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where applications are often restricted to univariate cases. Here, we propose a Bayesian kernel two-sample testing procedure based on modelling the difference between kernel mean embeddings in the reproducing kernel Hilbert space utilising the framework established by Flaxman et al (2016). The use of kernel methods enables its application to random variables in ge…
The elicitation of an ordinal judgment on multiple alternatives is often required in many psychological and behavioral experiments to investigate preference/choice orientation of a specific population. The Plackett-Luce model is one of the most popular and frequently applied parametric distributions to analyze rankings of a finite set of items. The present work introduces a Bayesian finite mixture of Plackett-Luce models to account for unobserved sample heterogeneity of partially ranked data. We describe an efficient way to incorporate the latent group structure in the data augmentation approa…
