Heterogeneity of response patterns is important in estimating the size of a closed population from multiple recapture data when capture patterns are different over time and location. In this paper, we extend the non-parametric one layer latent class model for multiple recapture data proposed by Manrique-Vallier (2016) to a nested latent class model with the first layer modeling individual heterogeneity and the second layer modeling location-time differences. Location-time groups with similar recording patterns are in the same top layer latent class and individuals within each top layer class are dependent. The nested latent class model incorporates hierarchical heterogeneity into the modeling to estimate population size from multi-list recapture data. This approach leads to more accurate population size estimation and reduced uncertainty. We apply the method to estimating casualties from the Syrian conflict.
We estimate the number of fatal victims of the Peruvian internal armed conflict between 1980-2000 using stratified seven-list Capture-Recapture methods based on Dirichlet process mixtures, which we extend to accommodate incomplete stratification information. We use matched data from six sources, originally analyzed by the Peruvian Truth and Reconciliation Commission in 2003, together with a new large dataset, originally published in 2006 by the Peruvian government. We deal with missing stratification labels by developing a general framework and estimation methods based on MCMC sampling for joi…
We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The model assumes that (i) each group is a member of a group-level latent class, and (ii) each unit is a member of a unit-level latent class nested within its group-level latent class. This structure allows the model to capture dependence among units in the same group. It also facilitates simultaneous modeling of variables at both group and unit levels. We develop …
The natural subgroups often seen in mark-recapture studies and the complexity of real mark-recapture data means that parametric and discrete style models can be insufficient. Non-parametric models avoid these often restrictive assumptions. We consider the non-parametric Dirichlet process for modelling latent individual heterogeneity in probability of observation and the probability of remaining in or out of a marine sanctuary. Simulation studies demonstrated accurate estimation of multiple groups of latent individual heterogeneity. Simulations were also used to identify the limits of the Diric…
The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for clustering probability distributions is the nested Dirichlet process, which however has the drawback of grouping distributions in a single cluster when ties are observed across samples. With the goal of achieving a flexible and effective clustering method for both samples and observations, we investigate a nonparametric prior that arises as the composition of two dif…
Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical prior that extends the hierarchical Dirichlet process of Teh et al. (2006) and that avoids the degeneracy issues of nested processes recently described by Camerlenghi et al. (2019a). We go beyond the simple yes/no answer to the homogeneity question and embed the proposed prior in a random partition model; this procedure allows us to give a more comprehensiv…
The latent Dirichlet allocation (LDA) model is a widely-used latent variable model in machine learning for text analysis. Inference for this model typically involves a single-site collapsed Gibbs sampling step for latent variables associated with observations. The efficiency of the sampling is critical to the success of the model in practical large scale applications. In this article, we introduce a blocking scheme to the collapsed Gibbs sampler for the LDA model which can, with a theoretical guarantee, improve chain mixing efficiency. We develop two procedures, an O(K)-step backward simulatio…
Deakin University（迪肯大学）；University of Michigan（密歇根大学）；Nuance Communications（Nuance通信公司）
We present a Bayesian nonparametric framework for multilevel clustering which utilizes group-level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using the Dirichlet process as the building block, our model constructs a product base-measure with a nested structure to accommodate content and context observations at multiple levels. The proposed model possesses properties that link the nested Dirichlet processes (nDP) and the Dirichlet process mixture models (DPM) in an interesting way: integrating out all cont…
Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of existing methods for modelling trees, including the popular nested Chinese restaurant process (nCRP). Then we define a general class of probability distributions over trees: the Dirichlet fragmentation process (DFP) through a novel combination of the theory of Dirichlet processes and random fragmentation processes. This DFP presents a stick-breaking constru…
University of Massachusetts（马萨诸塞大学）；Princeton University（普林斯顿大学）
Recent advances in topic models have explored complicated structured distributions to represent topic correlation. For example, the pachinko allocation model (PAM) captures arbitrary, nested, and possibly sparse correlations between topics using a directed acyclic graph (DAG). While PAM provides more flexibility and greater expressive power than previous models like latent Dirichlet allocation (LDA), it is also more difficult to determine the appropriate topic structure for a specific dataset. In this paper, we propose a nonparametric Bayesian prior for PAM based on a variant of the hierarchic…
Multivariate categorical data nested within households often include reported values that fail edit constraints---for example, a participating household reports a child's age as older than his biological parent's age---as well as missing values. Generally, agencies prefer datasets to be free from erroneous or missing values before analyzing them or disseminating them to secondary data users. We present a model-based engine for editing and imputation of household data based on a Bayesian hierarchical model that includes (i) a nested data Dirichlet process mixture of products of multinomial dist…
Detection heterogeneity is inherent to ecological data, arising from factors such as varied terrain or weather conditions, inconsistent sampling effort, or heterogeneity of individuals themselves. Incorporating additional covariates into a statistical model is one approach for addressing heterogeneity, but is no guarantee that any set of measurable covariates will adequately address the heterogeneity, and the presence of unmodelled heterogeneity has been shown to produce biases in the resulting inferences. Other approaches for addressing heterogeneity include the use of random effects, or fini…
Ranked data arise in many areas of application ranging from the ranking of up-regulated genes for cancer to the ranking of academic statistics journals. Complications can arise when rankers do not report a full ranking of all entities; for example, they might only report their top--$M$ ranked entities after seeing some or all entities. It can also be useful to know whether rankers are equally informative, and whether some entities are effectively judged to be exchangeable. When there is important subgroup structure in the data, summaries such as aggregate (overall) rankings can be misleading. …
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over the covariate domain. We propose a novel Bayesian nonparametric method reposing on the formalism of spatial modeling and a nested hierarchy of Dirichlet processes. We provide an analysis of the model properties, relating and contrasting the notions of local and global clusters. We also provide an efficient inference algorithm, and demonstrate the utility of …
Recurrent event data are common in clinical studies when participants are followed longitudinally, and are often subject to a terminal event. With the increasing popularity of large pragmatic trials with a heterogeneous source population, participants are often nested in clinics and can be either susceptible or structurally unsusceptible to the recurrent process. These complications require new modeling strategies to accommodate potential zero-event inflation as well as hierarchical data structures in both the terminal and non-terminal event processes. In this paper, we develop a Bayesian semi…
Insight Centre for Data Analytics（洞察数据分析中心）；University College Dublin（都柏林大学）；Maynooth University（梅努斯大学）
This paper focuses on the problem of hierarchical non-overlapping clustering of a dataset. In such a clustering, each data item is associated with exactly one leaf node and each internal node is associated with all the data items stored in the sub-tree beneath it, so that each level of the hierarchy corresponds to a partition of the dataset. We develop a novel Bayesian nonparametric method combining the nested Chinese Restaurant Process (nCRP) and the Hierarchical Dirichlet Process (HDP). Compared with other existing Bayesian approaches, our solution tackles data with complex latent mixture fe…
Finding a set of nested partitions of a dataset is useful to uncover relevant structure at different scales, and is often dealt with a data-dependent methodology. In this paper, we introduce a general two-step methodology for model-based hierarchical clustering. Considering the integrated classification likelihood criterion as an objective function, this work applies to every discrete latent variable models (DLVMs) where this quantity is tractable. The first step of the methodology involves maximizing the criterion with respect to the partition. Addressing the known problem of sub-optimal loca…
Driven by the multi-level structure of human intracranial electroencephalogram (iEEG) recordings of epileptic seizures, we introduce a new variant of a hierarchical Dirichlet Process---the multi-level clustering hierarchical Dirichlet Process (MLC-HDP)---that simultaneously clusters datasets on multiple levels. Our seizure dataset contains brain activity recorded in typically more than a hundred individual channels for each seizure of each patient. The MLC-HDP model clusters over channels-types, seizure-types, and patient-types simultaneously. We describe this model and its implementation in d…
