Related papers: A Bayesian Mixture Model for Clustering on the Sti…
In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions for the conjugate momentum onto topologically equivalent shapes.…
Multi-state models of cancer natural history are widely used for designing and evaluating cancer early detection strategies. Calibrating such models against longitudinal data from screened cohorts is challenging, especially when fitting…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the control parameters of a natural system that produce a given set of observed measurements.…
Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…
When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Markov melding joins together submodels that have a common quantity. One challenge is that the…
We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…
Motivated by examples from genetic association studies, this paper considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating…
Finite mixture and Markov-switching models generalize and, therefore, nest specifications featuring only one component. While specifying priors in the two: the general (mixture) model and its special (single-component) case, it may be…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
In mixture model-based clustering applications, it is common to fit several models from a family and report clustering results from only the `best' one. In such circumstances, selection of this best model is achieved using a model selection…
Clustering is the process of finding underlying group structures in data. Although mixture model-based clustering is firmly established in the multivariate case, there is a relative paucity of work on matrix variate distributions and none…
Recent work on overfitting Bayesian mixtures of distributions offers a powerful framework for clustering multivariate data using a latent Gaussian model which resembles the factor analysis model. The flexibility provided by overfitting…
We develop two models for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both are based on the mixture transition distribution, which constructs a transition probability tensor with additive mixing of…
This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
In this paper, we study the problem of sampling from distributions of the form p(x) \propto e^{-\beta f(x)} for some function f whose values and gradients we can query. This mode of access to f is natural in the scenarios in which such…
The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…