Related papers: Multiscale stick-breaking mixture models

Ensembles of decision trees are a useful tool for obtaining for obtaining flexible estimates of regression functions. Examples of these methods include gradient boosted decision trees, random forests, and Bayesian CART. Two potential…

Multiple Classifier Systems (MCSs) allow evaluation of the uncertainty of classification outcomes that is of crucial importance for safety critical applications. The uncertainty of classification is determined by a trade-off between the…

High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…

Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…

Bayesian phylogenetics is vital for understanding evolutionary dynamics, and requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric…

Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical…

It is shown that a simple Dirichlet process mixture of multivariate normals offers Bayesian density estimation with adaptive posterior convergence rates. Toward this, a novel sieve for non-parametric mixture densities is explored, and its…

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…

We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…

Spatial generalized linear mixed-effects models are popularly used to analyze spatially indexed univariate responses. However, with modern technology, it is common to observe vector-valued mixed-type responses, e.g., a combination of…

The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…

Spectral clustering views the similarity matrix as a weighted graph, and partitions the data by minimizing a graph-cut loss. Since it minimizes the across-cluster similarity, there is no need to model the distribution within each cluster.…

There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…

3D microscopy is key in the investigation of diverse biological systems, and the ever increasing availability of large datasets demands automatic cell identification methods that not only are accurate, but also can imply the uncertainty in…

The human body consists of microbiomes associated with the development and prevention of several diseases. These microbial organisms form several complex interactions that are informative to the scientific community for explaining disease…

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…

Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding.…

Proximal Markov Chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…