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In recent years there has been significant progress in algorithms and methods for inducing Bayesian networks from data. However, in complex data analysis problems, we need to go beyond being satisfied with inducing networks with high…

Loss-based clustering methods, such as k-means and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on…

Bayesian networks are probabilistic graphical models with a wide range of application areas including gene regulatory networks inference, risk analysis and image processing. Learning the structure of a Bayesian network (BNSL) from discrete…

Model averaging techniques based on resampling methods (such as bootstrapping or subsampling) have been utilized across many areas of statistics, often with the explicit goal of promoting stability in the resulting output. We provide a…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

In this paper we address the problem of performing statistical inference for large scale data sets i.e., Big Data. The volume and dimensionality of the data may be so high that it cannot be processed or stored in a single computing node. We…

We propose a general statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups. Our motivation comes from neuroscience, where an important problem is to identify,…

We present a method that models the evolution of an unbounded number of time series clusters by switching among an unknown number of regimes with linear dynamics. We develop a Bayesian non-parametric approach using a hierarchical Dirichlet…

Bayesian synthetic likelihood (BSL) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of…

We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…

The impracticality of posterior sampling has prevented the widespread adoption of spike-and-slab priors in high-dimensional applications. To alleviate the computational burden, optimization strategies have been proposed that quickly find…

To address the difficult problem of multi-step ahead prediction of non-parametric autoregressions, we consider a forward bootstrap approach. Employing a local constant estimator, we can analyze a general type of non-parametric time series…

This paper proposes a new nonparametric Bayesian bootstrap for a mixture model, by developing the traditional Bayesian bootstrap. We first reinterpret the Bayesian bootstrap, which uses the P\'olya-urn scheme, as a gradient ascent algorithm…

The bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets which are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its…

State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…

Nested sampling is a promising tool for Bayesian statistical analysis because it simultaneously performs parameter estimation and facilitates model comparison. MultiNest is one of the most popular nested sampling implementations, and has…

There is a growing interest in the estimation of the number of unseen features, mostly driven by biological applications. A recent work brought out a peculiar property of the popular completely random measures (CRMs) as prior models in…