Related papers: Regularization in regression: comparing Bayesian a…
We propose modified frequentist definition for the determination of confidence intervals for the case of Poisson statistics. Namely, we require that 1-\beta' \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha'. We show that this…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques…
Relevant methods of variable selection have been proposed in model-based clustering and classification. These methods are making use of backward or forward procedures to define the roles of the variables. Unfortunately, these stepwise…
In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard…
In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this…
Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…
This paper explores the intrinsic connections between the Bayesian false discovery rate (FDR) control procedures and their counterpart of frequentist procedures. We attempt to offer a unified view of FDR control within and beyond the…
Robust regression has attracted a great amount of attention in the literature recently, particularly for taking asymmetricity into account simultaneously and for high-dimensional analysis. However, the majority of research on the topics…
We apply classical and Bayesian lasso regularizations to a family of models with the presence of mixture and process variables. We analyse the performance of these estimates with respect to ordinary least squares estimators by a simulation…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
Bayesian optimization is a methodology for global optimization of unknown and expensive objectives. It combines a surrogate Bayesian regression model with an acquisition function to decide where to evaluate the objective. Typical regression…
We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…
Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is…
In this paper, a Bayesian approach is developed for simultaneously comparing multiple experimental treatments with a common control treatment in an exploratory clinical trial. The sample size is set to ensure that, at the end of the study,…
Probabilistic graphical models compactly represent joint distributions by decomposing them into factors over subsets of random variables. In Bayesian networks, the factors are conditional probability distributions. For many problems, common…
In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…
We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B),…