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The existing upper and lower bounds between entropy and error are mostly derived through an inequality means without linking to joint distributions. In fact, from either theoretical or application viewpoint, there exists a need to achieve a…
We propose a multivariate probability distribution that models a linear correlation between binary and continuous variables. The proposed distribution is a natural extension of the previously developed multivariate binary distribution. As…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
Parameters of sub-populations can be more relevant than super-population ones. For example, a healthcare provider may be interested in the effect of a treatment plan for a specific subset of their patients; policymakers may be concerned…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
A composite likelihood is a non-genuine likelihood function that allows to make inference on limited aspects of a model, such as marginal or conditional distributions. Composite likelihoods are not proper likelihoods and need therefore…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…
For irrational $\alpha$, $\{n\alpha\}$ is uniformly distributed mod 1 in the Weyl sense, and the asymptotic behavior of its discrepancy is completely known. In contrast, very few precise results exist for the discrepancy of subsequences…
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…
We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…
Approximate Bayesian Computation (ABC) is a popular inference method when likelihoods are hard to come by. Practical bottlenecks of ABC applications include selecting statistics that summarize the data without losing too much information or…
Conformal prediction (CP) is widely presented as distribution-free predictive inference with finite-sample marginal coverage under exchangeability. We argue that CP is best understood as a rank-calibrated descendant of the…
This book chapter introduces regression approaches and regression adjustment for Approximate Bayesian Computation (ABC). Regression adjustment adjusts parameter values after rejection sampling in order to account for the imperfect match…
For ill-posed inverse problems, a regularised solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set the solutions, as other posterior estimates can be used as a solution…
Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…
The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…