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Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior…

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…

We show that Skilling's method of induction leads to a unique general theory of inductive inference, the method of Maximum relative Entropy (ME). The main tool for updating probabilities is the logarithmic relative entropy; other entropies…

We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate…

Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating…

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…

Bayesian inference is now a leading technique for reconstructing phylogenetic trees from aligned sequence data. In this short note, we formally show that the maximum posterior tree topology provides a statistically consistent estimate of a…

Models of updating a set of priors either do not allow a decision maker to make inference about her priors (full bayesian updating or FB) or require an extreme degree of selection (maximum likelihood updating or ML). I characterize a…

The diversity of a community that cannot be fully counted must be inferred. The two preeminent inference methods are the MaxEnt method, which uses information in the form of constraints and Bayes' rule which uses information in the form of…

This paper uses decision-theoretic principles to obtain new insights into the assessment and updating of probabilities. First, a new foundation of Bayesianism is given. It does not require infinite atomless uncertainties as did Savage s…

We use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and…

In this paper, we explore adaptive inference based on variational Bayes. Although several studies have been conducted to analyze the contraction properties of variational posteriors, there is still a lack of a general and computationally…

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…

Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

We consider the common setting where one observes probability estimates for a large number of events, such as default risks for numerous bonds. Unfortunately, even with unbiased estimates, selecting events corresponding to the most extreme…

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…

In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished,…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…