Related papers: The General Formulation of Loss-Based Priors for P…

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based…

Inference and estimation are fundamental in statistics, system identification, and machine learning. When prior knowledge about the system is available, Bayesian analysis provides a natural framework for encoding it through a prior…

The notion of confidence distributions is applied to inference about the parameter in a simple autoregressive model, allowing the parameter to take the value one. This makes it possible to compare to asymptotic approximations in both the…

Uncertainty quantification is central to many applications of causal machine learning, yet principled Bayesian inference for causal effects remains challenging. Standard Bayesian approaches typically require specifying a probabilistic model…

This work proposes $\mu$GUIDE: a general Bayesian framework to estimate posterior distributions of tissue microstructure parameters from any given biophysical model or MRI signal representation, with exemplar demonstration in…

Modern generative models can produce realistic samples, however, balancing memorisation and generalisation remains an open problem. We approach this challenge from a Bayesian perspective by focusing on the parameter space of flow matching…

We develop the framework of Linear Simulation-based Inference (LSBI), an application of simulation-based inference where the likelihood is approximated by a Gaussian linear function of its parameters. We obtain analytical expressions for…

Simultaneously achieving parsimony and good predictive power in high dimensions is a main challenge in statistics. Non-local priors (NLPs) possess appealing properties for high-dimensional model choice, but their use for estimation has not…

Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…

It is common to hold prior beliefs that are not characterized by points in the parameter space but instead are relational in nature and can be described by a linear subspace. While some previous work has been done to account for such prior…

Objective probabilistic forecasts of future climate that include parameter uncertainty can be made by using the Bayesian prediction integral with the prior set to Jeffreys' Prior. The calculations involved in determining the prior can then…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a…

We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…

The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the…

In Bayesian statistics, the choice of the prior can have an important influence on the posterior and the parameter estimation, especially when few data samples are available. To limit the added subjectivity from a priori information, one…

We show that the predicted probability distributions for any $N$-parameter statistical model taking the form of an exponential family can be explicitly and analytically embedded isometrically in a $N{+}N$-dimensional Minkowski space. That…

We present a definition of the distance between probability distributions. Our definition is based on the $L_1$ norm on space of probability measures. We compare our distance with the well-known Kullback-Leibler divergence and with the…

Many common correlation structures assumed for data can be described through latent Gaussian models. When Bayesian inference is carried out, it is required to set the prior distribution for scale parameters that rules the model components,…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…