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Predictive uncertainty quantification is crucial for reliable decision-making in various applied domains. Bayesian neural networks offer a powerful framework for this task. However, defining meaningful priors and ensuring computational…
P-splines provide a flexible setting for modeling nonlinear model components based on a discretized penalty structure with a relatively simple computational backbone. Under a Bayesian inferential framework based on Markov chain Monte Carlo,…
Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…
Here we develop a method for performing nonparametric Bayesian inference on quantiles. Relying on geometric measure theory and employing a Hausdorff base measure, we are able to specify meaningful priors for the quantile while treating the…
One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…
Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be…
Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…
We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution $\mathcal{N}(\mu,\Sigma)$ in $\mathbb{R}^d$. All previous estimators are either…
We develop simple methods for constructing likelihoods and parameter priors for learning about the parameters and structure of a Bayesian network. In particular, we introduce several assumptions that permit the construction of likelihoods…
We consider the problem of predicting perturbation effects via causal models. In many applications, it is a priori unknown which mechanisms of a system are modified by an external perturbation, even though the features of the perturbation…
Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible, i.e. whether there exists a joint probability distribution which generates…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
Discrete Bayesian nonparametric models whose expectation is a convex linear combination of a point mass at some point of the support and a diffuse probability distribution allow to incorporate strong prior information, while still being…
Bayesian optimal design is a well-established approach to planning experiments. A distribution for the responses, i.e. a statistical model, is assumed which is dependent on unknown parameters. A utility function is then specified giving…
Gibbs type priors have been shown to be natural generalizations of Dirichlet process (DP) priors used for intricate applications of Bayesian nonparametric methods. This includes applications to mixture models and to species sampling models…
We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…
P\'{o}lya trees fix partitions and use random probabilities in order to construct random probability measures. With quantile pyramids we instead fix probabilities and use random partitions. For nonparametric Bayesian inference we use a…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
Learning a distribution conditional on a set of discrete-valued features is a commonly encountered task. This becomes more challenging with a high-dimensional feature set when there is the possibility of interaction between the features. In…