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In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using…
The specification of prior distributions is fundamental in Bayesian inference, yet it remains a significant bottleneck. The prior elicitation process is often a manual, subjective, and unscalable task. We propose a novel framework which…
In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion…
Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a…
We propose a novel method for closed-form predictive distribution modeling with neural nets. In quantifying prediction uncertainty, we build on Evidential Deep Learning, which has been impactful as being both simple to implement and giving…
The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…
Recent developments in statistical regression methodology shift away from pure mean regression towards distributional regression models. One important strand thereof is that of conditional transformation models (CTMs). CTMs infer the entire…
Information design is typically studied through the lens of Bayesian signaling, where signals shape beliefs purely based on their correlation with the true state of the world. However, behavioral economics and psychology emphasize that…
Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…
This paper proposes and axiomatizes a new updating rule: Relative Maximum Likelihood (RML) for ambiguous beliefs represented by a set of priors (C). This rule takes the form of applying Bayes' rule to a subset of C. This subset is a linear…
Exposures to environmental chemicals during gestation can alter health status later in life. Most studies of maternal exposure to chemicals during pregnancy have focused on a single chemical exposure observed at high temporal resolution.…
Bayesian Networks (BNs) are of interest from an explainable AI viewpoint, offering transparent probabilistic models for decision support. Baymex is a recently introduced multi-objective evolutionary algorithm for learning discretized BNs,…
Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…
In this paper we present a new Bayesian network model for classification that combines the naive-Bayes (NB) classifier and the finite-mixture (FM) classifier. The resulting classifier aims at relaxing the strong assumptions on which the two…
Recently we have presented the analytical relationship between choice probabilities, noise correlations and read-out weights in the classical feedforward decision-making framework (Haefner et al. 2013). The derivation assumed that…
We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data…
We consider the problem of state estimation from limited discrete and noisy measurements. In particular, we focus on modal state estimation, which approximates the unknown state of the system within a prescribed basis. We estimate the…
Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…