Related papers: Revisiting identification concepts in Bayesian ana…

In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…

The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…

Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of…

Causal inference quantifies cause-effect relationships by estimating counterfactual parameters from data. This entails using \emph{identification theory} to establish a link between counterfactual parameters of interest and distributions…

Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural…

Multi-category data arise in diverse fields including marketing, chemistry, public policy, genomics, political science, and ecology. We consider the problem of estimating ratios of category-specific means in a fully nonparametric setting,…

Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…

We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional…

We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…

Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that missing outcomes are missing completely at random. We follow a…

We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…

Bayesian nonparametric models offer a flexible and powerful framework for statistical model selection, enabling the adaptation of model complexity to the intricacies of diverse datasets. This survey intends to delve into the significance of…

There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

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…