Related papers: Finding a Posterior Domain Probability Distributio…

Various tasks encountered in real-world surveillance can be addressed by determining posteriors (e.g. by Bayesian inference or machine learning), based on which critical decisions must be taken. However, the surveillance domain (acquisition…

Dempster-Shafer theory of evidence is widely applied to uncertainty modelling and knowledge reasoning because of its advantages in dealing with uncertain information. But some conditions or requirements, such as exclusiveness hypothesis and…

When ignorance due to the lack of knowledge, modeled as epistemic uncertainty using Dempster-Shafer structures on closed intervals, is present in the model parameters, a new uncertainty propagation method is necessary to propagate both…

To develop an approach to utilizing continuous statistical information within the Dempster- Shafer framework, we combine methods proposed by Strat and by Shafero We first derive continuous possibility and mass functions from…

We present and examine a result related to uncertainty reasoning, namely that a certain plausibility space of Cox's type can be uniquely embedded in a minimal ordered field. This, although a purely mathematical result, can be claimed to…

Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…

Studying the effects of one-way variation of any number of parameters on any number of output probabilities quickly becomes infeasible in practice, especially if various evidence profiles are to be taken into consideration. To provide for…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

Refining one's hypotheses in the light of data is a common scientific practice; however, the dependency on the data introduces selection bias and can lead to specious statistical analysis. An approach for addressing this is via conditioning…

Missing data are often dealt with multiple imputation. A crucial part of the multiple imputation process is selecting sensible models to generate plausible values for incomplete data. A method based on posterior predictive checking is…

We provide a theoretical framework for a wide class of generalized posteriors that can be viewed as the natural Bayesian posterior counterpart of the class of M-estimators in the frequentist world. We call the members of this class…

The Dempster--Shafer (DS) theory is a powerful tool for probabilistic reasoning based on a formal calculus for combining evidence. DS theory has been widely used in computer science and engineering applications, but has yet to reach the…

When interpreting A/B tests, we typically focus only on the statistically significant results and take them by face value. This practice, termed post-selection inference in the statistical literature, may negatively affect both point…

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

In this article, we investigate posterior convergence of nonparametric binary and Poisson regression under possible model misspecification, assuming general stochastic process prior with appropriate properties. Our model setup and objective…

In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…

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…

Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior…

An important feature of Bayesian statistics is the opportunity to do sequential inference: the posterior distribution obtained after seeing a dataset can be used as prior for a second inference. However, when Monte Carlo sampling methods…

We investigate whether three types of post hoc model explanations--feature attribution, concept activation, and training point ranking--are effective for detecting a model's reliance on spurious signals in the training data. Specifically,…