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Bayesian paradigm takes advantage of well fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this…
The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the…
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…
Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…
Bayesian model selection is premised on the assumption that the data are generated from one of the postulated models. However, in many applications, all of these models are incorrect (that is, there is misspecification). When the models are…
This work introduces a Bayesian framework that unifies a wide class of opinion dynamics models. In this framework, an individual's opinion on a topic is the expected value of their belief, represented as a random variable with a prior…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
When it is acknowledged that all candidate parameterised statistical models are misspecified relative to the data generating process, the decision maker (DM) must currently concern themselves with inference for the parameter value…
Bayesian hierarchical models are frequently used in practical data analysis contexts. One interpretation of these models is that they provide an indirect way of assigning a prior for unknown parameters, through the introduction of…
Interim analyses are vital in clinical trials for early decision-making. While frequentist implications are well-established, the consequences of repeated Bayesian interim monitoring for efficacy, specifically regarding multiplicity, remain…
Inference and learning are commonly cast in terms of optimisation, yet the fundamental constraints governing uncertainty reduction remain unclear. This work presents a first-principles framework inherent to Bayesian updating, termed…
We study high-dimensional Bayesian linear regression with product priors. Using the nascent theory of non-linear large deviations (Chatterjee and Dembo,2016), we derive sufficient conditions for the leading-order correctness of the naive…
This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information…
We consider Bayesian sample size determination using a criterion that utilizes the first two moments of the expected posterior variance. We study the resulting sample size in dependence on the chosen prior and explore the success rate for…
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…
In the standard Bayesian framework data are assumed to be generated by a distribution parametrized by $\theta$ in a parameter space $\Theta$, over which a prior distribution $\pi$ is given. A Bayesian statistician quantifies the belief that…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
Datasets are growing not just in size but in complexity, creating a demand for rich models and quantification of uncertainty. Bayesian methods are an excellent fit for this demand, but scaling Bayesian inference is a challenge. In response…
A Bayesian view of data interpretation suggests that a visualization user should update their existing beliefs about a parameter's value in accordance with the amount of information about the parameter value captured by the new…
While Bayesian neural networks (BNNs) provide a sound and principled alternative to standard neural networks, an artificial sharpening of the posterior usually needs to be applied to reach comparable performance. This is in stark contrast…