Related papers: Bayesian Constraint Relaxation
We propose a score-based generative algorithm for sampling from power-scaled priors and likelihoods within the Bayesian inference framework. Our algorithm enables flexible control over prior-likelihood influence without requiring retraining…
Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…
Scientific experiments are usually expensive due to complex experimental preparation and processing. Experimental design is therefore involved with the task of finding the optimal experimental input that results in the desirable output by…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
Spline basis exploration via Bayesian model selection is a widely employed strategy for determining the optimal set of basis terms in nonparametric regression. However, despite its widespread use, this approach often encounters performance…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
Approximate Bayesian Computation (ABC) is a powerful method for carrying out Bayesian inference when the likelihood is computationally intractable. However, a drawback of ABC is that it is an approximate method that induces a systematic…
Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…
In the Bayesian framework power prior distributions are increasingly adopted in clinical trials and similar studies to incorporate external and past information, typically to inform the parameter associated to a treatment effect. Their use…
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…
We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection…
Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
We consider exact algorithms for Bayesian inference with model selection priors (including spike-and-slab priors) in the sparse normal sequence model. Because the best existing exact algorithm becomes numerically unstable for sample sizes…
Bayesian Neural Networks (BNNs) offer robust uncertainty quantification in model predictions, but training them presents a significant computational challenge. This is mainly due to the problem of sampling multimodal posterior distributions…
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.…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…
From a systems biology perspective the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that they usually miss a genuine connection with experimental…
How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…