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Bayesian posterior distributions naturally represent parameter uncertainty informed by data. However, when the parameter space is complex, as in many nonparametric settings where it is infinite-dimensional or combinatorially large, standard…
We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…
The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture…
Bayesian inference without the likelihood evaluation, or likelihood-free inference, has been a key research topic in simulation studies for gaining quantitatively validated simulation models on real-world datasets. As the likelihood…
In many modern applications, there is interest in analyzing enormous data sets that cannot be easily moved across computers or loaded into memory on a single computer. In such settings, it is very common to be interested in clustering.…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…
Computer models are widely used in science and engineering to simulate complex systems. However, these models are affected by several sources of uncertainty, which may limit their use for decision making in risk management. We present a…
Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too…
Combining data has become an indispensable tool for managing the current diversity and abundance of data. But, as data complexity and data volume swell, the computational demands of previously proposed models for combining data escalate…
Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…
Driven by the critical needs of biomanufacturing 4.0, we introduce a probabilistic knowledge graph hybrid model characterizing the risk- and science-based understanding of bioprocess mechanisms. It can faithfully capture the important…
Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…
An informative sampling design leads to the selection of units whose inclusion probabilities are correlated with the response variable of interest. Model inference performed on the resulting observed sample will be biased for the population…
There has been much recent interest in modifying Bayesian inference for misspecified models so that it is useful for specific purposes. One popular modified Bayesian inference method is "cutting feedback" which can be used when the model…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
Developing efficient solutions for inference problems in intelligent sensor networks is crucial for the next generation of location, tracking, and mapping services. This paper develops a scalable distributed probabilistic inference…
As deep learning models grow in complexity and the volume of training data increases, reducing storage and computational costs becomes increasingly important. Dataset distillation addresses this challenge by synthesizing a compact set of…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…
Statistical analysis of DNA mixtures is known to pose computational challenges due to the enormous state space of possible DNA profiles. We propose a Bayesian network representation for genotypes, allowing computations to be performed…