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A comprehensive artificial intelligence system needs to not only perceive the environment with different `senses' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty.…
Bayesian models of cognition hypothesize that human brains make sense of data by representing probability distributions and applying Bayes' rule to find the best explanation for available data. Understanding the neural mechanisms underlying…
Bayesian statistics plays a pivotal role in advancing medical science by enabling healthcare companies, regulators, and stakeholders to assess the safety and efficacy of new treatments, interventions, and medical procedures. The Bayesian…
Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
The extraction of any physical information from quasielastic neutron scattering spectra is generally done by fitting a model to the data by means of chi-square minimization procedure. However, as pointed out by the pioneering work of D.S.…
The Bayesian statistical paradigm provides a principled and coherent approach to probabilistic forecasting. Uncertainty about all unknowns that characterize any forecasting problem -- model, parameters, latent states -- is able to be…
A Bayesian approach is proposed for pulse shape discrimination of photons and neutrons in liquid organic scinitillators. Instead of drawing a decision boundary, each pulse is assigned a photon or neutron confidence probability. This allows…
We present a Bayesian hierarchical framework for a principled data analysis pipeline of peculiar velocity surveys, which makes explicit the inference problem of constraining cosmological parameters from redshift-independent distance…
Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…
Embedding methods have achieved success in face recognition by comparing facial features in a latent semantic space. However, in a fully unconstrained face setting, the facial features learned by the embedding model could be ambiguous or…
There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…
This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…
Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be…
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…
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,…
Big Data often presents as massive non-probability samples. Not only is the selection mechanism often unknown, but larger data volume amplifies the relative contribution of selection bias to total error. Existing bias adjustment approaches…
The optimization of composition and processing to obtain materials that exhibit desirable characteristics has historically relied on a combination of scientist intuition, trial and error, and luck. We propose a methodology that can…
Type inference refers to the task of inferring the data type of a given column of data. Current approaches often fail when data contains missing data and anomalies, which are found commonly in real-world data sets. In this paper, we propose…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…