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The $\mu$Dose system was developed to allow the measurement of environmental levels of natural radioactive isotopes. The system records $\alpha$ and $\beta$ particles along with four decay pairs arising from subsequent decays of…
Most conventional risk analysis methods rely on a single best estimate of exposure per person which does not allow for adjustment for exposure-related uncertainty. Here, we propose a Bayesian model averaging method to properly quantify the…
This paper focuses on utilizing two different Bayesian methods to deal with a variety of toy problems which occur in data analysis. In particular we implement the Variational Bayesian and Nested Sampling methods to tackle the problems of…
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…
Bayesian statistics is a cornerstone of imaging sciences, underpinning many and varied approaches from Markov random fields to score-based denoising diffusion models. In addition to powerful image estimation methods, the Bayesian paradigm…
We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…
Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to…
We propose a Bayesian approach to joint source separation and restoration for astrophysical diffuse sources. We constitute a prior statistical model for the source images by using their gradient maps. We assume a t-distribution for the…
This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm.…
A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the…
An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of…
Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory…
In this paper, we propose a nonparametric Bayesian approach for Lindsey and penalized Gaussian mixtures methods. We compare these methods with the Dirichlet process mixture model. Our approach is a Bayesian nonparametric method not based…
In this paper, we propose an approach for an application of Bayesian optimization using Sequential Monte Carlo (SMC) and concepts from the statistical physics of classical systems. Our method leverages the power of modern machine learning…
A Bayesian framework is attractive in the context of prediction, but a fast recursive update of the predictive distribution has apparently been out of reach, in part because Monte Carlo methods are generally used to compute the predictive.…
In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…
We introduce a novel Bayesian phase estimation technique based on adaptive grid refinement method. This method automatically chooses the number particles needed for accurate phase estimation using grid refinement and cell merging strategies…
Multi-state models of cancer natural history are widely used for designing and evaluating cancer early detection strategies. Calibrating such models against longitudinal data from screened cohorts is challenging, especially when fitting…
While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures.…
One of the big challenges in astrophysics is the comparison of complex simulations to observations. As many codes do not directly generate observables (e.g. hydrodynamic simulations), the last step in the modelling process is often a…