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Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…
Uncertainty quantification (UQ) is the process of systematically determining and characterizing the degree of confidence in computational model predictions. In the context of systems biology, especially with dynamic models, UQ is crucial…
For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…
Recent advances in molecular simulations allow the evaluation of previously unattainable observables, such as rate constants for protein folding. However, these calculations are usually computationally expensive and even significant…
Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design,…
We provide an approach to exploratory data analysis in matched observational studies with a single intervention and multiple endpoints. In such settings, the researcher would like to explore evidence for actual treatment effects among these…
The experimental problem of converting a measured binomial quantity, the fraction of events in a sample that pass a cut, into a physical binomial quantity, the fraction of events originating from a signal source, is described as a system of…
Monte Carlo simulations are widely used in nuclear physics to model experimental systems. In cases where there are significant unknown quantities, such as energies of states, an iterative process of simulating and fitting is often required…
In the real world, experimental data are rarely, if ever, distributed as a normal (Gaussian) distribution. As an example, a large set of data--such as the cross sections for particle scattering as a function of energy contained in the…
I describe an approach to fitting and comparison of radio spectra based on Bayesian analysis and realised using a new implementation of the nested sampling algorithm. Such an approach improves on the commonly used maximum-likelihood fitting…
The inability of artificial neural networks to assess the uncertainty of their predictions is an impediment to their widespread use. We distinguish two types of learnable uncertainty: model uncertainty due to a lack of training data and…
This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…
We introduce a novel Bayesian method that can detect multiple structural breaks in the mean and variance of a length $T$ time-series. Our method quantifies uncertainty by returning $\alpha$-level credible sets around the estimated locations…
Determining whether an algorithmic decision-making system discriminates against a specific demographic typically involves comparing a single point estimate of a fairness metric against a predefined threshold. This practice is statistically…
We demonstrate that two approximations to the chi^2 statistic as popularly employed by observational astronomers for fitting Poisson-distributed data can give rise to intrinsically biased model parameter estimates, even in the high counts…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
The information describing the conditions of a system or a person is constantly evolving and may become obsolete and contradict other information. A database, therefore, must be consistently updated upon the acquisition of new valid…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
This paper introduces diagnostic tests for the nature of lack of fit in ordinary differential equation models (ODEs) proposed for data. We present a hierarchy of three possible sources of lack of fit: unaccounted-for stochastic variation,…
The Best Estimate plus Uncertainty (BEPU) approach for nuclear systems modeling and simulation requires that the prediction uncertainty must be quantified in order to prove that the investigated design stays within acceptance criteria. A…