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Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…
We describe a method for fitting distributions to data which only requires knowledge of the parametric form of either the signal or the background but not both. The unknown distribution is fit using a non-parametric kernel density…
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…
Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement…
We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…
When we use simulation to assess the performance of stochastic systems, the input models used to drive simulation experiments are often estimated from finite real-world data. There exist both input model and simulation estimation…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
We present an error-diagnostic validation method for posterior distributions in Bayesian signal inference, an advancement of a previous work. It transfers deviations from the correct posterior into characteristic deviations from a uniform…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
The methods for parameter estimation under assumption of agreement between observation and model are reviewed. The distribution parameters are obtained for one set of experimental data by using different estimation methods under assumption…
The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…
Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…