Search for: All records

We describe and compare two formulations of inverse problems for a physics-based process model in the context of uncertainty and random variability: the Bayesian inverse problem and the stochastic inverse problem. We describe the foundations of the two problems in order to create a context for interpreting the applicability and solutions of inverse problems important for scientific and engineering inference. We conclude by comparing them to statistical approaches to related problems, including Bayesian calibration of computer models. 

Abstract The genome‐wide association studies (GWAS) typically use linear or logistic regression models to identify associations between phenotypes (traits) and genotypes (genetic variants) of interest. However, the use of regression with the additive assumption has potential limitations. First, the normality assumption of residuals is the one that is rarely seen in practice, and deviation from normality increases the Type‐I error rate. Second, building a model based on such an assumption ignores genetic structures, like, dominant, recessive, and protective‐risk cases. Ignoring genetic variants may result in spurious conclusions about the associations between a variant and a trait. We propose an assumption‐free model built upon data‐consistent inversion (DCI), which is a recently developed measure‐theoretic framework utilized for uncertainty quantification. This proposed DCI‐derived model builds a nonparametric distribution on model inputs that propagates to the distribution of observed data without the required normality assumption of residuals in the regression model. This characteristic enables the proposed DCI‐derived model to cover all genetic variants without emphasizing on additivity of the classic‐GWAS model. Simulations and a replication GWAS with data from the COPDGene demonstrate the ability of this model to control the Type‐I error rate at least as well as the classic‐GWAS (additive linear model) approach while having similar or greater power to discover variants in different genetic modes of transmission. 

ABSTRACT We present a novel method for generating sequential parameter estimates and quantifying epistemic uncertainty in dynamical systems within a data‐consistent (DC) framework. The DC framework differs from traditional Bayesian approaches due to the incorporation of the push‐forward of an initial density, which performs selective regularization in parameter directions not informed by the data in the resulting updated density. This extends a previous study that included the linear Gaussian theory within the DC framework and introduced the maximal updated density (MUD) estimate as an alternative to both least squares and maximum a posterior (MAP) estimates. In this work, we introduce algorithms for operational settings of MUD estimation in real‐ or near‐real time where spatio‐temporal datasets arrive in packets to provide updated estimates of parameters and identify potential parameter drift. Computational diagnostics within the DC framework prove critical for evaluating (1) the quality of the DC update and MUD estimate and (2) the detection of parameter value drift. The algorithms are applied to estimate (1) wind drag parameters in a high‐fidelity storm surge model, (2) thermal diffusivity field for a heat conductivity problem, and (3) changing infection and incubation rates of an epidemiological model.