Doctor of Philosophy

dissertationObservational studies are a frequently used "tool" in the field of road safety research because random assignments of safety treatments are not feasible or ethical. Data and modeling issues and challenges often plague observational road safety studies, and impact study results. The objective of this research was to explore a selected number of current data and modeling limitations in observational road safety studies and identify possible solutions. Three limitations were addressed in this research: (1) a majority of statistical road safety models use average annual daily traffic (AADT) to represent traffic volume and do not explicitly capture differences in traffic volume patterns throughout the day, even though crash risk is known to change by time of day, (2) statistical road safety models that use AADT on the "right-hand side" of the model equation do not explicitly account for the fact that these values for AADT are estimates with estimation errors, leading to potential bias in model estimation results, and (3) the current state-of-the-practice in road safety research often involves "starting over" with each study, choosing a model functional form based on the data fit, and letting the estimation results drive interpretations, without fully utilizing previous study results. These limitations were addressed by: (1) estimating the daily traffic patterns (by time of day) using geo-spatial interpolation methods, (2) accounting for measurement error in AADT estimates using measurement error models of expected crash frequency, and (3) incorporating prior knowledge on the safety effects of explanatory variables into regression models of expected crash frequency through informative priors in a Bayesian methodological framework. These alternative approaches to address the selected observational road safety study limitations were evaluated using data from rural, two-lane highways in the states of Utah and Washington. The datasets consisted of horizontal curve segments, for which crash data, roadway geometric features, operational characteristics, roadside features, and weather data were obtained. The results show that the methodological approaches developed in this research will allow road safety researchers and practitioners to accurately evaluate the expected road safety effects. These methods can further be used to increase the accuracy and repeatability of study results, and ultimately expand the current practice of evaluating regression models of expected crash frequency in observational road safety studies

A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning

We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences

Expert knowledge in geostatistical inference and prediction

Geostatistics provides an efficient tool for mapping environmental variables from observations and layers of explanatory variables. The number and configuration of the observations importantly determine the accuracy of geostatistical inference and prediction. Data collection is costly, and coarse sampling may lead to large uncertainties in interpolated maps. In such case, additional information may be gathered from experts who are knowledgeable about the spatial variability of environmental variables. Statistical expert elicitation has gradually become a mature research field and has proved to be able to extract from experts reliable information to form a sound scientific database. In this thesis, expert knowledge has been elicited and incorporated in geostatistical models for inference and prediction. Various extensions to the expert elicitation literature were required to make it suitable for elicitation of spatial data. The use of expert knowledge in geostatistical research is promising, yet challenging.</p

Bayesian hierarchical models for analysing the spatial distribution of bioclimatic indices

A methodological approach for modelling the spatial distribution of bioclimatic indices is proposed in this paper. The value of the bioclimatic index is modelled with a hierarchical Bayesian model that incorporates both structured and unstructured random effects. Selection of prior distributions is also discussed in order to better incorporate any possible prior knowledge about the parameters that could refer to the particular characteristics of bioclimatic indices. MCMC methods and distributed programming are used to obtain an approximation of the posterior distribution of the parameters and also the posterior predictive distribution of the indices. One main outcome of the proposal is the spatial bioclimatic probability distribution of each bioclimatic index, which allows researchers to obtain the probability of each location belonging to different bioclimates. The methodology is evaluated on two indices in the Island of Cyprus.Peer Reviewe

Inverse Uncertainty Quantification using the Modular Bayesian Approach based on Gaussian Process, Part 2: Application to TRACE

Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an improved modular Bayesian approach based on Gaussian Process (GP) for TRACE physical model parameters using the BWR Full-size Fine-Mesh Bundle Tests (BFBT) benchmark steady-state void fraction data. The model discrepancy is described with a GP emulator. Numerical tests have demonstrated that such treatment of model discrepancy can avoid over-fitting. Furthermore, we constructed a fast-running and accurate GP emulator to replace TRACE full model during Markov Chain Monte Carlo (MCMC) sampling. The computational cost was demonstrated to be reduced by several orders of magnitude. A sequential approach was also developed for efficient test source allocation (TSA) for inverse UQ and validation. This sequential TSA methodology first selects experimental tests for validation that has a full coverage of the test domain to avoid extrapolation of model discrepancy term when evaluated at input setting of tests for inverse UQ. Then it selects tests that tend to reside in the unfilled zones of the test domain for inverse UQ, so that one can extract the most information for posterior probability distributions of calibration parameters using only a relatively small number of tests. This research addresses the "lack of input uncertainty information" issue for TRACE physical input parameters, which was usually ignored or described using expert opinion or user self-assessment in previous work. The resulting posterior probability distributions of TRACE parameters can be used in future uncertainty, sensitivity and validation studies of TRACE code for nuclear reactor system design and safety analysis

High-dimensional Structured Additive Regression Models: Bayesian Regularisation, Smoothing and Predictive Performance

Data structures in modern applications frequently combine the necessity of flexible regression techniques such as nonlinear and spatial effects with high-dimensional covariate vectors. While estimation of the former is typically achieved by supplementing the likelihood with a suitable smoothness penalty, the latter are usually assigned shrinkage penalties that enforce sparse models. In this paper, we consider a Bayesian unifying perspective, where conditionally Gaussian priors can be assigned to all types of regression effects. Suitable hyperprior assumptions on the variances of the Gaussian distributions then induce the desired smoothness or sparseness properties. As a major advantage, general Markov chain Monte Carlo simulation algorithms can be developed that allow for the joint estimation of smooth and spatial effects and regularised coefficient vectors. Two applications demonstrate the usefulness of the proposed procedure: A geoadditive regression model for data from the Munich rental guide and an additive probit model for the prediction of consumer credit defaults. In both cases, high-dimensional vectors of categorical covariates will be included in the regression models. The predictive ability of the resulting high-dimensional structure additive regression models compared to expert models will be of particular relevance and will be evaluated on cross-validation test data