Longevity Basis Risk A methodology for assessing basis risk

This technical report details the methodology developed on behalf of the LBRWG to assess longevity basis risk. A user-guide which provides a high level summary of this report has also been produced. Together these documents form the key outputs of the first phase of a longevity basis risk project commissioned and funded by the IFoA and the LLMA, and undertaken on our behalf by Cass Business School and Hymans Robertson LLP

Multi-level Safety Performance Functions For High Speed Facilities

High speed facilities are considered the backbone of any successful transportation system; Interstates, freeways, and expressways carry the majority of daily trips on the transportation network. Although these types of roads are relatively considered the safest among other types of roads, they still experience many crashes, many of which are severe, which not only affect human lives but also can have tremendous economical and social impacts. These facts signify the necessity of enhancing the safety of these high speed facilities to ensure better and efficient operation. Safety problems could be assessed through several approaches that can help in mitigating the crash risk on long and short term basis. Therefore, the main focus of the research in this dissertation is to provide a framework of risk assessment to promote safety and enhance mobility on freeways and expressways. Multi-level Safety Performance Functions (SPFs) were developed at the aggregate level using historical crash data and the corresponding exposure and risk factors to identify and rank sites with promise (hot-spots). Additionally, SPFs were developed at the disaggregate level utilizing real-time weather data collected from meteorological stations located at the freeway section as well as traffic flow parameters collected from different detection systems such as Automatic Vehicle Identification (AVI) and Remote Traffic Microwave Sensors (RTMS). These disaggregate SPFs can identify real-time risks due to turbulent traffic conditions and their interactions with other risk factors. In this study, two main datasets were obtained from two different regions. Those datasets comprise historical crash data, roadway geometrical characteristics, aggregate weather and traffic parameters as well as real-time weather and traffic data. iii At the aggregate level, Bayesian hierarchical models with spatial and random effects were compared to Poisson models to examine the safety effects of roadway geometrics on crash occurrence along freeway sections that feature mountainous terrain and adverse weather. At the disaggregate level; a main framework of a proactive safety management system using traffic data collected from AVI and RTMS, real-time weather and geometrical characteristics was provided. Different statistical techniques were implemented. These techniques ranged from classical frequentist classification approaches to explain the relationship between an event (crash) occurring at a given time and a set of risk factors in real time to other more advanced models. Bayesian statistics with updating approach to update beliefs about the behavior of the parameter with prior knowledge in order to achieve more reliable estimation was implemented. Also a relatively recent and promising Machine Learning technique (Stochastic Gradient Boosting) was utilized to calibrate several models utilizing different datasets collected from mixed detection systems as well as real-time meteorological stations. The results from this study suggest that both levels of analyses are important, the aggregate level helps in providing good understanding of different safety problems, and developing policies and countermeasures to reduce the number of crashes in total. At the disaggregate level, real-time safety functions help toward more proactive traffic management system that will not only enhance the performance of the high speed facilities and the whole traffic network but also provide safer mobility for people and goods. In general, the proposed multi-level analyses are useful in providing roadway authorities with detailed information on where countermeasures must be implemented and when resources should be devoted. The study also proves that traffic data collected from different detection systems could be a useful asset that should be utilized iv appropriately not only to alleviate traffic congestion but also to mitigate increased safety risks. The overall proposed framework can maximize the benefit of the existing archived data for freeway authorities as well as for road users

Understanding and quantifying uncertainty due to multiple biases in meta-analyses of observational studies

There has been considerable interest recently in quantifying uncertainty beyond that due to random error in meta-analyses. This is particularly relevant to meta-analyses of observational studies, since error in estimates from these studies cannot be attributed to a randomization mechanism. Typically, observational studies are also subject to error due to measurement error, non-participation, and incomplete adjustment for confounding. Errors due to these sources are often referred to as bias. To quantify uncertainty due to bias, researchers have proposed using "bias models" and giving subjectively elicited probability distributions to parameters that are not identifiable in the models. In a typical meta-analysis, probability distributions involving tens of parameters will have to be elicited. At the same time, the resulting estimate and uncertainty interval of the overall (meta-analytic) effect measure will generally be very sensitive to this multi-dimensional subjectively-elicited distribution. To overcome some of the problems associated with the use of such a distribution, I propose an alternative method for eliciting and quantifying uncertainty due to bias. In the method of this thesis, the lower and upper bounds of bias parameters are elicited instead of probability distributions. The most extreme Bayesian posterior inference for the target parameter of interest within the specified bounds is sought through an algorithm. The resulting lower and upper bounds for the target parameter of interest have interpretation of a Robust Bayes analysis. In this thesis, the method is applied to a meta-analysis of childhood leukaemia and exposure to electromagnetic fields. The method of this thesis was found to produce uncertainty intervals that are generally more conservative in comparison with the standard approach. It is also proposed that the method be used as a tool for sensitivity analysis, and some interesting insight is gained from the childhood leukaemia data. [For supplementary files please contact author]

Computational Bayesian Methods Applied to Complex Problems in Bio and Astro Statistics

In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in a simulation to analyze how estimates of a parameter of interest change across sample sizes