# Statistics and Actuarial Science - Theses, Dissertations, and other Required Graduate Degree Essays

## Bayesian profile regression with evaluation on simulated data

Author:
Date created:
2016-01-06
Abstract:

Using regression analysis to make inference using data sets that contain a large number of potentially correlated covariates can be difficult. This large number of covariates have become more common in clinical observational studies due to the dramatic improvement in information capturing technology for clinical databases. For instance, in disease diagnosis and treatment, obtaining a number of indicators regarding patients’ organ function is much easier than before and these indicators can be highly correlated. We discuss Bayesian profile regression, an approach that deals with the large numbers of correlated covariates for the binary covariates commonly recorded in clinical databases. Clusters of patients with similar covariate profiles are formed through the application of a Dirichlet process prior and then associated with outcomes via a regression model. Methods for evaluating the clustering and making inference are described afterwards. We use simulated data to compare the performance of Bayesian profile regression to the LASSO, a popular alternative for data sets with a large number of predictors. To make these comparisons, we apply the recently developed R package PReMiuM, to fit the Bayesian profile regression.

Document type:
Graduating extended essay / Research project
File(s):
Supervisor(s):
Jinko Graham
Department:
Science: Department of Statistics and Actuarial Science
Thesis type:
(Project) M.Sc.

## Data integration methods for studying animal population dynamics

Author:
Date created:
2015-12-22
Abstract:

In this thesis, we develop new data integration methods to better understand animal population dynamics. In a first project, we study the problem of integrating aerial and access data from aerial-access creel surveys to estimate angling effort, catch and harvest. We propose new estimation methods, study their statistical properties theoretically and conduct a simulation study to compare their performance. We apply our methods to data from an annual Kootenay Lake (Canada) survey. In a second project, we present a new Bayesian modeling approach to integrate capture-recapture data with other sources of data without relying on the usual independence assumption. We use a simulation study to compare, under various scenarios, our approach with the usual approach of simply multiplying likelihoods. In the simulation study, the Monte Carlo RMSEs and expected posterior standard deviations obtained with our approach are always smaller than or equal to those obtained with the usual approach of simply multiplying likelihoods. Finally, we compare the performance of the two approaches using real data from a colony of Greater horseshoe bats (\emph{Rhinolophus ferrumequinum}) in the Valais, Switzerland. In a third project, we develop an explicit integrated population model to integrate capture-recapture survey data, dead recovery survey data and snorkel survey data to better understand the movement from the ocean to spawning grounds of Chinook salmon (\emph{Oncorhynchus tshawytscha}) on the West Coast of Vancouver Island, Canada. In addition to providing spawning escapement estimates, the model provides estimates of stream residence time and snorkel survey observer efficiency, which are crucial but currently lacking for the use of the area-under-the-curve method currently used to estimate escapement on the West Coast of Vancouver Island.

Document type:
Thesis
File(s):
Supervisor(s):
Richard Lockhart
Carl Schwarz
Department:
Science: Department of Statistics and Actuarial Science
Thesis type:
(Thesis) Ph.D.

## Statistical Inference under Latent Class Models, with Application to Risk Assessment in Cancer Survivorship Studies

Author:
Date created:
2015-11-12
Abstract:

Motivated by a cancer survivorship program, this PhD thesis aims to develop methodology for risk assessment, classification, and prediction. We formulate the primary data collected from a cohort with two underlying categories, the at-risk and not-at-risk classes, using latent class models, and we conduct both cross-sectional and longitudinal analyses. We begin with a maximum pseudo-likelihood estimator (pseudo-MLE) as an alternative to the maximum likelihood estimator (MLE) under a mixture Poisson distribution with event counts. The pseudo-MLE utilizes supplementary information on the not-at-risk class from a different population. It reduces the computational intensity and potentially increases the estimation efficiency. To obtain statistical methods that are more robust than likelihood-based methods to distribution misspecification, we adapt the well-established generalized estimating equations (GEE) approach under the mean-variance model corresponding to the mixture Poisson distribution. The inherent computing and efficiency issues in the application of GEEs motivate two sets of extended GEEs, using the primary data supplemented by information from the second population alone or together with the available information on individuals in the cohort who are deemed to belong to the at-risk class. We derive asymptotic properties of the proposed pseudo-MLE and the estimators from the extended GEEs, and we estimate their variances by extended Huber sandwich estimators. We use simulation to examine the finite-sample properties of the estimators in terms of both efficiency and robustness. The simulation studies verify the consistency of the proposed parameter estimators and their variance estimators. They also show that the pseudo-MLE has efficiency comparable to that of the MLE, and the extended GEE estimators are robust to distribution misspecification while maintaining satisfactory efficiency. Further, we present an extension of the favourable extended GEE estimator to longitudinal settings by adjusting for within-subject correlation. The proposed methodology is illustrated with physician claims from the cancer program. We fit different latent class models for the counts and costs of the physician visits by applying the proposed estimators. We use the parameter estimates to identify the risk of subsequent and ongoing problems arising from the subjects’ initial cancer diagnoses. We perform risk classification and prediction using the fitted latent class models.

Document type:
Thesis
File(s):
Supervisor(s):
X. Joan Hu
John J. Spinelli
Department:
Science: Department of Statistics and Actuarial Science
Thesis type:
(Thesis) Ph.D.

## Application of Relational Models in Mortality Immunization

Author:
Date created:
2015-07-29
Abstract:

The prediction of future mortality rates by any existing mortality projection models is hardly tobe exact, which causes an exposure to mortality and longevity risks for life insurance companies.Since a change in mortality rates has opposite impacts on the surpluses of life insurance andannuity products, hedging strategies of mortality and longevity risks can be implemented bycreating an insurance portfolio of both life insurance and annuity products. In this project, wedevelop a framework of implementing non-size free matching strategies to hedge against mortalityand longevity risks. We apply relational models to capture the mortality movements byassuming that the simulated mortality sequence is a proportional and/or a constant change ofthe expected one, and the amount of the changes varies in the length of the sequence. Withthe magnitude of the proportional and/or constant changes, we determine the optimal weightsof allocating the life insurance and annuity products in a portfolio for mortality immunizationaccording to each of the proposed matching strategies. Comparing the hedging performanceof non-size free matching strategies with size free ones proposed by Lin and Tsai (2014), wedemonstrate that non-size free matching strategies can hedge against mortality and longevityrisks more effectively than the corresponding size free ones.

Document type:
Thesis
File(s):
Supervisor(s):
Cary Tsai
Department:
Science: Department of Biomedical Physiology and Kinesiology
Thesis type:
(Thesis) M.Sc.

## Understanding the impact of heteroscedasticity on the predictive ability of modern regression methods

Author:
Date created:
2015-08-17
Abstract:

As the size and complexity of modern data sets grows, more and more prediction methods are developed. Despite the growing sophistication of methods, there is not a well-developed literature on how heteroscedasticity affects modern regression methods. We aim to understand the impact of heteroscedasticity on the predictive ability of modern regression methods. We accomplish this by reviewing the visualization and diagnosis of heteroscedasticity, as well as developing a measure for quantifying it. These methods are used on 42 real data sets in order to understand the prevalence and magnitude typical'' to data. We use the knowledge from this analysis to develop a simulation study that explores the predictive ability of nine regression methods. We vary a number of factors to determine how they influence prediction accuracy in conjunction with, and separately from, heteroscedasticity. These factors include data linearity, the number of explanatory variables, the proportion of unimportant explanatory variables, and the signal-to-noise ratio. We compare prediction accuracy with and without a variance-stabilizing log-transformation. The predictive ability of each method is compared by using the mean squared error, which is a popular measure of regression accuracy, and the median absolute standardized deviation, a measure that accounts for the potential of heteroscedasticity.

Document type:
Graduating extended essay / Research project
File(s):
Supervisor(s):
Thomas Loughin
Department:
Science: Department of Statistics and Actuarial Science
Thesis type:
(Project) M.Sc.

## A Pseudo Non-Parametric Buhlmann Credibility Approach to Modeling Mortality Rates

Author:
Date created:
2015-07-29
Abstract:

Credibility theory is applied in property and casualty insurance to perform prospective experiencerating, i.e., to determine the future premiums to charge based on both past experienceand the underlying group rate. Insurance companies assign a credibility factor Z to a specificpolicyholder’s own past data, and put 1 − Z onto the prior mean which is the group rate determinedby actuaries to reflect the expected value for all risk classes. This partial credibilitytakes advantage of both policyholder’s own experience and the entire group’s characteristics,and thus increases the accuracy of estimated value so that the insurance companies can staycompetitive in the market. Faced with its popular applications in property and casualty insurance,this project aims to apply the credibility theory to projected mortality rates from threeexisting mortality models. The approach presented in this project violates one of the conditions,and thus produces the pseudo non-parametric Bühlmann estimates of the forecasted mortalityrates. Numerical results show that the accuracy of forecasted mortality rates are significantlyimproved after applying the non-parametric Bühlmann method to the Lee-Carter model, theCBD model, and the linear regression-random walk (LR-RW) model. A measure of mean absolutepercentage error (MAPE) is adopted to compare the performances in terms of accuracy ofmortality prediction.

Document type:
Graduating extended essay / Research project
File(s):
Supervisor(s):
Cary Tsai
Department:
Science:
Thesis type:
(Project) M.Sc.

## An approach to constructing "good" two-level orthogonal factorial designs with large run sizes

Author:
Date created:
2015-07-20
Abstract:

Due to the increasing demand for two-level fractional factorials in areas of science and technology, it is highly desirable to have a simple and convenient method available for constructing optimal factorials. Minimum G_2-aberration is a popular criterion to use for selecting optimal designs. However, direct application of this criterion is challenging for large designs. In this project, we propose an approach to constructing a "good" factorial with a large run size using two small minimum G_2-aberration designs. Theoretical results are derived that allow the word length pattern of the large design to be obtained from those of the two small designs. Regular 64-run factorials are used to evaluate this approach. The designs from our approach are very close to the corresponding minimum aberration designs, and they are even equivalent to the corresponding minimum aberration designs, when the number of factors is large.

Document type:
Graduating extended essay / Research project
File(s):
Supervisor(s):
Boxin Tang
Department:
Science:
Thesis type:
(Project) M.Sc.

## How does climate change affect forest fire rate in British Columbia?

Author:
Date created:
2015-08-20
Abstract:

Climate change is known to be an important risk of forest fire. Studies have shown an increased risk of fire because of rising temperatures, drier conditions, more lightning from stronger storms, added dry fuel for fires and a longer fire season and "global warming makes forests more susceptible to fire." In this paper, we use modern functional data analysis methods to explore the variations of forest fire rate in British Columbia, Canada among 63 consecutive years (1950-2012), and to investigate the historical effect of temperature and precipitation on forest fire rate. Functional principle component analysis shows that forest fire rate has increased since 2004 compared to years before that. Historical functional linear model shows that the concurrent effect of temperature and precipitation are both strong. Higher temperature and less precipitation lead to more forest fire. Temperature from January to July has a historical effect on forest fire rate from August to November, while only short term effect of precipitation up to two months is detected.

Document type:
Graduating extended essay / Research project
File(s):
Supervisor(s):
Bin Zhao
Department:
Science: Department of Statistics and Actuarial Science
Thesis type:
(Project) M.Sc.

## Threshold-free measure for assessing the performance of risk prediction with censored data

Author:
Date created:
2015-07-24
Abstract:

The area under the receiver operating characteristic curve (AUC) is a popular threshold-free metric to retrospectively measure the discriminatory performance of medical tests. In risk prediction or medical screening, main interests often focus on accurately predicting the future risk of an event of interest or prospectively stratifying individuals into risk categories. Thus, AUC might not be optimal in assessing the predictive performance for such purposes. Alternative accuracy measures have been proposed, such as the positive predictive value (PPV). Yuan et al. (2015) proposed a threshold-free metric, the average positive predictive value (AP), which is the area under the PPV versus true positive fraction (TPF) curve, when the outcome is binary disease status. In this thesis, we propose the time-dependent AP when the outcome is censored event time. Empirical estimates of the time-dependent AP (AP_t0) are developed, where the inverse weighted probability technique is applied to deal with censoring. In addition, inference procedures — using bootstrap and perturbation resampling—are proposed to construct confidence intervals. We conduct simulation studies to investigate the performance of the proposed estimation and inference procedures in finite samples. The method is also illustrated through a real data analysis.

Document type:
Graduating extended essay / Research project
File(s):
Supervisor(s):
Qian Zhou
Yan Yuan
Department:
Science: Statistics and Actuarial Science
Thesis type:
(Project) M.Sc.

## The optimal payment reduction ratios for a catastrophe bond

Author:
Date created:
2015-01-15
Abstract:

Catastrophe bonds, also known as CAT bonds, are insurance-linked securities that help to transfer catastrophe risks from insurance industry to bond holders. If there is a catastrophe, the CAT bond is triggered and the future bond payments are reduced. This projects first presents a general pricing formula for a CAT bond with coupon payments, which can be adapted to various assumptions for a catastrophe loss process. Next, it gives formulas for the optimal payment reduction ratios which maximize two measurements of risk reduction, hedge effectiveness rate (HER) and hedge effectiveness (HE), respectively, and examines how the optimal payment reduction ratios help reinsurance or insurance companies to mitigate extreme catastrophe losses. Last, it shows how strike price, maturity, parameters of the catastrophe loss process and different interest rate assumptions affect the optimal payment reduction ratios. Numerical examples are also given for illustrations.

Document type:
Graduating extended essay / Research project
File(s):
Supervisor(s):
Cary Tsai
Department:
Science: Statistics and Actuarial Science
Thesis type:
(Project) M.Sc.