Residual analysis has long been an effective tool for evaluating earthquake forecast models. In this thesis, we not only present simple numerical summaries, but also focus on graphical residual methods including pixel-based approaches, Voronoi methods and super-thinned residuals. Competing models in the Collaboratory for the Study of Earthquake Predictability (CSEP) are evaluated and compared using the residual analysis techniques, and the goodness-of-fit and deficiencies are assessed for each model.

Objective: Prevalence of type II diabetes is higher in diagnosed patients with schizophrenia when compared with the general adult population. With the propagation of electronic health records (EHR), we assess whether electronic health record phenotyping can improve diabetes mellitus type 2 (T2DM) screening when compared to conventional diabetic screening metrics in patients with schizophrenia.

Method: EHR data from 1267 patients with schizophrenia was used to develop a pre-screening tool for current T2DM using logistic regression and random forest models. Three types of models were created: the first used conventional diabetic screening criteria (BMI, age, gender, etc.) and their interactions. The second utilized conventional factors plus prescribed medications. The third

utilized conventional factors, prescriptions, and diagnoses as determined by ICD-9 codes.

Results: EHR phenotyping models utilizing conventional factors, prescriptions, and diagnosis information (EHR-DX) had improved ability to detect T2DM, when compared to models containing conventional (EHR-conventional) or conventional & prescription metrics (EHR-RX). Conversely, there was not a statistically significant improvement in T2DM detection between models containing conventional metrics and models containing conventional & prescription metrics (likelihood ratio test, p < 0.001). The AUC for the full EHR DX, EHR RX, and conventional models using logistic regression were 85.8%, 74.8%, and 72.7% respectively.

Several ICD codes were shown to have a significant association with diabetes diagnosis, including several from established predictors or comorbidities, such as prediabetes and heart disease. Associations between antipsychotic drugs and diabetes diagnosis were generally insignificant and lacked a discernible positive or negative association trend.

This dissertation investigates the strengths and weaknesses of the current methods of residual analysis for spatial point process models. The primary focus is on the manner in which the space should be partitioned to form residuals. It proposes a new method whereby the differences between the modeled conditional intensity and the observed number of points are assessed over the Voronoi cells generated by the observations. The resulting residuals are substantially less skewed and can be used to construct diagnostic methods of greater statistical power than residuals based on a regular rectangular grid. These advantages are particularly evident for point processes with conditional intensities close to zero, such as those in seismology. Performance is compared using simulated data and applied to models for Southern California earthquakes.

Point processes have long been used as an effective modeling technique in the forecasting of earthquakes. In this dissertation, we evaluate the ability of earthquake focal mechanisms to predict the locational direction of future events and the usefulness of more complicated point process models including such covariates. We also introduce a new computational method for estimating parameters of point processes models using the Stoyan-Grabarnik estimator which avoids the need to numerically compute the intractable integral term needed to compute estimates via maximum likelihood.

There currently exist several “black box” software libraries for the automatic forecasting of time series. Popular among these are the 'forecast' and 'bsts' packages for R, which have

functions to automatically fit several common classes of time series models, such as the

autoregressive integrated moving average (ARIMA) and the family of exponential smoothing

models, among others. It is often the case that what one gains from the ease in fitting these

automatic methods comes at the cost of predictive performance. In this paper, we propose

several methods to improve the prediction accuracy of automatic time series forecasting, all of

which relate to creating ensembles of models automatically fit from these packages. We

explore different ways that one can construct these ensembles and evaluate each on a

benchmark time series dataset. In addition, we provide the R code used to construct these ensembles.

Severity scoring systems are frequently used in hospital intensive care units to assess patient wellness and mortality probability. Accurate mortality predictions are vital to provide appropriate and timely treatments to critical patients. However, commonly used severity scores have been found to make inaccurate mortality predictions. In this paper, we assess and compare four popular severity scores for both discrimination and calibration. We apply logistic regression, random forest, and neural network classification techniques in order to present new mortality prediction models, and compare their performance with pre-existing scores. We also compare the use of a basic set of predictor features that can be easily collected in the ICU environment with an expanded predictor set including laboratory diagnostics. Newly developed models improved on existing severity scores in terms of discrimination, with random forest providing the best results, but often demonstrated poor calibration. The expanded variable set did not improve model performance.

Employing over 10 million people, with an annual expenditure averaging over $1.2 trillion, the U.S. construction industry is massive in both scale and reach. Every day, thousands of construction builds are underway across the country, each with a unique set of costs contributing to its overall budget. For many, the cost of commodities, or materials used to build a project, is a huge variable that changes constantly and can negatively impact a project both financially and temporally. Being able to better understand and predict the way the prices these commodities change over time could lead to huge savings of time and money for anyone at the planning stages of a construction project. Statistical time series modeling is one effective way to increase this understanding and prediction abilities. This thesis models and forecasts the price indices of three construction commodities integral to the industry: lumber, iron/steel, and concrete. For each commodity, the month-to-month percentage changes of nearly 100 years of index values are modeled using Autoregressive Moving Average (ARMA) models, which are selected based on multiple model selection criteria. The models are then used to forecast an 8-month period directly following the end of the data series, which corresponds to the first 8 months of 2022. In doing so, it is found that the lumber model using ARMA methods makes forecasts indicative of what has happened in reality in the first half of 2022, where as the iron/steel and concrete models have much more difficulty in doing so.

Data analytics and machine learning have become vital applications in the world of sports, providing glimpses of statistically probable, mathematically formulated future states while helping teams and individual athletes make smarter decisions. The sport of tennis, featuring a relatively low number of moving parts, a bevy of readily available data and a global interest, is ripe for advanced forecasting analysis. In the following, the method of adaptive least squares is leveraged in conjunction with Kalman filtering to create time-variant match statistics for professional tennis players. Once the adaptive model is constructed, the sigmoid function is utilized to transform forecasted delta set values into forecasted probabilities of winning for any given matchup. The most successful model constructed from the web-scraped pool of data is continuously improving and correctly forecasts tennis match outcomes 63.54% of the time, exceeding the prediction accuracy if outcomes were chosen solely based on professional rankings.

It is common to use geostatistical techniques to analyze epidemiological data. However, we might gain further insight by viewing these types of data as a point pattern due to the spatial nature of the dataset which would allow us to use the spatial information of each point and apply point process techniques. Point process techniques are applied to the avian influenza virus data, and a summary statistic called the weighted cross J-function is proposed. The ordinary cross J-function is extended to a weighted version by incorporating weights to account for inhomogeneity because this dataset appears to exhibit non-constant intensity. Unlike the ordinary cross J-function, the weighted cross J-function takes into account the varying background rate of the point process by incorporating weights for each point in the point patterns. The advantage of the weighted cross J -function is that it is used to measure the interaction between events in two point processes and to detect clustering or inhibition between them, in order to recognize where spatial interaction appears most prevalent. We introduce the weighted cross J-function, discuss its properties, demonstrate it with simulations and show its application to the African Avian Flu dataset.

Point process modeling is used to predict the conditional intensity of wildfire ignitions in California from 2008 to 2012. Weather variables from the closest station record are used as model covariates. To reduce computation requirements of maximum likelihood estimation, the Stoyan-Grabarnik statistic is employed. Models of various combinations and number of variables are examined, as well as models for specifically naturally occurring fires caused by lightning and fires caused by humans.