Microbialites are a product of trapping and binding of sediment by microbial communities, and are considered to be some of the most ancient records of life on Earth. It is widely held that microbialites are limited to extreme, hypersaline environments. However, literature also shows evidence of their occurrence in a wider range of environments. The goal of this thesis is to explore geochemical properties of aquatic environments in which microbialites have been found. We apply statistical techniques to distinguish any common traits in microbialite environments. These techniques ultimately could be used to address the question are microbialites restricted to hypersaline environments, other environments with specific characteristics, or are they more broadly distributed? A dataset containing hydrographic characteristics of several microbialite sites with data on pH, conductivity, alkalinity, and concentrations of several major anions and cations was constructed from previously published studies. Qualitative inspection of these data show that microbialites are not restricted to hypersaline environments, as they are present at Pavilion Lake, a freshwater body. In order to group the water samples by their natural similarities and differences, a clustering approach was chosen for analysis. K-means clustering with partial distances was applied to the dataset with missing values, and separated the data into 2 distinct but geochemically similar clusters. One of the clusters is formed by samples from atoll Kiritimati, and the second cluster contains all other observations. Then, the missing values were imputed by $k$-nearest neighbor method, producing a complete dataset that can be used for further multivariate analysis. We find that microbialites occur within environments spanning a range of salinities (as indicated by conductivity), pH values, and ionic compositions. Furthermore, pH seems to define geochemical profile of this dataset and its clustering. Clustering and imputation procedure outlined here can be applied to an expanded dataset on microbialite characteristics in order to determine if unique properties are associated with microbialite-containing environments, and can also serve as an outline for analysis of such datasets with missing data.

In this dissertation, I look at four distinct systems that all embody a similar challenge to modeling complex scenarios from noisy multidimensional historical data. In many scenarios, it is important to form an opinion, make a prediction, implement a business decision, or make an investment based upon expected future system behavior. All systems embody an amount of uncertainty, and quantify- ing that uncertainty using statistical methods, allows for better decision making. Three distinct scenarios are discussed with novel application of statistical methods to best quantify the endogenous uncertainty and aid in optimal decision making. Two chapters focus on predicting the winners of a horse race, one on predicting movement of a stock index, and the fourth on molding response from an online advertising effort.

The first horse racing chapter uses a hierarchical Bayesian approach to model- ing running speed, using a novel grouping of races into "profiles" and then pooling information across those profiles to improve predictive accuracy. The second horse racing chapter implements a novel conditional logistic regression that is modified by frailty parameter derived from winning payoff, and then regularized with a LASSO. High speed parallel algorithms, running on a GPU, were hand coded to optimize tuning LASSO parameters in rapid time.

The chapter on stock index prediction explores the application of ensemble filters. I show how an ensemble of filters on individual member stocks is a better predictor of index direction than a filter directly on the index.

The chapter on advertising explores how the clicks and sales from an Ad- Words campaign may be modeled with a re-paramaterized Beta distribution to better capture variance. Empirical data from a live campaign is studied, with a hierarchical Bayesian framework for brand features solved using a Metropolis within Gibbs algorithm.

Modern portfolio theory says that unsystematic risk can always be diversified away. Although it is unrealistic to achieve perfect diversification, people developed different strategies trying to find an optimal portfolio. In this paper, issues of how to make a diversified portfolio are discussed. Six models of tactical portfolio construction strategies are used to make the optimal portfolios using the historical data from Jan. 2007 to Dec. 2009. From the out-of-sample test by market data from Jan. 2010 to Dec. 2011, the classic Markowitz portfolio has the highest wealth added. By comparing the portfolio evaluation parameters, Sharpe ratio suits an individual investor most. And Bayesian portfolio with informative prior scores highest by Sharpe ratio regardless its sensitivity to the accurate market prediction. The paper also demonstrates the application of statistical software R and the "stockPortfolio" package in the stock investment field.

In their study "Does the Stock Market Overreact?", Debondt and Thaler proposed the overreaction hypothesis, which states that if a stock experiences significant price movement, then a subsequent price movement in the opposite direction is likely to follow. Moreover, the level of extremeness is positively correlated between the initial and the following price movement. In this study we would adopt the similar algorithm, using the data of recent three decades to test the overreaction hypothesis. Besides, the study of overreaction has shed light to the research of "January Effect" in stock market. A linear regression model will be used to test the existence of "January Effect", by analyzing the stocks with greater losses

during a 5-year period.

The extent to which the apparent increase in wildfire incidence and burn area in California from 1990 to 2006 is affected by population and temperature increases is examined. Using generalized linear models with random effects, we focus on the estimated impacts of increases in mean daily temperatures and populations in different counties on wildfire in those counties, after essentially controlling for the overall differences between counties in their overall mean temperatures and populations. We find that temperature increase appears to have a significant positive impact on both total burn area and number of observed wildfires. Population growth appears to have a much less pronounced impact on total burn area than do annual temperature increases, and population growth appears to be negatively correlated with the total number of observed wildfires. These effects are especially pronounced in the winter season and in Southern California counties.

This work presents an alternative derivation of the asymptotic distribution of Ripley's K-function for a homogeneous Poisson process and shows how it can be combined with point process residual analysis in order to test for different classes of point process models. This can be doen with the mean K-function of thinned residuals (K_M ) or a weighted analogue called the weighted or inhomogeneous K-function (K_W ). The asymptotic distributions of K_M and K_W are derived for inhomogeneous Poisson processes. Both statistics can be used as measures of goodness-of-fit for point process models.

Forest fires are one of the biggest ecological disasters in Canada. Counts and sizes of fires vary substantially from year to year. In this study, the data is collected from Northwest Territories in Canada. We assume that fire counts appear to follow the Gamma-Poisson distribution, and fire sizes approximately follow the Gamma-Exponential distribution. The Maximum Likelihood Estimation and Random Search are used to estimate the parameters of two models. Identifiability issues regarding parameters in the two models are explored. The Kolmogorov–Smirnov test is used to check for goodness of fit. For fire sizes data, although the Kolmogorov–Smirnov test shows a low p-value, by plotting theoretical and empirical distribution, we can see that the Gamma-Exponential distribution fits adequately.

My research was strongly influenced by ongoing Next Generation Attenuation projects (NGA), which is sponsored by Pacific Earthquake Engineering Research Center (PEER). This far, PEER has sponsored two landmark national projects for developing NGA relationship in active tectonic regions. The result of these two projects will be incorporated into national hazard maps developed by United States Geological Survey (USGS). However, since the national seismic hazard maps include stable continental regions and subduction zones, it is desired to ex- tend those studies to other tectonic regions. NGA-Subduction project has recently been initiated to address Subduction Zones (SZ).

For this project, I collaborated with PEER researcher for processing the data of main shock recordings of the Tohoku earthquake. I also analyzed the data to evaluate the implications of this data set with respect to magnitude-, distance-, and site-scaling in existing GMPEs for SZs. The Mw = 9.0 Tohoku-oki Japan earthquake produced approximately 2000 ground motion recordings. We consider 1238 three-component accelerograms corrected with component-specific low-cut filters. The recordings have rupture distances between 44 and 1000km, time-veraged shear wave velocities of Vs30 = 90 to 1900ms−1, and usable response spectral periods of 0.01 to > 10 s. The data support the notion that the increase of ground motions with magnitude saturates at large magnitudes. High frequency ground motions demonstrate faster attenuation with distance in backarc than in forearc regions, which is only captured by one of the four considered ground motion prediction equations for subduction earthquakes. Recordings within 100 km of the fault are used to estimate event terms, which are generally positive (indicating model under-prediction) at short periods and zero or negative (over-prediction) at long periods. We find site amplification to scale minimally with Vs30 at high frequencies, in contrast with other active tectonic regions, but to scale strongly with Vs30 at low frequencies.

It is envisioned that the research outlined herein could help earthquake engi- neering community to design infrastructures which are more resistant to earth- quakes by improving ground motion prediction capabilities.

The game of basketball has witnessed constant evolution, necessitating the use of statistical data for predicting winners. While the odds of winning a championship are traditionally 1 in 30 each year, strategic positioning in various statistical categories can surpass this baseline, regardless of a team’s annual ranking. By analyzing data and identifying crucial variables, it becomes evident that basketball outcomes are not predetermined. This study employs modern data science methods to make predictions for future years or generations, emphasiz- ing the importance of selecting accurate via cross-validation for the machine learning (ML) techniques. All data used in this study is sourced from Basketball-Reference. This study debunks the fallacy that a team solely relying on prominent three-point shooters guarantees championship success. It underscores the significance of other factors and variables in deter- mining outcomes. The analysis emphasizes the importance of relying on objective statistical analysis rather than subjective perceptions. Factors like overtime play and defensive prowess in blocks significantly impact a team’s likelihood of becoming an NBA champion, reinforcing the need for data-driven insights and accurate predictions.

The major goal of this thesis is to discuss and test some of the models and fundamental elements of the Modern Portfolio Theory in order to learn about whether the optimal portfolios constructed on the theory formulate the best asset allocation in reality. In an effort to solve this question, three different models are tested by three fundamental elements of the theory respectively. The outcomes for each model and element are discussed and evaluated.

The empirical result shows that the models are inconsistent, which leads to the conclusion that optimal portfolios based on Modern Portfolio Theory are not the best asset allocation strategies in the real investment world. The main reason can be concluded that the models based on the theory make oversimplified approximations of the reality.