Spatial-temporal data arises in many applications, for example, environment sciences and disease mapping. This dissertation focuses on Gaussian spatial-temporal data. To make statistical inference for Gaussian spatial-temporal data, we developed a special class of spatial-temporal Gaussian state-space models in which the state vectors are constructed following spatial-temporal Gaussian autoregressions that...
Markov chains, discovered over one hundred years ago by Andrey Markov in an
attempt to analyze the distribution of vowels and consonants in Russian poetry, have
evolved in multiple fields over the last century to become a mainstay of statistical
modeling and computation. maRkov is a package of software to...
Earthquakes are complicated processes varying in time, space and magnitude. The occurrence of a major earthquake event called mainshock is preceded and followed in time by diminishing seismic activities known as foreshocks and aftershocks respectively. The process of identifying mainshocks, aftershocks, and foreshocks in a given earthquake catalog is known...
We explore the possibility of estimating sparse inverse covariance matrices when for scientific reasons the covariance matrix is restricted to be a non-negative matrix. The process mirrors the graphical lasso process developed by Friedman and others(2008) that did not have this additional constraint.Accordingly, the Lasso procedure is done through coordinate...
Dynkin’s (Bull. Amer. Math. Soc. 3 (1980) 975–999) seminal work associates a multidimensional transient symmetric Markov process with a multidimensional Gaussian random field. This association, known as Dynkin’s isomorphism, has profoundly influenced the studies of Markov properties of generalized Gaussian random fields. Extending Dykin’s isomorphism, we study here a particular...
DNA microarray technology is a powerful tool for analyzing patterns in gene expression data for thousands of genes. Due to a number of systematic variations in microarray experiments, the raw gene expression data is often obfuscated by undesirable technical noises. Various normalization techniques were designed in an attempt to remove...
Anomaly detection aims at detecting the points that appear different than the majority of the data, such that they are suspected to be generated from a different distribution. Anomaly detectors have been applied in many different fields, such as detecting fraudulent behaviors in bank transaction, finding broken sensors in a...
Question answering forums like Reddit have been quite effective in improving social interaction and disseminating useful information. Community members ask a variety of questions related to a subject which are answered by other community members. The answers are given ratings by other members. In this thesis we study the problem...
Anadromous salmonid populations in the Pacific Northwest have declined over the past 150 years. In 1999, wild spring Chinook salmon (Oncorhynchus tshawytscha) were federally listed as threatened within the Willamette Basin, OR. Currently, practices to restore wild populations in the upper Willamette Basin involve trapping wild adults at the base...
Methods that are applied to smooth distribution functions are useful in many applications. Areas of application include economics, financial markets and survival analysis. The empirical cumulative distribution function (ecdf) is unbiased and its asymptotic distribution is normal. However, the jump discontinuities of $\frac{1}{n}$ are undesirable in estimation because it makes...