Markov Chain Monte Carlo methods may be used to determine normalizations and moments of distributions. However, these methods may perform poorly when starting from distributions that have little overlap with the target. We develop a homotopy based iterative process of incremental importance sampling to normalize distributions when observations can only...
The HyperLogLog (HLL) algorithm is used to estimate the cardinality of large sets. This thesis gives a novel analysis of the HyperLogLog algorithm by using techniques from statistics and probability. Initially, closed form bounds for the mean and variance of the max of n independent and identically distributed geometric random...
The California Current Ecosystem (CCE) is a dynamic marine ecosystem from which many socioeconomically important fisheries species are harvested. In this thesis, a genotyping-by-sequencing (GBS) approach was used to examine genomic variation in an early life stage of the Dungeness crab (Cancer magister), which constitutes the most valuable single-species commercial...
Gene regulation is a complex mechanism that controls the spatial and temporal expression of genes in a living cell. My dissertation studies focus on two problems. First, tissue-specific gene expression prediction from DNA sequence and chromatin state, and second, the accurate discovery of small over-represented regulatory circuits in gene regulatory...
In this thesis I will look at a definition of computable randomness from Algorithmic Information Theory as defined by Andre Nies through the lens of Computable Analaysis asdefined by Klaus Weihrauch. I will show that despite the fact that these two paradigmsgenerate distinct classes of computable supermartingales, the class of...
Pardoxes in voting has been an interest of voting theorists since the 1800's when Condorcet demonstrated the key example of a voting paradox: voters with individually transitive rankings produce an election outcome which is not transitive. With Arrow's Impossibility Theorem, the hope of finding a fair voting method which accurately...
Bacteria are abundant in marine environments. They play important roles in nutrient cycling and form symbiotic interactions with eukaryotes. However, the vast majority of bacterial taxa are difficult to maintain in laboratory cultures, meaning that most microbiological research of the past century has focused on a small subset of bacteria....
Tree-like patterns are ubiquitous in nature. Botanical trees, river networks, and blood systems are the most well-known examples of complex hierarchical systems met in observations. Interestingly, many of such systems exhibit statistical self-similarity. There are two main types of self-similarity: Horton self-similarity and Tokunaga self-similarity. Although there is an increased...