Physical Sciences and Mathematics Commons^™

Estimation And Inference For Spatial And Spatio-Temporal Mixed Effects Models, Casey M. Jelsema

Dissertations

One of the most common goals of geostatistical analysis is that of spatial prediction, in other words: filling in the blank areas of the map. There are two popular methods for accomplishing spatial prediction. Either kriging, or Bayesian hierarchical models. Both methods require the inverse of the spatial covariance matrix of the data. As the sample size, n, becomes large, both of these methods become impractical. Reduced rank spatial models (RRSM) allow prediction on massive datasets without compromising the complexity of the spatial process. This dissertation focuses on RRSMs, particularly situations where the data follow non-Gaussian distributions.

The manner in …

A Robust Estimate For The Bifurcating Autoregressive Model With Application To Cell Lineage Data, Tamer M. E. Elbayoumi

Dissertations

The bifurcating autoregressive model (BAR) is commonly used to model binary tree data. One application for this model relates to cell lineage data in biology. The purpose of studying the cell lineage process is to know whether the observed correlations between related cells are due to similarities in the environmental, inherited effects, or a combination of both of them. Because outliers in this kind of data are quite common, the need for a robust estimation procedure is necessary. A weighted L1 (WL1) estimate for estimating the parameters of the BAR model is considered. When the weights are constant, the estimate …