Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

Random effect models have been widely applied in many fields of research. However, models with uncertain design matrices for random effects have been little investigated before. In some applications with such problems, an expectation method has been used for simplicity. This method does not include the extra information of uncertainty in the design matrix is not included. The closed solution for this problem is generally difficult to attain. We therefore propose an two-step algorithm for estimating the parameters, especially the variance components in the model. The implementation is based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm. As an example, a simulated genetics dataset was analyzed. The results showed that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method. By introducing heuristic search and optimization methods, the algorithm can possibly be developed to infer the 'model-based' best design matrix and the corresponding best estimates.

A Psychoanalytic Reading of Vladimir and Estragon in Samuel Beckett’s Waiting for Godot

Much has been written about Samuel Beckett’s Waiting for Godot, but as far as I am aware no one has compared the two characters of Vladimir and Estragon in order to analyse what makes Vladimir more willing to wait than Estragon. This essay claims that Vladimir is more willing to wait because he cannot deal with the fact that they might be waiting in vain and he involves himself more in his surrounding than Estragon. It is Vladimir who waits for Godot, not Estragon, and Vladimir believes that Godot will have all the answers. This will be explored by examining four topics, all of which will be dealt with from a psychoanalytical point of view and in relation to waiting. Consciousness in relation to the decision to wait; Uncertainty in relation to the unknown outcome of waiting; Coping mechanisms in relation to ways of dealing with waiting; Ways of waiting in relation to waiting-time and two kinds of waiting-characters.

Novel Statistical Methods in Quantitative Genetics : Modeling Genetic Variance for Quantitative Trait Loci Mapping and Genomic Evaluation

This thesis develops and evaluates statistical methods for different types of genetic analyses, including quantitative trait loci (QTL) analysis, genome-wide association study (GWAS), and genomic evaluation. The main contribution of the thesis is to provide novel insights in modeling genetic variance, especially via random effects models. In variance component QTL analysis, a full likelihood model accounting for uncertainty in the identity-by-descent (IBD) matrix was developed. It was found to be able to correctly adjust the bias in genetic variance component estimation and gain power in QTL mapping in terms of precision.  Double hierarchical generalized linear models, and a non-iterative simplified version, were implemented and applied to fit data of an entire genome. These whole genome models were shown to have good performance in both QTL mapping and genomic prediction. A re-analysis of a publicly available GWAS data set identified significant loci in Arabidopsis that control phenotypic variance instead of mean, which validated the idea of variance-controlling genes.  The works in the thesis are accompanied by R packages available online, including a general statistical tool for fitting random effects models (hglm), an efficient generalized ridge regression for high-dimensional data (bigRR), a double-layer mixed model for genomic data analysis (iQTL), a stochastic IBD matrix calculator (MCIBD), a computational interface for QTL mapping (qtl.outbred), and a GWAS analysis tool for mapping variance-controlling loci (vGWAS).

The Power of the Synthetic Control Method

The synthetic control method (SCM) is a new, popular method developed for the purpose of estimating the effect of an intervention when only one single unit has been exposed. Other similar, unexposed units are combined into a synthetic control unit intended to mimic the evolution in the exposed unit, had it not been subject to exposure. As the inference relies on only a single observational unit, the statistical inferential issue is a challenge. In this paper, we examine the statistical properties of the estimator, study a number of features potentially yielding uncertainty in the estimator, discuss the rationale for statistical inference in relation to SCM, and provide a Web-app for researchers to aid in their decision of whether SCM is powerful for a specific case study. We conclude that SCM is powerful with a limited number of controls in the donor pool and a fairly short pre-intervention time period. This holds as long as the parameter of interest is a parametric specification of the intervention effect, and the duration of post-intervention period is reasonably long, and the fit of the synthetic control unit to the exposed unit in the pre-intervention period is good.