Estimation and Inference via Computational Statistics Algorithms

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Statistical computation is essential in order to analyse large data sets accurately using complicated statistical models. The algorithms used have to be efficient and accurate and reliable in order for the analysis to be valid and useful, and lead to high-quality statistical inference and estimates of key unknown quantities. I plan to use my NSERC research grant to investigate computational statistics algorithms, especially Markov chain Monte Carlo (MCMC) algorithms, from a variety of perspectives. Much of my work will concern the theoretical foundations of the algorithms, analysing their convergence and performance and improvements using mathematical probability theory. I also plan to study different algorithm designs and improvements. In addition, I will try to apply these algorithms to data sets from a variety of subjects. In all cases, I will focus on the properties, performance, and application of these algorithms. Some specific methodological and theoretical questions which I plan to investigate include: * How can the popular mode-merging simulated and parallel tempering MCMC algorithms be improved so that tall narrow modes are not ignored at high temperatures? * What is the optimal scaling and acceptance rate of Metropolis algorithms when applied to target distributions which are much more general than the special cases studied in previous papers? * How is the estimation accuracy of a MCMC algorithm affected when it is slightly "perturbed", due to the approximate computations required of certain modern MCMC applications? * How does the computational complexity of "model-selection" MCMC algorithms grow as the number of parameters and amount of data go to infinity? * How can MCMC algorithms be better "adapted", to improve their performance on the fly, while still converging to the correct quantities? I also plan to apply computational statistics algorithm to various large-scale real data sets, including: * Cancer treatment patient data: What hidden patterns can be found concerning which medical treatments work best for which sorts of patients? * Student grade data: What factors influence students' choice of subject major and future success? * Forest growth data: Can "ground truth" measurements for samples of tree populations from Canadian forests be compared to publicly-available images from satellites, to calibrate the satellite images for future tree estimates?