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?**