Quantitative TradingIdalion Capital, London UK & DeLand FLA, US
Bayesian Stochastic Computation, with Application to Model Selection and Inverse Problems
Several problems in Bayesian statistics that involve significant stochastic computation are explored. The considered problems either involve model selection or statistical inverse problems. The first three chapters of the thesis consider model selection. The first problem analyzed is model selection in multiple linear regression. Several approaches are compared and a new algorithm for searching in large model spaces is introduced. The second problem considered is choice among probit models with binary covariates; Again, the key to successful computation is the introduction of a fast search algorithm. The third problem considered is comparison of Expected Posterior Priors with other commonly used techniques in model selection. The second part of the thesis introduces an example of the construction of fast simulators for assessment and propagation of input uncertainty when using complex computer models. This is studied in the context of microsimulation of traffic systems. The last chapter of the thesis introduces Bayesian methods for analysis of multiscale stochastic volatility models and tests its performance on foreign exchange data. This chapter involves what could be termed an informal approach to selection between stochastic volatility models with different number of scales.