Bayesian Inference via Filtering Equations for Ultrahigh Frequency Data (II): Model Selection

Grace X. Hu, David R. Kuipers, Yong Zeng
2018 SIAM/ASA Journal on Uncertainty Quantification  
For the general partially-observed framework of Markov processes with marked point process observations proposed in [6], we develop the corresponding Bayesian model selection via filtering equations to quantify model uncertainty. To achieve this, we first derive the unnormalized filtering equation and the system of ratio filtering equations to, respectively, characterize the evolution of the marginal likelihood and the corresponding Bayes factors. Then, we prove a powerful weak convergence
more » ... ak convergence theorem. The theorem enables us to employ Markov chain approximation method to construct consistent, easily-parallelizable, recursive algorithms to calculate the related Bayes factors and posterior model probabilities of the candidate models in real time for streaming ultra-high frequency data. The general model selection theory is again illustrated by the four specific models built for U.S. Treasury Notes transactions data from GovPX via simulation and empirical studies.
doi:10.1137/16m1094774 fatcat:exynnrajlnaahka4kyeybvjt54