Geometric stick-breaking processes for continuous-time Bayesian nonparametric modeling |
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Authors: | Ramsés H Mena Matteo Ruggiero |
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Institution: | a Universidad Nacional Autónoma de México, A.P. 20-726, 01000 Mexico D.F., Mexico b University of Pavia and Collegio Carlo Alberto via San Felice 5, Pavia and Via Real Collegio 30, Moncalieri, Italy c University of Kent CT2 7NZ, Canterbury, UK |
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Abstract: | We propose a new class of time dependent random probability measures and show how this can be used for Bayesian nonparametric inference in continuous time. By means of a nonparametric hierarchical model we define a random process with geometric stick-breaking representation and dependence structure induced via a one dimensional diffusion process of Wright-Fisher type. The sequence is shown to be a strongly stationary measure-valued process with continuous sample paths which, despite the simplicity of the weights structure, can be used for inferential purposes on the trajectory of a discretely observed continuous-time phenomenon. A simple estimation procedure is presented and illustrated with simulated and real financial data. |
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Keywords: | Bayesian nonparametric inference Dependent process Measure-valued diffusion Stationary process Stick-breaking representation Wright-Fisher process |
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