Bayesian temporal density estimation with autoregressive species sampling models |
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Authors: | Youngin Jo Seongil Jo Yung-Seop Lee Jaeyong Lee |
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Affiliation: | 1. Kakao corporation, Seongnam 13494, Republic of Korea;2. Department of Statistics (Institute of Applied Statistics), Chonbuk National University, Jeonju 54896, Republic of Korea;3. Department of Statistics, Dongguk University-Seoul, Seoul 04620, Republic of Korea;4. Department of Statistics, Seoul National University, Seoul 08826, Republic of Korea |
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Abstract: | We propose a novel Bayesian nonparametric (BNP) model, which is built on a class of species sampling models, for estimating density functions of temporal data. In particular, we introduce species sampling mixture models with temporal dependence. To accommodate temporal dependence, we define dependent species sampling models by modeling random support points and weights through an autoregressive model, and then we construct the mixture models based on the collection of these dependent species sampling models. We propose an algorithm to generate posterior samples and present simulation studies to compare the performance of the proposed models with competitors that are based on Dirichlet process mixture models. We apply our method to the estimation of densities for the price of apartment in Seoul, the closing price in Korea Composite Stock Price Index (KOSPI), and climate variables (daily maximum temperature and precipitation) of around the Korean peninsula. |
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Keywords: | primary 62C10 secondary 62G07 Autoregressive species sampling models Dependent random probability measures Mixture models Temporal structured data |
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