Author:
Daiki Koizumi
Affiliation:
Otaru University of Commerce, 3–5–21, Midori, Otaru-city, Hokkaido, 045–8501, Japan
Keyword(s):
Probability Model, Bayes Decision Theory, Nonstationary Geometric Distribution, Hierarchical Bayesian Model, Time Series Analysis.
Abstract:
This paper considers a prediction problem with a nonstationary geometric distribution in terms of Bayes decision theory. The proposed nonstationary statistical model contains a single hyperparameter, which is used to express the nonstationarity of the parameter of the geometric distribution. Furthermore, the proposed predictive algorithm is based on both the posterior distribution of the nonstationary parameter and the predictive distribution for data, operating with a Bayesian context. Each predictive estimator satisfies the Bayes optimality, which guarantees a minimum mean error rate with the proposed nonstationary probability model, a loss function, and a prior distribution of the parameter in terms of Bayes decision theory. Furthermore, an approximate maximum likelihood estimation method for the hyperparameter based on numerical calculation has been considered. Finally, the predictive performance of the proposed algorithm has been evaluated in terms of both the model selection th
eory and the predictive mean squared error by comparison with the stationary geometric distribution using real web traffic data.
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