過度離散之泊松混合模型之統計推論

Component Inference on Mixture Model of Overdispersion Poisson

陳維梁(Wei-Liang Chen)

指導教授 ： 高竹嵐

國立交通大學/理學院/統計學研究所/碩士(2019年)

摘要

PIN(probability of informed trading)又稱知情交易率，其模型背景預期股票市場交易情形會是由三個泊松分布混合而成，如果能推論資料的分群狀況就能計算PIN。然而我們從實際資料的分布中觀測到資料是由過度離散的泊松分布(Overdispersion Poisson )混合而成，從而如何對此種分布進行有效的分群，在使用rebmix、Mclust、flexmix等套件都未有較佳的結果下，我們選用StepSignalMargiLike套件進行分群，在模擬實驗中得到相對不錯的效果，我們最終使用它來對實際資料進行分群與參數估計。

關鍵字

分群

並列摘要

PIN is also known as the probability of informed trading,under which we expect the stock market trading situation to be a mixture of three discrete types following Poisson distributions. If we can decode the groups from the data, we can calculate the PIN.However,by closely examine the data,we found out that the data comes from a mixture of overdispersion Poisson distribution ,which give raise to the need of effectively inference the group from such mixture distribution .After using rebmix, Mclust, flexmix with no effective results, we turn to StepSignalMargiLike package , which is a semi-Bayesian approach, and have better performance under simulation studies.We therefore use StepSignalMargiLike on our PIN data.

並列關鍵字

clustering

參考文獻

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Nagode, Marko. "Multivariate normal mixture modeling, clustering and classification with the rebmix package." arXiv preprint arXiv:1801.08788 (2018).

Scollnik, David PM. "Bayesian analysis of two overdispersed Poisson regression models." Communications in Statistics-Theory and Methods 24.11 (1995): 2901-2918.

Nagode, Marko. "Finite mixture modeling via rebmix." Journal of Algorithms and Optimization 3.2 (2015): 14-28.