Statistics

2111 Submissions

[3] viXra:2111.0150 [pdf] submitted on 2021-11-28 14:29:35

Bayesian Inference Via Generalized Thermodynamic Integration

Authors: F. Llorente, L. Martino, D. Delgado
Comments: 17 Pages.

The idea of using a path of tempered posterior distributions has been widely applied in the literature for the computation of marginal likelihoods (a.k.a., Bayesian evidence). Thermodynamic integration, path sampling and annealing importance sampling are well-known examples of algorithms belonging to this family of methods. In this work, we introduce a generalized thermodynamic integration (GTI) scheme which is able to perform a complete Bayesian inference, i.e., GTI can approximate generic posterior exceptions (not only the marginal likelihood). Several scenarios of application of GTI are discussed and different numerical simulations are provided.
Category: Statistics

[2] viXra:2111.0145 [pdf] replaced on 2025-03-23 16:12:27

Effective Sample Size Approximations as Entropy Measures

Authors: L. Martino, V. Elvira
Comments: 31 Pages.

In this work, we analyze alternative effective sample size (ESS) metrics for importance sampling algorithms, and discuss a possible extended range of applications. We show the relationship between the ESS expressions used in the literature and two entropy families, the Renyi and Tsallis entropy. The Renyi entropy is connected to the Huggins-Roy's ESS family introduced in [22]. We prove that that all the ESS functions included in the Huggins-Roy's family fulfill all the desirable theoretical conditions. We analyzed and remark the connections with several other fields, such as the Hill numbers introduced in ecology, the Gini inequality coefficient employed in economics, and the Gini impurity index used mainly in machine learning, to name a few. Finally, by numerical simulations, we study the performance of different ESS expressions contained in the previous ESS families in terms of approximation of the theoretical ESS definition, and show the application of ESS formulas in a variable selection problem.
Category: Statistics

[1] viXra:2111.0012 [pdf] submitted on 2021-11-02 20:50:03

A Revised Comparison Between Fama and French Five-Factor Model and Three-Factor Model——based on China's a-Share Market

Authors: Zhijing Zhang, Yue Yu, Qinghua Ma, Haixiang Yao
Comments: 18 Pages.

In allusion to some contradicting results in existing research, this paper selects China's latest stock data from 2005 to 2020 for empirical analysis. By choosing this periods’ data, we avoid the periods of China's significant stock market reforms to reduce the impact of the government's policy on the factor effect. In this paper, the redundant factors (HML, CMA) are orthogonalized, and the regression analysis of 5*5 portfolio of Size-B/M and Size-Inv is carried out with these two orthogonalized factors. It found that the HML and the CMA are still significant in many portfolios, indicating that they have a strong explanatory ability, which is also consistent with the results of GRS test. All these show that the five-factor model has a better ability to explain the excess return rate. In the concrete analysis, this paper uses the methods of the five- factor 25-group portfolio returns calculation, the five-factor regression analysis, the orthogonal treatment, the five-factor 25-group regression and the GRS test to more comprehensively explain the excellent explanatory ability of the five-factor model to the excess return. Then, we analyze the possible reasons for the strong explanatory ability of the HML, CMA and RMW from the aspects of price to book ratio, turnover rate and correlation coefficient. We also give a detailed explanation of the results, and analyze the changes of China's stock market policy and investors' investment style recent years. Finally, this paper attempts to put forward some useful suggestions on the development of asset pricing model and China's stock market.
Category: Statistics