International Journal of Nonlinear Analysis and Applications

Bayesian parameter estimation in addiction model

Document Type : Research Paper

Authors

Department of Mathematics, College of Science, University of Baghdad, Iraq

Abstract

In this paper, we investigated the performance of Bayesian Computational methods for estimating the parameters of the multinomial Logistic regression model. We discussed two of the most common Bayesian computational algorithms: the Random walk Metropolis-Hastings (RWM) and Slice algorithms and their application to estimating the parameters of the addiction model as well as comparing the performance of these algorithms using the mean square error  (MSE) criterion. The results revealed that the performance of the algorithms is excellent, with a slight superiority to the RWM algorithm. 

Keywords

[1] N.A. . Aziz, Z. Ali, N.M. Nor, A. Baharum and M. Omar, Modeling multinomial logistic regression on characteristics of smokers after the smoke-free campaign in the area of Melaka, AIP Conf. Proc. 1750(1) (2016) 60020.
[2] G.C. Cawley, N.L.C. Talbot and M. Girolami, Sparse multinomial logistic regression via bayesian l1 regularisation,
Adv. Neural Inf. Process. Syst. 19 (2007) 209.
[3] A.M. El-Habil, An application on multinomial logistic regression model, Pakistan J. Statist. Oper. Res. 8(2) (2012)
271–291.
[4] S. Fr¨uhwirth-Schnatter and R. Fr¨uhwirth, Data augmentation and MCMC for binary and multinomial logit
models, Statist. Modell. Regression Structures (2010) 111–132.
[5] J. Geweke, Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, Federal
Reserve Bank of Minneapolis, Research Department Minneapolis, 148 (1991).
[6] P.J. Green, K. Latuszy´nski, M. Pereyra and C.P. Robert, Bayesian computation: a summary of the current state,
and samples backwards and forwards, Stat. Comput., 25(4) (2015) 835–862.[7] S. Kwon, D. Kim and S. Lee, An efficient algorithm for the non-convex penalized multinomial logistic regression,
Commun. Statist. Appl. Methods 27(1) (2020) 129-–140.
[8] R.M. Neal, Slice sampling, Ann. Statist. 13(3) (2003) 705–741.
[9] C. Robert and G. Casella, A short history of Markov chain Monte Carlo: Subjective recollections from incomplete
data, Statist. Sci. 26(1) (2011) 102–115.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 3059-3071
  • Receive Date: 01 December 2021
  • Revise Date: 30 December 2021
  • Accept Date: 03 January 2022
  • First Publish Date: 09 January 2022