On Finite and Non-Finite Bayesian Mixture Models

Yıl 2023, Sayı: 45, 57 - 72, 31.12.2023

Rasaki Olawale Olanrewaju Sodiq Adejare Olanrewaju Adedeji Adigun Oyınloye Wasiu Adesoji Adepoju

https://doi.org/10.53570/jnt.1358754

Öz

In this paper, a Bayesian paradigm of a mixture model with finite and non-finite components is expounded for a generic prior and likelihood that can be of any distributional random noise. The mixture model consists of stylized properties-proportional allocation, sample size allocation, and latent (unobserved) variable for similar probabilistic generalization. The Expectation-Maximization (EM) algorithm technique of parameter estimation was adopted to estimate the stated stylized parameters. The Markov Chain Monte Carlo (MCMC) and Metropolis–Hastings sampler algorithms were adopted as an alternative to the EM algorithm when it is not analytically feasible, that is, when the unobserved variable cannot be replaced by imposed expectations (means) and when there is need for correction of exploration of posterior distribution by means of acceptance ratio quantity, respectively. Label switching for exchangeability of posterior distribution via truncated or alternating prior distributional form was imposed on the posterior distribution for robust tailoring inference through Maximum a Posterior (MAP) index. In conclusion, it was deduced via simulation study that the number of components grows large for all permutations to be considered for subsample permutations.

Anahtar Kelimeler

Bayesian paradigm, expectation-maximization, MCMC, proportional allocation, metropolis–hastings

Proje Numarası

None

Kaynakça

• A. Gelman, J. Carlin, H. Stern, D. Dunson, A. Vehtari, D. Rubin, Bayesian Data Analysis, 3rd Edition, Chapman and Hall, New York, 2013.
• G. Wioletta, The Advantages of Bayesian Methods over Classical Methods in the Context of Credible Intervals, Information Systems in Management 4 (1) (2015) 53–63.
• C. Charlton, J. Rasbash, W. J. Browne, M. Healy, B. Cameron, MLwiN. In: Centre for Multilevel Modeling (2020), https://www.bristol.ac.uk/cmm/, Accessed 20 Sep 2023.
• J. E. Johndrow, A. Smith, N. Pillai, N. Dunson, MCMC for Imbalanced Categorical Data, Journal of the American Statistical Association 114 (527) (2019) 1394¬–1403.
• R. O. Olanrewaju, S. A. Olanrewaju, L. A. Nafiu, Multinomial Naive Bayes Classifier: Bayesian versus Non-parametric Classifier Approach, European Journal of Statistics 2 (8) (2022) 1–14.
• R. O. Olanrewaju, Bayesian Approach: An Alternative to Periodogram and Time Axes Estimation for Known and Unknown White Noise, International Journal of Mathematical Sciences and Computing 2 (5) (2018) 22–33.
• U. Simola, J. Cisewski-Kehe, L. R. Wolpert, Approximate Bayesian Computation for Finite Mixture Models, Journal of Statistical Computation and Simulation 91 (6) (2021) 1155–1174.
• A. Hairault, C. P. Robert, J. Rousseau, Evidence Estimation in Finite and Infinite Mixture Models and Applications (2022) 43 pages, https://arxiv.org/abs/2205.05416.
• A. R. Hassan, R. O. Olanrewaju, Q. C. Chukwudum, S. A. Olanrewaju, S. E. Fadugba, Comparison Study of Generative and Discriminative Models for Classification of Classifiers, International Journal of Mathematics and Computer Simulation 16 (12) (2022) 76–87.
• M. Betancourt, A Conceptual Introduction to Hamiltonian Monte Carlo (2017) 60 pages, https://arxiv.org/abs/1701.02434.
• J. F. Ojo, R. O. Olanrewaju, S. A. Folorunsho, Bayesian Logistic Regression Using Gaussian Naıve Bayes (GNB), Journal of Medical and Applied Biosciences 9 (2) (2017) 1–18.
• R. O. Olanrewwaju, L. O. Adekola, E. Oseni, S. A. Phillips, A. A. Oyinloye, Disintegration of Price Ordered Probit Model: An Application to Prices of Cereal Crops in Nigeria, African Journal of Applied Statistics 7 (1) (2020) 781–804.
• S. Virolainen, A Mixture Autoregressive Model Based on Gaussian and Student-t-Soft Distributions, Studies in Nonlinear Dynamics & Econometrics 26 (4) (2022) 559–580.
• R. O. Olanrewaju, A. G. Waititu, L. A. Nafiu, Bull and Bear Dynamics of the Nigeria Stock Returns Transitory via Mingled Autoregressive Random Processes, Open Journal of Statistics 11 (2021) 870–885.
• R. O. Olanrewaju, A. G. Waititu, L. A. Nafiu, On the Estimation of k-Regimes Switching of Mixture Autoregressive Model via Weibull Distributional Random Noise, International Journal of Probability and Statistics 10 (1) (2021) 1–8.
• J. F. Ojo, R. O. Olanrewaju, On Mixture Auto-Regressive (MAR) Using Naira-Dollar Exchange Rates, Journal of Nigeria Association Mathematical Physics 38 (12) (2016) 155-165.
• R. O. Olanrewaju, S. A. Olanrewaju, An Alternative Mean Variance Portfolio Theoretical Framework: Nigeria Banks’ Market Shares Analysis, Global Journal of Business, Economics, and Management 11 (3) (2021) 220–234.
• R. O. Olanrewaju, On the Application of Generalized Beta-G Family of Distributions to Prices of Cereals, Journal of Mathematical Finance 11 (4) (2021) 670–685.
• R. O. Olanrewaju, M. A. Jallow, S. A. Olanrewaju, An Analysis of the Atlantic Ocean Random Cosine and Sine Alternate Wavy ARIMA Functions, International Journal of Intelligent Systems and Applications 14 (5) (2022) 22–34.
• J. F. Olanrewaju, R. O. Olanrewaju, S. A. Folorunso, Performance of all Nigeria Banks’ Shares using Student-t Mixture Autoregressive Model, Journal of Engineering and Applied 9 (1) (2017) 69–82.