Research Article
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Year 2023, , 57 - 72, 31.12.2023

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

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

Abstract

Project Number

None

References

  • 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.

On Finite and Non-Finite Bayesian Mixture Models

Year 2023, , 57 - 72, 31.12.2023

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

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

Abstract

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.

Keywords

Bayesian paradigm expectation-maximization MCMC proportional allocation metropolis–hastings

Project Number

None

References

  • 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.
There are 20 citations in total.

Details

Primary Language English
Subjects Statistical Analysis, Statistical Theory, Theory of Sampling
Journal Section Research Article
Authors

Rasaki Olawale Olanrewaju 0000-0002-2575-9254

Sodiq Adejare Olanrewaju 0009-0006-4494-2421

Adedeji Adigun Oyınloye 0009-0007-4551-5170

Wasiu Adesoji Adepoju 0009-0002-3852-7361

Project Number None
Early Pub Date December 30, 2023
Publication Date December 31, 2023
Submission Date September 21, 2023
Published in Issue Year 2023

Cite

APA Olanrewaju, R. O., Olanrewaju, S. A., Oyınloye, A. A., Adepoju, W. A. (2023). On Finite and Non-Finite Bayesian Mixture Models. Journal of New Theory(45), 57-72. https://doi.org/10.53570/jnt.1358754
AMA Olanrewaju RO, Olanrewaju SA, Oyınloye AA, Adepoju WA. On Finite and Non-Finite Bayesian Mixture Models. JNT. December 2023;(45):57-72. doi:10.53570/jnt.1358754
Chicago Olanrewaju, Rasaki Olawale, Sodiq Adejare Olanrewaju, Adedeji Adigun Oyınloye, and Wasiu Adesoji Adepoju. “On Finite and Non-Finite Bayesian Mixture Models”. Journal of New Theory, no. 45 (December 2023): 57-72. https://doi.org/10.53570/jnt.1358754.
EndNote Olanrewaju RO, Olanrewaju SA, Oyınloye AA, Adepoju WA (December 1, 2023) On Finite and Non-Finite Bayesian Mixture Models. Journal of New Theory 45 57–72.
IEEE R. O. Olanrewaju, S. A. Olanrewaju, A. A. Oyınloye, and W. A. Adepoju, “On Finite and Non-Finite Bayesian Mixture Models”, JNT, no. 45, pp. 57–72, December 2023, doi: 10.53570/jnt.1358754.
ISNAD Olanrewaju, Rasaki Olawale et al. “On Finite and Non-Finite Bayesian Mixture Models”. Journal of New Theory 45 (December 2023), 57-72. https://doi.org/10.53570/jnt.1358754.
JAMA Olanrewaju RO, Olanrewaju SA, Oyınloye AA, Adepoju WA. On Finite and Non-Finite Bayesian Mixture Models. JNT. 2023;:57–72.
MLA Olanrewaju, Rasaki Olawale et al. “On Finite and Non-Finite Bayesian Mixture Models”. Journal of New Theory, no. 45, 2023, pp. 57-72, doi:10.53570/jnt.1358754.
Vancouver Olanrewaju RO, Olanrewaju SA, Oyınloye AA, Adepoju WA. On Finite and Non-Finite Bayesian Mixture Models. JNT. 2023(45):57-72.


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