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Current Issue [Vol. 12, No. 03] [March 2026]
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| Paper Title | :: | Bayesian inference for data with Gaussian behavior with unknown mean and variance and its relationship with the Student 's t- test , application to annual maximum concentrations of ozone in Mexico City |
| Author Name | :: | M. Sc. Zenteno Jiménez José Roberto |
| Country | :: | Mexico |
| Page Number | :: | 01-13 |
A recap will be made on Bayesian inference models with unknown mean (mu) and variance ( 𝜎2). These models use conjugate prior distributions, commonly a Normal-Gamma or Inverse Normal-Gamma distribution, to jointly estimate the parameters and the model when the variance is unknown. A modification is made to find the same parameters jointly. This can be seen in the article "Fundamentals for Obtaining New Probability Distribution Functions with Bayesian Inference with Gaussian and Near Gaussian Behavior," which demonstrates the use of Bayesian inference with only the known variance and modifies the algorithm's input data to estimate the mean. As will be seen below, both methods yield the same result.
Keywords: Bayesian Inference, Normal pdf, t Student pdf, Likelihood, Inverse Normal-Gamma pdf
Keywords: Bayesian Inference, Normal pdf, t Student pdf, Likelihood, Inverse Normal-Gamma pdf
[1]. Davison, A.C., & Smith, R.L. (1990). Models for exceedances over high thresholds. Journal of the Royal Statistical Society: Series B (Methodological), 52 (3), 393–442. https://doi.org/10.1111/j.2517-6161.1990.tb01796.x
[2]. Gelman, A., Carlin, JB, Stern, HS, Dunson, DB, Vehtari , A., & Rubin, DB (2013).Bayesian Data Analysis (3rd ed.). CRC Press.
[3]. Hosking, J. R. M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society: Series B (Methodological), 52 (1), 105–124.
[4]. Li, Z. (2011). Applications of Gaussian Mixture Model to Weather Observations. IEEE Geoscience and Remote Sensing Letters , 8 (6), 1155–1159. https://doi.org/10.1109/LGRS.2011.2158183
[5]. Robert, CP (2007). The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation (2nd ed.). Springer.
[2]. Gelman, A., Carlin, JB, Stern, HS, Dunson, DB, Vehtari , A., & Rubin, DB (2013).Bayesian Data Analysis (3rd ed.). CRC Press.
[3]. Hosking, J. R. M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society: Series B (Methodological), 52 (1), 105–124.
[4]. Li, Z. (2011). Applications of Gaussian Mixture Model to Weather Observations. IEEE Geoscience and Remote Sensing Letters , 8 (6), 1155–1159. https://doi.org/10.1109/LGRS.2011.2158183
[5]. Robert, CP (2007). The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation (2nd ed.). Springer.
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| Paper Title | :: | Analysis of the solution of nth-order nonlinear mixed partial differential equations using the Adomian decomposition method and the ZJ transform |
| Author Name | :: | M. Sc. Zenteno Jiménez José Roberto |
| Country | :: | Mexico |
| Page Number | :: | 14-20 |
In this new article, the Adomian Decomposition Method is presented, along with the application of the ZJ transform together for the solution of nonlinear Mixed PDEs of order n with p+q =n, where n is a positive integer, with good effectiveness and potential of this hybrid approach to obtain approximate analytical solutions of nonlinear problems.
Keywords: ZJ Transform, Adomian Decomposition Method, Adomian Polynomials, Nonlinear Differential Equations, Series, Mixed Nonlinear Partial Differential Equations.
Keywords: ZJ Transform, Adomian Decomposition Method, Adomian Polynomials, Nonlinear Differential Equations, Series, Mixed Nonlinear Partial Differential Equations.
[1]. Adomian, G. (1988). Nonlinear stochastic operator equations. AcademicPress.
[2]. Adomian, G. (1994). Solving nonlinear partial differential equations with Adomian's decomposition method. Journal of Mathematics Analysis and Applications, 186 (3), 802-814.
[3]. Cherruault, Y. (1989). Convergence of Adomian's method. Kybernetes, 18 (2), 31-38.
[4]. Datta , Mousumi & Habiba , Umme & Hossain, (2020). Elzaki Substitution Method for Solving Nonlinear Partial Differential Equations with Mixed Partial Derivatives Using Adomain Polynomial. 10.12691/ijpdea-8-1-2.
[5]. Datta , Mousumi & Hossain, Md. Babul & Habiba, Umme. (2022). Elzaki Substitution Method with Adomian Polynomials for Solving Initial Value Problems of n th Order Non-linear Mixed Type Partial Differential Equations. 649-662.
[2]. Adomian, G. (1994). Solving nonlinear partial differential equations with Adomian's decomposition method. Journal of Mathematics Analysis and Applications, 186 (3), 802-814.
[3]. Cherruault, Y. (1989). Convergence of Adomian's method. Kybernetes, 18 (2), 31-38.
[4]. Datta , Mousumi & Habiba , Umme & Hossain, (2020). Elzaki Substitution Method for Solving Nonlinear Partial Differential Equations with Mixed Partial Derivatives Using Adomain Polynomial. 10.12691/ijpdea-8-1-2.
[5]. Datta , Mousumi & Hossain, Md. Babul & Habiba, Umme. (2022). Elzaki Substitution Method with Adomian Polynomials for Solving Initial Value Problems of n th Order Non-linear Mixed Type Partial Differential Equations. 649-662.