Bayesian Analysis for a Fractional Population Growth Model

Ariza-Hernandez, Francisco J.; Sanchez-Ortiz, Jorge; Arciga-Alejandre, Martin P.; Vivas-Cruz, Luis X.

doi:10.1155/2017/9654506

Cited by 8 publications

(4 citation statements)

References 27 publications

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“…Other researchers who compared the Bayesian and Maximum Likelihood estimates include Simbolon et al [17], who compared the Bayesian and maximum likelihood method of estimating the shape parameter of the Kumaraswamy distribution, Singh et al [4], who considered the classical and Bayesian estimation of the parameter and reliability characteristic of extension of the exponential distribution, Kim and Han [3] who considered the maximum likelihood estimation and Bayes estimation of the parameters of the Generalized Exponential Distribution based on progressive first failure censored samples and Ariza-Hernandez et al [18], using different loss functions, different criteria for comparison and arriving at different conclusions under the various prevailing circumstances.…”

Section: Literature Reviewmentioning

confidence: 99%

Bayesian Estimation of the Parameters of the Odd Generalized Exponentiated - Inverse Exponential Distribution (OGE -IED)

Gayus

Doguwa

2022

AJPAS

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The Odd Generalized Exponentiated-Inverse Exponential Distribution, a three parameter distribution, is a hybrid of the Generalized Exponential distribution. Each of the parameters were assigned a gamma prior independently resulting to a posterior distribution that is mathematically intractable impossible to obtain marginal posterior distribution for two of the parameters, and a likelihood function that is not known traditionally to R or other statistical software. Resort was made to STAN in order to obtain Bayesian estimates - leveraging on STAN’s provision for user-defined distribution functions. Two datasets were used; remission times (in months) of bladder cancer patients and COVID-19 Survey data in Andalusia, Spain. In the end, the Maximum Likelihood estimates maximized the likelihood more than the Bayesian estimates - though with a slight margin of not more than 0.77. On the other hand, the Bayesian estimates proved to be more stable yielding very negligible standard errors compared to the Maximum Likelihood estimates.

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Section: Literature Reviewmentioning

confidence: 99%

Bayesian Estimation of the Parameters of the Odd Generalized Exponentiated - Inverse Exponential Distribution (OGE -IED)

Gayus

Doguwa

2022

AJPAS

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“…Under certain conditions, these models can more closely describe phenomena whose dynamics in time is anomalous [4]. For example, the population growth model is one of the most popular models to describe the population growth in the time; however, when the growth is faster or slower than exponential, then its fractional version of this model has a better fit (see Ariza et al [5]).…”

Section: Introductionmentioning

confidence: 99%

“…There are few works related to the estimation of the order of the derivative in dynamic systems.To mention a few, Mitkowski and Obraczka [6] performed deterministic estimation of parameters in a population model of fractional order, and afterwards Obraczka and Mitkowski [7] performed parameter identification in a partial differential equation of fractional order. More recently, Ariza et al [5] made an estimate of the parameters, from the Bayesian viewpoint, of a fractional population growth model. However, there is no evidence of the estimation of the order of the derivative of a fractional logistic model.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Derivative Order Estimation for a Fractional Logistic Model

et al. 2020

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In this paper, we consider the inverse problem of derivative order estimation in a fractional logistic model. In order to solve the direct problem, we use the Grünwald-Letnikov fractional derivative, then the inverse problem is tackled within a Bayesian perspective. To construct the likelihood function, we propose an explicit numerical scheme based on the truncated series of the derivative definition. By MCMC samples of the marginal posterior distributions, we estimate the order of the derivative and the growth rate parameter in the dynamic model, as well as the noise in the observations. To evaluate the methodology, a simulation was performed using synthetic data, where the bias and mean square error are calculated, the results give evidence of the effectiveness for the method and the suitable performance of the proposed model. Moreover, an example with real data is presented as evidence of the relevance of using a fractional model.

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“…Awotunde et al (2016) show there is deviation between real data obtained and the model using Darcy s law from Darcy (1856), which is why new models must be implemented. Ariza-Hernandez et al (2017) utilize a Bayesian approach to solve the inverse problem of a fractional population growth model. They employ the Plummer (2012) JAGS (Just Another Gibbs Sampler) software to generate Markov Chain Monte Carlo (MCMC) samples, which for more information on MCMC, see Gilks et al (1996).…”

Section: Introductionmentioning

confidence: 99%

A Bayesian Estimation for the Fractional Order of the Differential Equation that Models Transport in Unconventional Hydrocarbon Reservoirs

Whitlinger,

Boone,

Ghanam

2017

Preprint

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The extraction of natural gas from the earth has been shown to be governed by differential equations concerning flow through a porous material. Recently, models such as fractional differential equations have been developed to model this phenomenon. One key issue with these models is estimating the fraction of the differential equation. Traditional methods such as maximum likelihood, least squares, and even method of moments are not available to estimate this parameter as traditional calculus methods do not apply. We develop a Bayesian approach to estimate the fraction of the order of the differential equation that models transport in unconventional hydrocarbon reservoirs. In this paper, we use this approach to adequately quantify the uncertainties associated with the error and predictions. A simulation study is presented as well to assess the utility of the modeling approach.

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Bayesian Analysis for a Fractional Population Growth Model

Cited by 8 publications

References 27 publications

Bayesian Estimation of the Parameters of the Odd Generalized Exponentiated - Inverse Exponential Distribution (OGE -IED)

Bayesian Estimation of the Parameters of the Odd Generalized Exponentiated - Inverse Exponential Distribution (OGE -IED)

Bayesian Derivative Order Estimation for a Fractional Logistic Model

A Bayesian Estimation for the Fractional Order of the Differential Equation that Models Transport in Unconventional Hydrocarbon Reservoirs

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