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3. Criterion to Determine the Sample Size in Stochastic Simulation Processes.

Author

Molina-Muñoz, Juan Daniel and Christen, José Andrés

Subjects
*STOCHASTIC processes, *MARKOV chain Monte Carlo, *SAMPLE size (Statistics), *MONTE Carlo method, *STOCHASTIC integrals
Abstract

Objective: To propose a criterion to determine the sample size in stochastic simulations of MC (Monte Carlo) and MCMC (Markov chain Monte Carlo), guaranteeing certain precision estimating parameters. It is intended that the accuracy is guaranteed in a dimensionless way. Materials and methods: This paper proposes a criterion is proposed that seeks to meet the stated objective. In addition, a methodology for its application. Results and discussion: The application of the methodology is presented in 3 different contexts: MC simulation in which the sample of interest presents moderate variability, MC simulation in which the sample of interest presents excessive variability, and MCMC simulation. In all cases, adequate estimates of the number of MC and MCMC runs are obtained from relatively small samples. Furthermore, the application of the methodology represents only a marginal additional computational cost. Conclusions: The criterion presented in this paper allows for determining the sample size in stochastic simulations, guaranteeing dimensionless precision in estimating parameters. [ABSTRACT FROM AUTHOR]

Published
2022
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4. Bayesian Evaluation for Uncertainty of Indirect Measurements in Comparison with GUM and Monte Carlo.

Author

Molina-Muñoz, Juan Daniel, Giraldo-Jaramillo, Luis Fernando, and Delgado-Trejos, Edilson

Subjects
*PROBABILITY density function, *HYDROSTATIC pressure, *MONTE Carlo method, *BAYESIAN field theory
Abstract

Objective: To propose a methodological procedure that serves as a guide for applying techniques in the measurement uncertainty evaluation, such as GUM, MMC, and Bayes; in addition, to develop an application in a nontrivial case study. Materials and methods: In this paper, a set of steps are proposed that allow validating the measurement uncertainty evaluation from techniques such as GUM, MMC, and Bayes; these were applied as a strategy to evaluate the uncertainty of an indirect measurement process that sought to determine the level of a fluid by measuring the hydrostatic pressure generated by it at rest on the bottom of a container. The results obtained with each technique were compared. Results and discussion: the use of the GUM was found to be valid for the case under study, and the results obtained by applying the Bayesian approach and the MC technique provided highly useful complementary information, such as the Probability Density Function (PDF) of the measurand, which enables a better description of the phenomenon. Likewise, the posterior PDF obtained with Bayes allowed us to approximate closer values around the true values of the measurand, and the ranges of the possible values were broader than those offered by the MMC and the GUM. Conclusions: In the context of the case under study, the Bayesian approach presents more realistic results than GUM and MMC; in addition to the conceptual advantage presented by Bayes, the possibility of updating the results of the uncertainty evaluation in the presence of new evidence. [ABSTRACT FROM AUTHOR]

Published
2022
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5. Análisis de distribuciones a priori de los parámetros de escala del modelo ZIP

Author

Molina Muñoz, Juan Daniel, Ramírez Guevara, Isabel Cristina, Molina Muñoz, Juan Daniel, and Ramírez Guevara, Isabel Cristina

Abstract

In this paper, it is proposed the evaluation of a set of prior distributions for the scale parameters of the Zero-Inflated Poisson Regression model (ZIP). Traditionally the inverse-gamma distribution is used as prior for scale parameters. Some studies have shown that when the values of the hyperparameters of this distribution are very small, inferences are not adequate. We focus on evaluating three prior distributions for modeling scale parameters: inverse-gamma; half Cauchy and scaled beta 2 (SBeta2). The half Cauchy has been used in the situation in question and has proven to work properly. The SBeta2 is a heavy-tailed distribution that has better performance at the origin and at the right tail. A simulation study is developed, with which we intend to analyze the effect of the priordistributionassignedtothescaleparametersontheshrinkageoftheposterior estimates of parameters. Besides, the presence of outliers is evaluated regarding the adjustment of the corresponden values. This is done for each of the three prior distributions considering. The analysis focuses shrinkage of the posterior estimates of parameters and adjustment of outliers because the main criticisms on the use of the inverse-gamma distribution concentrate on this two issues. Finally an application is presented with real data., En el presente artículo se plantea la evaluación de un conjunto de distribuciones a priori para los parámetros de escala del modelo de regresión Poisson inflado con ceros (conocido como modelo ZIP por sus siglas en inglés). Tradicionalmente se utiliza la distribución gamma-inversa como a priori para los parámetros de escala. Algunos estudios han mostrado que cuando los valores de los hiperparámetros de esta distribución son muy pequeños, las inferencias a posteriori no son adecuadas. El interés se centra en evaluar tres distribuciones a priori para los parámetros de escala del modelo: la gamma-inversa; la Half Cauchy que se ha usado para la situación planteada y que ha demostrado funcionar adecuadamente; y la beta 2 escalada (SBeta2) la cual es una distribución de colas pesadas que tiene un mejor comportamiento en el origen y en la cola derecha.Se desarrolla un estudio de simulación, con el que se pretende analizar el efecto de la distribución a priori asignada a los parámetros de escala sobre el encogimiento de los parámetros a posteriori del modelo; además se evalúa ante la presencia de observaciones atípicas cómo es el ajuste que el modelo realiza de estas, con cada una de las distribuciones a priori candidatas para los parámetros de escala. El análisis se centra en estas dos características (encogimiento de los parámetros a posteriori y ajuste de observaciones atípicas) pues son estas las principales críticas que diferentes autores plantean al uso de la distribución gamma-inversa como a priori para los parámetros de escala. Finalmente se presenta una aplicación con datos reales.

Published
2017

6. Análisis de distribuciones a priori de los parámetros de escala del modelo de regresión Poisson inflado con ceros

Author

Molina Muñoz, Juan Daniel and Ramírez Guevara, Isabel Crisitna

Subjects
Inverted-gamma distribution, Modelo ZIP, Distribución SBeta2, Half Cauchy distribution, 51 Matemáticas / Mathematics, Distribución gamma-inversa, Scales parameters, Inferencia Bayesiana, Bayesian inference, Distribución Half Cauchy, ZIP model, SBeta2 distribution, Parámetros de escala
Abstract

En el presente trabajo se plantea la evaluación de un conjunto de distribuciones a priori para los parámetros de escala del modelo de regresión Poisson inflado con ceros (conocido como modelo ZIP por sus siglas en inglés). Tradicionalmente se utiliza la distribución gamma-inversa como a priori para los parámetros de escala. Algunos estudios han mostrado que cuando los valores de los hiperparámetros de esta distribución son muy pequeños, las inferencias a posteriori no son adecuadas. El interés se centra en evaluar tres distribuciones a priori para los parámetros de escala del modelo: la gamma-inversa; la Half Cauchy que se ha usado para la situación planteada y que ha demostrado funcionar adecuadamente; y la beta 2 escalada (SBeta2) la cual es una distribución de colas pesadas que tiene un mejor comportamiento en el origen y en la cola derecha. Se desarrolla un estudio de simulación, con el que se pretende analizar el efecto de la distribución a priori asignada a los parámetros de escala sobre el encogimiento de los parámetros a posteriori del modelo; además se evalúa ante la presencia de observaciones atípicas cómo es el ajuste que el modelo realiza de estas, con cada una de las distribuciones a priori candidatas para los parámetros de escala. El análisis se centra en estas dos características (encogimiento de los parámetros a posteriori y ajuste de observaciones atípicas) pues son estas las principales críticas que diferentes autores plantean al uso de la distribución gamma-inversa como a priori para los parámetros de escala. Finalmente se presenta una aplicación con datos reales de cultivo de manzanas. Abstract: In this thesis, is propose the evaluation of a set of prior distributions for the scales parameters of the Zero-Inflated Poisson Regression model (ZIP). Traditionally the inverse-gamma distribution is used like prior for scales parameters. Some studies have shown that when the values of the hyperparameters of this distribution are very small, subsequent inferences are not adequate. Our focus is on evaluating three priors for model's scales parameters: inverted gamma; the Half Cauchy that has been used to the situation in question and that has proven to work properly; and scaled beta 2 (SBeta2) which is a heavy-tailed distribution that has a better performance at the origin and at the right tailed. A simulation study is developed, with which we intend to analyze the effect of the prior distribution assigned to the scales parameters on the shrinkage of the posterior model's parameters; also is evaluated with the presence of outliers how the model performs adjustment of these, for each of the candidates prior distributions for the parameters of scale. The analysis focuses on these two characteristics (shrinkage of the posterior parameters and adjustment of outliers) because these are the main criticisms different authors suggest to the use of inverse-gamma distribution like a priori for parameters of scale. Finally is presented an application with real data of growing apples. Maestría

Published
2016

8. Análisis de distribuciones a priori para los parámetros de escala del modelo ZIP.

Author

Molina Muñoz, Juan Daniel and Ramírez Guevara, Isabel Cristina

Abstract

Copyright of Comunicaciones en Estadística is the property of Universidad Santo Tomas and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Published
2017
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