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TamaƱo de muestra necesario para que la estimaciĆ³n de intervalos Frecuentista y Bayesiano coincidan dentro de un error predeterminado
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Abstract
Por lo general, se acepta que a medida que aumenta el tamaƱo de un conjunto
de datos, el efecto de la distribuciĆ³n previa en el intervalo de credibilidad Bayesiano
disminuye y estos intervalos se acercan a los correspondientes intervalos de confianza
Frecuentista. En esta tesis, se estudia la pregunta de cuƔn grande es el tamaƱo de
muestra que se necesita para tener cierta certeza de que los intervalos de confianza y
los intervalos de credibilidad sean similares dentro de un error prescrito. Esto, con el
propĆ³sito de afirmar cual es el tamaƱo de muestra necesario para que los dos enfoques
de la estadĆstica coincidan en la estimaciĆ³n por intervalos. Hay respuestas explĆcitas
para varios casos estĆ”ndar como la estimaciĆ³n de la media y la desviaciĆ³n estĆ”ndar
de una distribuciĆ³n Normal, la probabilidad de Ć©xito en los ensayos de Bernoulli y las
tasas de la distribuciĆ³n de Poisson, GeomĆ©trica y Exponencial. Para este trabajo se
desarrollĆ³ una calculadora en lĆnea que estĆ” disponible en https://server-deiver
.shinyapps.io/sample_size_frequentist_and_bayesian/. Ćsta calcula intervalos
de confianza, intervalos de credibilidad y el tamaƱo de muestra necesario para que
estos intervalos sean iguales dentro de un error predeterminado. La calculadora no
requiere que el usuario tenga algĆŗn conocimiento de R.
It is generally accepted that as the size of a dataset increases, the in uence of the prior distribution on the Bayesian credible intervals decreases and these intervals approach the corresponding Frequentist confidence intervals. In this thesis, me study how large the sample size needs to be to have some certainty that the confidence intervals and credible intervals are within a prescribed error. There are explicit results for several standard cases such as estimation of the mean and the standard deviation from a Normal distribution, the success probability in Bernoulli trials, and the rates of Poisson, Geometric, and Exponential distributions. For the purpose of this work, me developed a calculator that is available online at https://serverdeiver .shinyapps.io/sample_size_frequentist_and_bayesian/. It calculates confidence intervals, credible intervals and the necessary sample size so that these intervals are equal within a predetermined error. The calculator does not require the user to have any knowledge of R.
It is generally accepted that as the size of a dataset increases, the in uence of the prior distribution on the Bayesian credible intervals decreases and these intervals approach the corresponding Frequentist confidence intervals. In this thesis, me study how large the sample size needs to be to have some certainty that the confidence intervals and credible intervals are within a prescribed error. There are explicit results for several standard cases such as estimation of the mean and the standard deviation from a Normal distribution, the success probability in Bernoulli trials, and the rates of Poisson, Geometric, and Exponential distributions. For the purpose of this work, me developed a calculator that is available online at https://serverdeiver .shinyapps.io/sample_size_frequentist_and_bayesian/. It calculates confidence intervals, credible intervals and the necessary sample size so that these intervals are equal within a predetermined error. The calculator does not require the user to have any knowledge of R.
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2018-11-30
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Keywords
intervalo de credibilidad Bayesiano, intervalos de confianza Frecuentista, tamaƱo de muestra, Bayesian intervals, Frequentist intervals