En esta nota presentamos un método general para calcular la edad de un sistema de soleras a lo largo del tiempo, que generaliza y unifica resultados obtenidos por Baker et al. (1952), que puede ser fácilmente programado para cualquier sistema de criaderas, de modo que sea sencillo simular el comportamiento del mismo según diversas condiciones iniciales y en función de ciertos parámetros que pueden ser regulados a priori como la frecuencia de las extracciones, el número de andanas y la proporción...
La idea de casi-admisibilidad, esto es, admisibilidad salvo conjuntos de medida nula, se extiende a situaciones más generales que las hasta ahora consideradas. Se estudia el problema de su existencia y la relación con una subclase de las reglas de Bayes; en particular su relación con la regla de Cromwell. La idea de soporte de una distribución se extiende a esta nueva situación y se relaciona con el concepto clásico de soporte y otros conceptos como el de regularidad.
La distribución de Behrens-Fisher generalizada se define como convolución de dos distribuciones t de Student y se relaciona con la distribución gamma invertida por medio de un teorema de representación como una mixtura, respecto del parámetro de escala, de distribuciones normales cuando la distribución de mezcla es la convolución de dos distribuciones gamma invertidas. Un resultado importante de este artículo establece que la distribución de Behrens-Fisher con grados de libertad impares es mixtura...
An elementary axiomatic foundation for decision theory is presented at a general enough level to cover standard applications of Bayesian methods. The intuitive meaning of both axioms and results is stressed. It is argued that statistical inference is a particular decision problem to which the axiomatic argument fully applies.
In this paper the theoretical and practical implications of dropping -from the basic Bayesian coherence principles- the assumption of comparability of every pair of acts is examined. The resulting theory is shown to be still perfectly coherent and has Bayesian theory as a particular case. In particular we question the need of weakening or ruling out some of the axioms that constitute the coherence principles; what are their practical implications; how this drive to the notion of partial information...
Hypothesis testing is a model selection problem for which the solution proposed by the two main statistical streams of thought, frequentists and Bayesians, substantially differ. One may think that this fact might be due to the prior chosen in the Bayesian analysis and that a convenient prior selection may reconcile both approaches. However, the Bayesian robustness viewpoint has shown that, in general, this is not so and hence a profound disagreement between both approaches exists. In this paper...
En este artículo se prueba que el sencillo método propuesto por De Groot para llegar a un consenso cuando los varios decisores tienen opiniones diferentes expresadas en términos de distribuciones de probabilidad es compatible con la regla de Bayes cuando se tiene en cuenta la información muestral. Se demuestra que si se calculan primero las distribuciones a posteriori y después se aplica el método de De Groot para alcanzar un consenso (cuando esto sea posible), es lo mismo que realizar primero el...
The problem of approximating mixtures of distributions has received considerable attention recently. In this paper we consider problems of estimating the mixing proportions of a finite mixture from a Bayesian perspective. The problems which arise from this methodology are basically approximations of finite measures of distributions. We propose two approximating methods and prove that under certain conditions both methods are asymptotically equivalent to a third method, which turns out to be simpler...
En este artículo se estudia, desde una perspectiva bayesiana, un proceso AR(1) con errores exponenciales, ARE(1): para ello se construye una nueva familia de distribuciones conjugadas, denotada por CDG, que permite construir una especie de filtro de Kalman para la estimación recursiva de los parámetros del modelo.
Testing that some regression coefficients are equal to zero is an important problem in many applications. Homoscedasticity is not necessarily a realistic condition in this setting and, as a consequence, no frequentist test there exist. Approximate tests have been proposed. In this paper a Bayesian analysis of this problem is carried out, from a default Bayesian model choice perspective. Explicit expressions for intrinsic priors are provided, and it is shown that the corresponding Bayes factor is...
In the Bayesian approach, the Bayes factor is the main tool for model selection and hypothesis testing. When prior information is weak, "default" or "automatic" priors, which are typicaIly improper, are commonly used but, unfortunately, the Bayes factor is defined up to a multiplicative constant. In this paper we revise some recent but already popular methodologies, intrinsic and lractional, to deal with improper priors in model selection and hypothesis testing. Special attention is paid to the...
In this paper, the problem of inference with misclassified multinomial data is addressed. Over the last years there has been a significant upsurge of interest in the development of Bayesian methods to make inferences with misclassified data. The wide range of applications for several sampling schemes and the importance of including initial information make Bayesian analysis an essential tool to be used in this context. A review of the existing literature followed by a methodological discussion is...
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