The elimination of nuisance parameters has classically been tackled by various ad hoc devices, and has led to a number of attemps to define partial sufficiency and ancillarity. The Bayesian approach is clearly defined. This paper examines some classical procedures in order to see when they can be given a Bayesian justification.
In the fuzzy setting, we define a collector of fuzzy information without probability, which allows us to consider the reliability of the observers. This problem is transformed in a system of functional equations. We give the general solution of that system for collectors which are compatible with composition law of the kind “inf”.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
We investigate a relation about subadditivity of functions. Based on subadditivity of functions, we consider some conditions for continuous -norms to act as the weakest -norm -based addition. This work extends some results of Marková-Stupňanová [15], Mesiar [18].
Estudiamos un problema abierto en los fundamentos de la estadística, el de modelizar imprecisión en preferencias y creencias dentro del marco de la utilidad esperada. Este problema fundamenta el análisis de sensibilidad en estadística bayesiana. Proporcionamos una solución en términos de utilidades esperadas dependientes del estado.
Partially efficiency balanced (PEB) designs with m efficiency classes have been defined by Puri and Nigam [15] as block designs which have simple analysis and, if properly used, allow the important contrasts to be estimated with desired efficiency. Such designs can be made available in varying replications and/or unequal block sizes. However, any block design is a PEB design with m efficiency classes for some m < v, where v is the number of treatments in the design. So the term "PEB" itself is...
This paper considers the problem of making statistical inferences about group judgements and group decisions using Qualitative Controlled Feedback, from the Bayesian point of view. The qualitative controlled feedback procedure was first introduced by Press (1978), for a single question of interest. The procedure in first reviewed here including the extension of the model to the multiple question case. We develop a model for responses of the panel on each stage. Many questions are treated simultaneously...
In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...