An introduction to the imprecise Dirichlet model for multinomial data

An introduction to the imprecise Dirichlet model for multinomial data

Predictive inference under exchangeability - and the Imprecise Dirichlet Multinomial Model

Coherent reasoning under uncertainty can be represented in a very general manner by coherent sets of desirable gambles. In this framework, and for a given finite category set, coherent predictive inference under exchangeability can be represented using Bernstein coherent cones of multivariate polynomials on the simplex generated by this category set. This is a powerful generalisation of de Fine...

Learning from multinomial data: a nonparametric predictive alternative to the Imprecise Dirichlet Model

A new model for learning from multinomial data has recently been developed, giving predictive inferences in the form of lower and upper probabilities for a future observation. Apart from the past observations, no information on the sample space is assumed, so explicitly no assumptions are made on the number of possible categories. In this paper, we briefly present the general lower and upper pr...

The imprecise Dirichlet model

INTRODUCTION 2 The " Bag of marbles " example " Bag of marbles " problems (Walley, 1996) • " I have. .. a closed bag of coloured marbles. I intend to shake the bag, to reach into it and to draw out one marble. What is the probability that I will draw a red marble? " • " Suppose that we draw a sequence of marbles whose colours are (in order): blue, green, blue, blue, green, red.

An Extension to Imprecise Data Envelopment Analysis

The standard data envelopment analysis (DEA) method assumes that the values for inputs and outputs are exact. While DEA assumes exact data, the existing imprecise DEA (IDEA) assumes that the values for some inputs and outputs are only known to lie within bounded intervals, and other data are known only up to an order. In many real applications of DEA, there are cases in which some of the input ...