Catálogo de publicaciones - libros

In the first years of the 19th century Gauss and Legendre independently invented least-squares estimation in order to estimate planetary orbits. Based on complete confidence in Newtonian dynamics, they overcame the challenge of noisy and inconsistent astronomic observations [4]. Least-squares estimation is the paradigm of optimal estimation and system identification.

In the Theory of Evidence it is assumed that there is an exact amount of information that makes the evidences of the focal sets (i.e. their masses) sum to 1. But it is not difficult to think of situations where this is not the case and the mass assignments sum less or more than 1.

The aim of this paper is to define the product operation on the family of IF-events and the notion of joint IF-observable. We formulate the version of conditional IFprobability on IF-events, too.

One of the important problems of IF-sets theory ([1])is the creation of the probability theory on the family ℱ of all IF-events. We present here two ways how to solve this problem. The first one is an embedding of ℱ to a convenient MV-algebra. The second is a substituting the notions of an MV-algebra by a more general notions of so-called L-lattice.

Several problems are connected, in the literature, to causality: prediction, explanation, action, planning and natural language processing… In a recent paper, Halpern and Pearl introduced an elegant definition of causal (partial) explanation in the structural-model approach, which is based on their notions of weak and actual cause [5]. Our purpose in this paper is to partially modify this definition, rather than to use a probability (quantitative modelisation) we suggest to affect a degree of possibility (a more qualitative modelisation) which is nearer to the human way of reasoning, by using the possibilistic logic. A stratification of all possible partial explanations will be given to the agent for a given request, the explanations in the first strate are more possible than those belonging to the other strates. We compute the complexity of this strafication.

A Markov chain model in generalised settings of interval probabilities is presented. Instead of the usual assumption of constant transitional probability matrix, we assume that at each step a transitional matrix is chosen from a set of matrices that corresponds to a structure of an interval probability matrix. We set up the model and show how to obtain intervals corresponding to sets of distributions at consecutive steps. We also state the problem of invariant distributions and examine possible approaches to their estimation in terms of convex sets of distributions, and in a special case in terms of interval probabilities.

In this paper, the mathematical apparatus of significance testing is used to study the relationship between the truthness of a complex statistical hypothesis, , and those of its constituents, , = 1…, within the independent setup and under the principle of compositionality.

Vague or imprecise concepts are fundamental to natural language. Human beings are constantly using imprecise language to communicate each other. We usually say ‘John is tall and strong’ but not ‘John is exactly 1.85 meters in height and he can lift 100kg weights’. Humans have a remarkable capability to perform a wide variety of physical and mental tasks without any measurements. This capability partitionsof objects into granules, with a granule being a clump of objects drawn together by indistinguishability, similarity, proximity or function [8]. We will focus on developing an understanding of how we can use vague concepts to convey information and meaning as part of a general strategy for practical reasoning and decision making.

We deal with DNA combinatorial code constructions, as found in the literature, taking the point of view of possibilistic information theory and possibilistic coding theory. The possibilistic framework allows one to tackle an intriguing informationtheoretic question: what is channel noise in molecular computation? We examine in detail two representative DNA string distances used for DNA code constructions and point out the merits of the first and the demerits of the second. The two string distances are based on the reverse Hamming distance as required to account for hybridisation of DNA strings.

Motivated by a preliminary series of expert interviews we consider a possibility measure for the subjective uncertainty on climate model parameter values. We consider 5 key uncertain parameters in the climate model CLIMBER-2 that represents a system of thousands of ordinary differential equations. We derive an emulator for the model and determine the model’s mapping of parameter uncertainty on output uncertainty for climate sensitivity. Climate sensitivity represents a central climate system characteristic important for policy advice, however subject to huge uncertainty. While the ratio of output/input uncertainty induced by a single-parameter perturbation resembles the respective ratio when using a standard probability measure, we find the ratio qualitatively larger in the 5-dimensional situation. We explain this curse of dimension effect by a Gaussian analogue toy system.