Carmelo Rodríguez

A system for relevance analysis of performance indicators in higher education using Bayesian networks

In this paper, we propose a methodology for relevance analysis of performance indicators in higher education based on the use of Bayesian networks. These graphical models provide, at first glance, a snapshot of the relevant relationships among the variables under consideration. We analyse the behaviour of the proposed methodology in a practical case, showing that it is a useful tool to help decision making when elaborating policies based on performance indicators. The methodology has been implemented in a software that interacts with the Elvira package for graphical models, and that is available to the administration board at the University of Almería (Spain) through a web interface. The software also implements a new method for constructing composite indicators by using a Bayesian network regression model.

SELECTIVE NAIVE BAYES FOR REGRESSION BASED ON MIXTURES OF TRUNCATED EXPONENTIALS

Naive Bayes models have been successfully used in classification problems where the class variable is discrete. These models have also been applied to regression or prediction problems, i.e. classification problems where the class variable is continuous, but usually under the assumption that the joint distribution of the feature variables and the class is multivariate Gaussian. In this paper we are interested in regression problems where some of the feature variables are discrete while the others are continuous. We propose a Naive Bayes predictor based on the approximation of the joint distribution by a Mixture of Truncated Exponentials (MTE). We have followed a filter-wrapper procedure for selecting the variables to be used in the construction of the model. This scheme is based on the mutual information between each of the candidate variables and the class. Since the mutual information can not be computed exactly for the MTE distribution, we introduce an unbiased estimator of it, based on Monte Carlo methods. We test the performance of the proposed model in artificial and real-world datasets.

Approximate factorisation of probability trees

Bayesian networks are efficient tools for probabilistic reasoning over large sets of variables, due to the fact that the joint distribution factorises according to the structure of the network, which captures conditional independence relations among the variables. Beyond conditional independence, the concept of asymmetric (or context specific) independence makes possible the definition of even more efficient reasoning schemes, based on the representation of probability functions through probability trees. In this paper we investigate how it is possible to achieve a finer factorisation by decomposing the original factors for which some conditions hold. We also introduce the concept of approximate factorisation and apply this methodology to the Lazy-Penniless propagation algorithm.

Ecological monitoring in a discrete-time prey–predator model

The paper is aimed at the methodological development of ecological monitoring in discrete-time dynamic models. In earlier papers, in the framework of continuous-time models, we have shown how a systems-theoretical methodology can be applied to the monitoring of the state process of a system of interacting populations, also estimating certain abiotic environmental changes such as pollution, climatic or seasonal changes. In practice, however, there may be good reasons to use discrete-time models. (For instance, there may be discrete cycles in the development of the populations, or observations can be made only at discrete time steps.) Therefore the present paper is devoted to the development of the monitoring methodology in the framework of discrete-time models of population ecology. By monitoring we mean that, observing only certain component(s) of the system, we reconstruct the whole state process. This may be necessary, e.g., when in a complex ecosystem the observation of the densities of certain species is impossible, or too expensive. For the first presentation of the offered methodology, we have chosen a discrete-time version of the classical Lotka-Volterra prey-predator model. This is a minimal but not trivial system where the methodology can still be presented. We also show how this methodology can be applied to estimate the effect of an abiotic environmental change, using a component of the population system as an environmental indicator. Although this approach is illustrated in a simplest possible case, it can be easily extended to larger ecosystems with several interacting populations and different types of abiotic environmental effects.

A-optimal designs for heteroscedastic multifactor regression models

Abstract This paper searches for A-optimal designs for Kronecker product and additive regression models when the errors are heteroscedastic. Sufficient conditions are given so that A-optimal designs for the multifactor models can be built from A-optimal designs for their sub-models with a single factor. The results of an efficiency study carried out to check the adequacy of the products of optimal designs for uni-factor marginal models when these are used to estimate different multi-factor models are also reported.

D -Optimal Designs for Regression Models with Length-Biased Poisson Response

This paper is concerned with the search for locally optimal designs when the observations of the response variable arise from a weighted distribution in an exponential family. The expression for the information matrices for length-biased distributions from an exponential family are obtained. Locally D-optimal designs are derived for regression models whose response variable follows a weighted Poisson distribution. Two link functions are considered for these models.

Some results on optimality in models with heteroscedastic errors from partial optimum designs

This paper studies optimum designs for linear models when the errors are heteroscedastic. Sufficient conditions are given in order to obtainD-, A- andE-optimum designs for a complete regression model from partial optimum designs for some sub-parameters. A result about optimality for a complete model from the optimality for the submodels is included.

Optimal designs with respect to Elfving's partial minimax criterion for heteroscedastic polynomial regression

In this paper we consider optimal desings relating to Elfvings partial minimax criterion for a polynomial regression model with a known heteroscedastic structure. Sufficient conditions are found under which, an optimal design for an individual parameter, is also minimax optimal for a subset of parameters that includes the former.

Game-theoretical model for marketing cooperative in fisheries

The classical game-theoretical models described the conflict in fisheries arising from harvesting a ‘common pool resource’ which without an efficient regulation leads to an overexploitation of a renewable but not unlimited resource, known as the ‘tragedy of the commons’. Unlike these studies, the present paper deals with a marketing cooperative of micro or small enterprises in fishing industry, formed to negotiate a contracted price with large buyers, sharing risk among members of the cooperative. In the paper a game-theoretical model for the behaviour in this cooperative is set up. By the time of the actual commercialization of the product, the market price may be higher than what the cooperative can guarantee for members, negotiated on beforehand. Therefore some “unfaithful” members may be interested in selling at least a part of their product on the free market, the cooperative, however, can punish them for this. This conflict is modelled with a multi-person normal form game. An evolutionary dynamics is proposed for the continuous change of the applied strategies, which in the long term leads to a particular Nash equilibrium, considered the solution of the game. This strategy dynamics is continuously influenced by an “exosystem” describing the dynamics of fishing, based on a classical fishing effort model. This approach focuses only on the conflict within the marketing cooperative, since it is supposed that the single enterprises fish from independent resources.

Observation and control in models of population genetics

Abstract Mathematical systems theory and optimal control have been mostly developed in the context of engineering. In this paper it is shown how these techniques can be applied in population genetics. Based on the classical Fishers selection model, first a very natural monitoring problem is studied: can the change of the genetic state of a population (described in terms of allele frequencies) be uniquely recovered from the observation of the frequencies of certain phenotypes? We give sufficient conditions for a positive answer to this question in a typical case of heterosis (when mixed genotypes are better than the pure ones, implying stable coexistence of all allele types). The second question is: How to effectively estimate the genetic composition of the population from phenotypic observation? The answer is observer design, which is carried out for two different dominance structures, determining the manifestation of the genetic state. In a model of artificial selection, we show how the population can be steered into equilibrium where maximal mean fitness is attained. Finally, the application of the above methodology is also extended to selection–mutation models, where both fitness parameters and mutation rates are controlled.