Juan M. Rodríguez-Díaz

• University of Salamanca

The objective of this work is to characterize the combustion process of ethanol flames under cellular conditions. Ethanol is considered an alternative fuel and can be used to replace fossil fuels. To investigate the behavior of ethanol as a fuel, some of its combustion properties are measured and characterized, such as laminar burning velocity and...

This study addresses the complex dynamics of alcohol elimination in the human body, very important in forensic and healthcare areas. Existing models often oversimplify with the assumption of linear elimination kinetics, limiting practical application. This study presents a novel non‐linear model for estimating blood alcohol concentration after mult...

Maxi-min efficiency criteria are a kind of multi-objective criteria, since they enable us to take into consideration several tasks expressed by different component-wise criteria. However, they are difficult to manage because of their lack of differentiability. As a consequence, maxi-min efficiency designs are frequently built through heuristic and...

In designed experiments quite often several variables are observed, which complicates the covariance structure of the data, especially when the objective is to observe the evolution of different characteristics along the time. Initial studies have been made assuming that the samples were taken on the same experimental unit, and thus some characteri...

Several studies have examined victim blaming in rape scenarios. However, there is limited research on the analysis of the perception of blame when two or more perpetrators are involved. The present article explores the perception of blame in cases involving rape based on the level of resistance shown by the victim and the presence of one or more pe...

The objective is to study the evolution of different characteristics of a population through time. These response variables may be related for each experimental unit, and in addition, the observations for each response may as well be correlated with time, producing a complex correlation structure. The number of responses that can be observed is usu...

Workers who are occupationally exposed to radioactive aerosols are usually subjected to periodic controls of internal contamination by performing bioassays (whole body or partial body monitoring and measurement of excreta samples). The intakes are also estimated by using Static Air Samples (SAS). These measurements are used to estimate the radioact...

For primary school students, the difficulty in solving mathematical problems is highly related to language capacity. A correct solution can only be achieved after being able to deal with different abstract concepts through several stages: comprehension, processing, symbolic representation and relation of the concepts with the right mathematical ope...

An accelerated life test of a product or material consists of the observation of its failure time when it is subjected to conditions that stress the usual ones. The purpose is to obtain the parameters of the distribution of the time-to-failure for usual conditions through the observed failure times. A widely used method to provoke an early failure...

Compositional data play an important role in many disciplines, when the interest is in studying not the total amount but the relative importance or frequency of the involved variables. Due to these proportion/sum constraints, the data belong to a restricted space, the simplex. A special algebraic structure is needed to deal with these kind of data....

In many scientific disciplines, experiments are conducted in order to get information about the model or about different characteristics of the data. Quite often more than one variable is measured, giving rise to multiresponse models. For these models it is usual to assume correlation between different-type observations taken on the same point, and...

After incorporation of radioactive substances, workers are routinely checked by bioassays (isotopic activity excreted via urine, measurements of radionuclides retained in the whole body or in the lungs, etc.). From the results, the isotopic activity incorporated by the worker is inferred, as well as the values of other parameters related to the met...

The Michaelis-Menten (MM)model is extensively used in biochemistry to describe reaction kinetics. However, deviations from MM kinetics can occur, usually due to an inhibition effect on the amount of substrate. Two different models, describing the kinetic reaction when this type of inhibition occurs, are introduced. Optimal experimental designs meth...

In the optimal design of experiments setup different optimality criteria can be considered depending on the objectives of the practitioner. One of the most used is -optimality, which for a given model looks for the design that minimizes the variance of the linear combination of the parameters’ estimators given by vector . -optimal designs are neede...

Many industrial experiments involve random factors. The random blocks model defines a covariance structure in the data, thus generalized least square estimators of the parameters are used, and their covariance matrix is usually computed using the inverse of the generalized least square estimators information matrix. Many optimality criteria are bas...

Many scientific processes, specially in pharmacokinetics (PK) and pharmacodynamics (PD) studies, are defined by a system of ordinary differential equations (ODE). If there are unknown parameters that need to be estimated, the optimal experimental design approach offers quality estimators for the different objectives of the practitioners. When compu...

In the context of nonlinear models, the analytical expression of the Fisher information matrix is essential to compute optimum designs. The Fisher information matrix of the random effects logistic regression model is proved to be equivalent to the information matrix of the linearized model, which depends on some integrals. Some algebraic approximat...

One of the initial tasks in a spatio-temporal context is the assessment of whether spatial or temporal dependence is present or not and if present at what intensity. This chapter addresses these questions and possible improvements over random sampling in coping with them. It concentrates on the question of how to optimally select coordinates/predic...

The aim of this paper is to provide guidelines for the statistically efficient estimation of parameters of a modified Arrhenius model for chemical kinetics. A modified Arrhenius model is used for instance by modeling a flux of methane in troposphere or by chemical kinetics for reactions at membranes. D-optimal and filling designs for the Generalize...

The paper is concerned with further developing a spatial sampling method based upon optimal design concepts motivated by an application in the area of biodiversity monitoring. Statistical techniques for detecting spatial patterns in the distribution of species richness now have some long tradition in this field, specifically the use of correlograms...

D s- and KL-optimum designs are computed for discriminating between univariate logistic regression models with or without random effects. Both these competing optimum designs are constructed numerically. The main problem in finding them is the computation of some integrals at each step of the numerical procedure. In order to improve the convergence...

The model that describes the retention in lungs of radioisotope particles is studied in this paper, considering the situation of an accident in facilities that handle radioactive materials. Optimal times to make the bioassays are computed for D- and c-optimality, and efficiencies for the computed designs are provided and compared. Moreover, the tes...

The aim of this article is to find optimal or nearly optimal designs for experiments to detect spatial dependence that might be in the data. The questions to be answered are: how to optimally select predictor values to detect the spatial structure (if it is existent) and how to avoid to spuriously detect spatial dependence if there is no such struc...

The Arrhenius equation is widely used to describe the relationship between the rate of a chemical reaction and the temperature. However, in some cases more precision is needed and a Modified Arrhenius (MA) model, allowing the linear parameter to be temperature-dependent, appears as the correct alternative to the plain model. Optimal designs for the...

In this paper, we investigate the effect of employing a parametrized covariance function in a regression experiment on corresponding optimum designs. We demonstrate these effects in the framework of a real example for measuring the lung’s retention of radioactive particles. Also, two different covariance functions are considered, and it is shown th...

The research on optimal experimental designs for nonlinear regression models is of great interest because these models are used to characterize chemical, biological or agricultural phenomena. Much of them involve an exponential decay. In this paper, locally D- and c-optimal designs are derived analytically for Poisson and negative binomial regressi...

Bioassays can be used to estimate the initial intake I for the case of an acute intake exposure for an individual worker. To evaluate the effective dose, apart from I, we need to know other parameters such as activity median aerodynamic diameter (AMAD) or the fraction absorption ( f1) in the blood from the GI tract, but in an accident situation the...

The volume contains the proceedings of the 8th Workshop on Model-Oriented Design and Analysis. This book offers leading and pioneering work on optimal experimental designs, both from a mathematical/statistical point of view and with regard to real applications. Scientists from all over the world, from Eastern and Western Europe, the USA, Latin-Amer...

A partir de nuevos modelos de retención de partículas radiactivas en el cuerpo humano se calcularán diseños óptimos para la estimación de los parámetros principales, así como contrastes sobre los mismos. d2

The flow of internally deposited radioisotope particles inside the body of people exposed to inhalation, ingestion, injection or other ways is usually evaluated using compartmental models (see Sanchez & Lopez-Fidalgo, (2003, and Lopez-Fidalgo & Sanchez, 2005). The International Commission on Radiological Protection (ICRP, 1994) describes the model...

Elfving’s method is a well known graphical procedure for obtaining c-optimal designs. Although the method is valid for any dimension it is rarely used for more than two parameters. Its usefulness seems to be constrained by the difficulty on the construction of the Elfving set. In this paper a computational procedure for finding c-optimal designs us...

A new biparametric class of criteria for Optimal Experimental Design generalizing the families of φp and Characteristic Criteria is presented. Some properties of the Characteristic Criteria are provided: in particular, differentiability, monotonicity and convexity. A statistical interpretation is also offered. Optimal designs with respect to Charac...

Using the characteristic polynomial coefficients of the inverse of the information matrix, design criteria can be defined between A- and D-optimality (López-Fidalgo and Rodríguez-Díaz, 1998). With a slight modification of the classical algorithms, the gradient expression allows us to find some optimal characteristic designs for polynomial regressio...

En Diseño Óptimo de Experimentos existen diferentes criterios de optimización. Este artículo se ocupa esencialmente de la creación de una nueva clase de criterios, llamados Criterios Característicos, que se basan en los coeficientes del polinomio característico de la matriz de covarianzas. Dicha familia engloba dos de los criterios mas utilizados,...

Many optimality criteria have been used in the literature of experimental design. Two of the most common are A-optimality and D-optimality. They are the first and the last coefficients of the characteristic polynomial of the inverse information matrix. In this paper, criteria from the remaining coefficients are considered, and some properties are s...

This paper considers maximum likelihood estimators for generalized linear models with Poisson responses. An application of this paper is to calibrate and test equipment of measurements of radioactive particles with Poisson response. The method is applied to a numerical example that is solved using a MATHEMATICA program.

1 Historical notes From the middle of the 19th century on several equations relating the rate constant k of a chemical reaction to the temperature T have appeared in literature. All of them were developed experimentally and the most popular ones try to fit linearly ln(k) against T , 1/T or ln(T). The fact that this different plots gave reasonably g...

Tesis doctoral, volumen 67 de la Colección Vítor El trabajo se sitíua en la teoría del Diseño Óptimo de Experimentos. Esta disciplina trata de realizar la mejor elección posible de los observables en los que se basará un experimento para obtener información acerca de un objeto. The present work in set in the Optimal Experimental Designs theory. Thi...