0000000000013977
AUTHOR
Juan Carlos Cortés
A probabilistic estimation and prediction technique for dynamic continuous social science models: The evolution of the attitude of the Basque Country population towards ETA as a case study
In this paper, a computational technique to deal with uncertainty in dynamic continuous models in Social Sciences is presented.Considering data from surveys,the method consists of determining the probability distribution of the survey output and this allows to sample data and fit the model to the sampled data using a goodness-of-fit criterion based the χ2-test. Taking the fitted parameters that were not rejected by the χ2-test, substituting them into the model and computing their outputs, 95% confidence intervals in each time instant capturing the uncertainty of the survey data (probabilistic estimation) is built. Using the same set of obtained model parameters, a prediction over …
Introducing randomness in the analysis of chemical reactions: An analysis based on random differential equations and probability density functions
[EN] In this work we consider a particular randomized kinetic model for reaction-deactivation of hydrogen peroxide decomposition. We apply the Random Variable Transformation technique to obtain the first probability density function of the solution stochastic process under general conditions. From the rst probability density function, we can obtain fundamental statistical information, such as the mean and the variance of the solution, at every instant time. The transformation considered in the application of the Random Variable Transformation technique is not unique. Then, the first probability density function can take different expressions, although essentially equivalent in terms of comp…
A comprehensive probabilistic analysis of approximate SIR‐type epidemiological models via full randomized discrete‐time Markov chain formulation with applications
Spanish Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-P; Generalitat Valenciana, Grant/Award Number: APOSTD/2019/128; Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-P
Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach
Due to errors in measurements and inherent variability in the quantities of interest, models based on random differential equations give more realistic results than their deterministic counterpart. The generalized polynomial chaos (gPC) is a powerful technique used to approximate the solution of these equations when the random inputs follow standard probability distributions. But in many cases these random inputs do not have a standard probability distribution. In this paper, we present a step-by-step constructive methodology to implement directly a useful version of adaptive gPC for arbitrary distributions, extending the applicability of the gPC. The paper mainly focuses on the computation…
Modelling the dynamics of the students’ academic performance in the German region of the North Rhine-Westphalia: an epidemiological approach with uncertainty
Student academic underachievement is a concern of paramount importance in Europe, where around 15% of the students in the last high school courses do not achieve the minimum knowledge academic requirement. In this paper, we propose a model based on a system of differential equations to study the dynamics of the students academic performance in the German region of North Rhine-Westphalia. This approach is supported by the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. This model allows us to forecast the student academic performance by means of confidence intervals over the next few years.
First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities
[EN] Random initial value problems to non-homogeneous first-order linear differential equations with complex coefficients are probabilistically solved by computing the first probability density of the solution. For the sake of generality, coefficients and initial condition are assumed to be absolutely continuous complex random variables with an arbitrary joint probability density function. The probability of stability, as well as the density of the equilibrium point, are explicitly determined. The Random Variable Transformation technique is extensively utilized to conduct the overall analysis. Several examples are included to illustrate all the theoretical findings.
A Probabilistic Analysis to Quantify the Effect of March 11, 2004, Attacks in Madrid on the March 14 Elections in Spain: A Dynamic Modelling Approach
[EN] The bomb attacks in Madrid three days before the general elections of March 14, 2004, and their possible influence on the victory of PSOE (Spanish Workers Socialist Party), defeating PP (Popular Party), have been a matter of study from several points of view (i.e., sociological, political, or statistical). In this paper, we present a dynamic model based on a system of differential equations such that it, using data from Spanish CIS (National Center of Sociological Research), describes the evolution of voting intention of the Spanish people over time. Using this model, we conclude that the probability is very low that the PSOE would have won had the attack not happened.Moreover, after t…
Analysing the effect of public health campaigns on reducing excess weight: a modelling approach for the Spanish Autonomous Region of the Community of Valencia.
Abstract Excess weight is fast becoming a serious health concern in the developed and developing world. The concern of the public health sector has lead to the development of public health campaigns, focusing on two-fold goals: to inform the public as to the health risks inherent in being overweight, and the benefits of a change in nutritional behaviour. Recent studies indicate that the effects of the average public health campaign on the target community is around 5%. In this study we aim to quantify the effect of different public health campaigns on lifestyle behaviour in the target populations in order to bring about weightloss in a significant number of people over the next few years. T…
Probabilistic European Country Risk Score Forecasting Using a Diffusion Model
Over the last few years, global crisis has shaken confidence in most European economies. As a consequence, a lack of confidence has spread amongst European countries leading to Europe’s financial instability. Therefore, forecasting the next future of economic situation involves high levels of uncertainty. In this respect, it would be interesting to use tools which allow to predict the trends and evolution of each country’s confidence rating. The Country Risk Score (CRS) represents a good indicator to measure the current situation of a country regarding measures of economic, political and financial Risk in order to determine country Risk ratings. CRS is underscored by Euromoney Agency and is…
Non-parametric probabilistic forecasting of academic performance in Spanish high school using an epidemiological modelling approach
Academic underachievement is a concern of paramount importance in Europe, and particularly in Spain, where around of 30% of the students in the last two courses in high school do not achieve the minimum knowledge academic requirement. In order to analyse this problem, we propose a mathematical model via a system of ordinary differential equations to study the dynamics of the academic performance in Spain. Our approach is based on the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. Moreover, in order to consider the uncertainty in the estimation of model parameters, a bootstrapping approach is employed. This technique permits to for…
Solving continuous models with dependent uncertainty: a computational approach
This paper presents a computational study on a quasi-Galerkin projection-based method to deal with a class of systems of random ordinary differential equations (r.o.d.e.'s) which is assumed to depend on a finite number of random variables (r.v.'s). This class of systems of r.o.d.e.'s appears in different areas, particularly in epidemiology modelling. In contrast with the other available Galerkin-based techniques, such as the generalized Polynomial Chaos, the proposed method expands the solution directly in terms of the random inputs rather than auxiliary r.v.'s. Theoretically, Galerkin projection-based methods take advantage of orthogonality with the aim of simplifying the involved computat…
Modeling and predicting the Spanish Bachillerato academic results over the next few years using a random network model
[EN] Academic performance is a concern of paramount importance in Spain, where around of 30% of the students in the last two courses in high school, before to access to the labor market or to the university, do not achieve the minimum knowledge required according to the Spanish educational law in force. In order to analyze this problem, we propose a random network model to study the dynamics of the academic performance in Spain. Our approach is based on the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. Moreover, in order to consider the uncertainty in the estimation of model parameters, we perform a lot of simulations taking as t…
Forecasting Latin America’s Country Risk Scores by Means of a Dynamic Diffusion Model
Over the last years, worldwide financial market instability has shaken confidence in global economies. Global financial crisis and changes in sovereign debts ratings have affected the Latin American financial markets and their economies. However, Latin American s relative resilience to the more acute rise in risk seen in other regions like Europe during last years is offering investors new options for improving risk-return trade-offs. Therefore, forecasting the future of economic situation involves high levels of uncertainty. The Country Risk Score (CRS) represents a broadly used indicator to measure the current situation of a country regarding measures of economic, political, and financial…
Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator
[EN] In this work, we consider control problems represented by a linear differential equation assuming that all the coefficients are random variables and with an additive control that is a stochastic process. Specifically, we will work with controllable problems in which the initial condition and the final target are random variables. The probability density function of the solution and the control has been calculated. The theoretical results have been applied to study, from a probabilistic standpoint, a damped oscillator.
Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters
[EN] In spite of its simple formulation via a nonlinear differential equation, the Gompertz model has been widely applied to describe the dynamics of biological and biophysical parts of complex systems (growth of living organisms, number of bacteria, volume of infected cells, etc.). Its parameters or coefficients and the initial condition represent biological quantities (usually, rates and number of individual/particles, respectively) whose nature is random rather than deterministic. In this paper, we present a complete uncertainty quantification analysis of the randomized Gomperz model via the computation of an explicit expression to the first probability density function of its solution s…
Predicting mobile apps spread: An epidemiological random network modeling approach
[EN] The mobile applications business is a really big market, growing constantly. In app marketing, a key issue is to predict future app installations. The influence of the peers seems to be very relevant when downloading apps. Therefore, the study of the evolution of mobile apps spread may be approached using a proper network model that considers the influence of peers. Influence of peers and other social contagions have been successfully described using models of epidemiological type. Hence, in this paper we propose an epidemiological random network model with realistic parameters to predict the evolution of downloads of apps. With this model, we are able to predict the behavior of an app…
The dynamics over the next few years of the Spanish mobile telecommunications market share: a mathematical modelling approach
Taking into account available data from 2002 to 2009 about the market share percentages of the Spanish mobile telecommunications service providers, a dynamic diffusion model to study the evolution of the clients’ change between the different companies during the period 2010–2016 is proposed. The constructed model provides a tool for forecasting short-term trends about the customers’ preferences with respect to mobile network operators taking into account both, autonomous decisions due to direct marketing and advertising strategies, and also decisions adopted through interaction via social influence. The model can provide insights to companies for designing strategies in order to gain market…
Statistical Analysis of Biological Models with Uncertainty
In this contribution relevant biological models, based on random differential equations, are studied. For the sake of generality, we assume that the initial condition and the biological model parameters are dependent random variables with arbitrary probability distributions. We present a general methodology that enables us to provide a full probabilistic description of the solution stochastic process for each stochastic model. The statistical analysis is performed through the calculation of the first probability function by applying the random variable transformation technique. From the first probability density function, we can calculate any one-dimensional moment of the solution, includin…
Solving fully randomized first-order linear control systems: Application to study the dynamics of a damped oscillator with parametric noise under stochastic control
[EN] This paper is devoted to study random linear control systems where the initial condition, the final target, and the elements of matrices defining the coefficients are random variables, while the control is a stochastic process. The so-called Random Variable Transformation technique is adapted to obtain closed-form expressions of the probability density functions of the solution and of the control. The theoretical findings are applied to study the dynamics of a damped oscillator subject to parametric noise.