Mathematical Models In Social Sciences Research Articles

Bayesvl: an R package for user-friendly Bayesian regression modelling

Compared with traditional statistics, only a few social scientists employ Bayesian analyses. The existing software programs for implementing Bayesian analyses such as OpenBUGS, WinBUGS, JAGS, and rstanarm can be daunting given that their complex computer codes involve a steep learning curve. In contrast, this paper introduces a new open software for implementing Bayesian network modelling and analysis: the bayesvl R package. The package aims at providing an intuitive gateway for beginners of Bayesian statistics to construct and analyse mathematical models in social sciences. To achieve this aim, the bayesvl package integrates three core functions seamlessly: (i) designing Bayesian network models using directed acyclic graphs (DAGs) of bnlearn, (ii) generating attractive visualization of ggplot2, and (iii) simulating data and computing posterior distribution using the Markov chain Monte Carlo (MCMC) algorithms of rstan and rethinking. A case example illustrates how the bayesvl package helps leverage users’ intuition in creating and evaluating mathematical models of their social scientific problems while minimizing the daunting aspect of writing complex computer codes.

¿Sistemas dinámicos en ciencias sociales?

Dynamical systems are a specific kind of complex systems, namely: self-reference systems, autopoietic systems, disipative systems, adaptative complex systems, etc. In the context of mathematical modelling in social sciences, this article introduces a basic definition of dynamical systems and its main concepts. A background about key applications in social sciences is shown, and a specific case of the artisanal fisheries in which dynamical systems are certainly useful. Finally, some of the current research challenges of dynamical systems in social sciences are discussed.

¿Sistemas dinámicos en ciencias sociales?

Dynamical systems are a specific kind of complex systems, namely: self-reference systems, autopoietic systems, disipative systems, adaptative complex systems, etc. In the context of mathematical modelling in social sciences, this article introduces a basic definition of dynamical systems and its main concepts. A background about key applications in social sciences is shown, and a specific case of the artisanal fisheries in which dynamical systems are certainly useful. Finally, some of the current research challenges of dynamical systems in social sciences are discussed.

Testability and meaning of mathematical models in social sciences

The terms “model,” “theory,” and “law” are being used with a variety of meanings in practice as well as in theory. Depending on the definition of the contents of these terms they have to satisfy different requirements. The author focuses his attention on mathematical models and their use in Operations Research and Management Science. After pointing out the difference between “theories,” “laws,” and “models,” criteria for the quality of models are defined and problems of model building discussed. It is considered particularly important that factual models—as opposed to formal models—are designed in such a way that they are testable. A factual model which is not testable can neither be confirmed nor falsified and can therefore never claim to be factually true. Problems and ways of building and testing models in the social sciences are then illustrated by considering approaches to model human decision making in fuzzy environments.