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Using Bayesian dynamical systems, model averaging and neural networks to determine interactions between socio-economic indicators
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Univ Leeds, Sch Math, Leeds, W Yorkshire, England.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2018 (English)In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 13, no 5, article id e0196355Article in journal (Refereed) Published
Abstract [en]

Social and economic systems produce complex and nonlinear relationships in the indicator variables that describe them. We present a Bayesian methodology to analyze the dynamical relationships between indicator variables by identifying the nonlinear functions that best describe their interactions. We search for the 'best' explicit functions by fitting data using Bayesian linear regression on a vast number of models and then comparing their Bayes factors. The model with the highest Bayes factor, having the best trade-off between explanatory power and interpretability, is chosen as the 'best' model. To be able to compare a vast number of models, we use conjugate priors, resulting in fast computation times. We check the robustness of our approach by comparison with more prediction oriented approaches such as model averaging and neural networks. Our modelling approach is illustrated using the classical example of how democracy and economic growth relate to each other. We find that the best dynamical model for democracy suggests that long term democratic increase is only possible if the economic situation gets better. No robust model explaining economic development using these two variables was found.

Place, publisher, year, edition, pages
PUBLIC LIBRARY SCIENCE , 2018. Vol. 13, no 5, article id e0196355
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-359665DOI: 10.1371/journal.pone.0196355ISI: 000431757400027PubMedID: 29742126OAI: oai:DiVA.org:uu-359665DiVA, id: diva2:1245542
Available from: 2018-09-05 Created: 2018-09-05 Last updated: 2018-10-30Bibliographically approved
In thesis
1. Gaussian process models of social change
Open this publication in new window or tab >>Gaussian process models of social change
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Social systems produce complex and nonlinear relationships in the indicator variables that describe them. Traditional statistical regression techniques are commonly used in the social sciences to study such systems. These techniques, such as standard linear regression, can prevent the discovery of the complex underlying mechanisms and rely too much on the expertise and prior beliefs of the data analyst. In this thesis, we present two methodologies that are designed to allow the data to inform us about these complex relations and provide us with interpretable models of the dynamics.

The first methodology is a Bayesian approach to analysing the relationship between indicator variables by finding the parametric functions that best describe their interactions. The parametric functions with the highest model evidence are found by fitting a large number of potential models to the data using Bayesian linear regression and comparing their respective model evidence. The methodology is computationally fast due to the use of conjugate priors, and this allows for inference on large sets of models. The second methodology is based on a Gaussian processes framework and is designed to overcome the limitations of the first modelling approach. This approach balances the interpretability of more traditional parametric statistical methods with the predictability and flexibility of non-parametric Gaussian processes.

This thesis contains four papers where we apply the methodologies to both real-life problems in the social sciences as well as on synthetic data sets. In paper I, the first methodology (Bayesian linear regression) is applied to the classic problem of how democracy and economic development interact. In paper II and IV, we apply the second methodology (Gaussian processes) to study changes in the political landscape and demographic shifts in Sweden in the last decades. In paper III, we apply the second methodology on a synthetic data set to perform parameter estimation on complex dynamical systems.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2018. p. 51
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 111
Keywords
Gaussian processes, Bayesian statistics, Dynamical systems, Social sciences
National Category
Mathematics
Research subject
Applied Mathematics and Statistics
Identifiers
urn:nbn:se:uu:diva-364656 (URN)978-91-506-2734-3 (ISBN)
Public defence
2018-12-21, Polhemsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2018-11-30 Created: 2018-10-30 Last updated: 2018-11-30

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Sumpter, David J. T.

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