Transitive Mate Preferences

Rational mate choices are central to individual happiness and collective social goods. Yet, few studies assess mate choice rationality from the decision-theoretic perspective. Here we present an experimental test of rationality in human mate preferences through the lens of transitivity, a fundamental hallmark of rational decision-making. In the experiment, participants made repeated binary choices between pairs of potential romantic partners in both short-term and long-term mating contexts. We tested the transitivity of mate preferences by systematically comparing four prominent transitive models with four models that allow for intransitive preferences on the choice data. Overall, all transitive models provided better accounts than the intransitive models in Bayesian model selection and strong stochastic transitivity (SST), the most restrictive transitive model, outperformed other transitive models. On the individual level, participants rarely displayed intransitive cycles and most of them were best described by transitive models in Bayesian model selection. Our paper presents a systematic evaluation of transitivity in mate preferences and sheds new light on our understanding of human mating behavior.

Surrogate-based Bayesian comparison of computationally expensive models: application to microbially induced calcite precipitation

Geochemical processes in subsurface reservoirs affected by microbial activity change the material properties of porous media. This is a complex biogeochemical process in subsurface reservoirs that currently contains strong conceptual uncertainty. This means, several modeling approaches describing the biogeochemical process are plausible and modelers face the uncertainty of choosing the most appropriate one. The considered models differ in the underlying hypotheses about the process structure. Once observation data become available, a rigorous Bayesian model selection accompanied by a Bayesian model justifiability analysis could be employed to choose the most appropriate model, i.e. the one that describes the underlying physical processes best in the light of the available data. However, biogeochemical modeling is computationally very demanding because it conceptualizes different phases, biomass dynamics, geochemistry, precipitation and dissolution in porous media. Therefore, the Bayesian framework cannot be based directly on the full computational models as this would require too many expensive model evaluations. To circumvent this problem, we suggest to perform both Bayesian model selection and justifiability analysis after constructing surrogates for the competing biogeochemical models. Here, we will use the arbitrary polynomial chaos expansion. Considering that surrogate representations are only approximations of the analyzed original models, we account for the approximation error in the Bayesian analysis by introducing novel correction factors for the resulting model weights. Thereby, we extend the Bayesian model justifiability analysis and assess model similarities for computationally expensive models. We demonstrate the method on a representative scenario for microbially induced calcite precipitation in a porous medium. Our extension of the justifiability analysis provides a suitable approach for the comparison of computationally demanding models and gives an insight on the necessary amount of data for a reliable model performance.

An introduction to thermodynamic integration and application to dynamic causal models

In generative modeling of neuroimaging data, such as dynamic causal modeling (DCM), one typically considers several alternative models, either to determine the most plausible explanation for observed data (Bayesian model selection) or to account for model uncertainty (Bayesian model averaging). Both procedures rest on estimates of the model evidence, a principled trade-off between model accuracy and complexity. In the context of DCM, the log evidence is usually approximated using variational Bayes. Although this approach is highly efficient, it makes distributional assumptions and is vulnerable to local extrema. This paper introduces the use of thermodynamic integration (TI) for Bayesian model selection and averaging in the context of DCM. TI is based on Markov chain Monte Carlo sampling which is asymptotically exact but orders of magnitude slower than variational Bayes. In this paper, we explain the theoretical foundations of TI, covering key concepts such as the free energy and its origins in statistical physics. Our aim is to convey an in-depth understanding of the method starting from its historical origin in statistical physics. In addition, we demonstrate the practical application of TI via a series of examples which serve to guide the user in applying this method. Furthermore, these examples demonstrate that, given an efficient implementation and hardware capable of parallel processing, the challenge of high computational demand can be overcome successfully. The TI implementation presented in this paper is freely available as part of the open source software TAPAS.

A Bayesian model selection approach for mediation analysis

Mediation analysis is a powerful tool for discovery of causal relationships. We describe a Bayesian model selection approach to mediation analysis that is implemented in our bmediatR software. Using simulations, we show that bmediatR performs as well or better than established methods including the Sobel test, while allowing greater flexibility in both model specification and in the types of inference that are possible. We applied bmediatR to genetic data from mice and human cell lines to demonstrate its ability to derive biologically meaningful findings. The Bayesian model selection framework is extensible to support a wide variety of mediation models.