Appendix C: Diagnostics for the Bayesian analyses

This appendix presents diagnostics for the Bayesian analyses. In each study, prior predictive checks are presented before posterior predictive checks. Furthermore, in each of these checks, the models presented first have the default Gaussian distribution, whereas the next series have an exponentially modified Gaussian (dubbed ‘ex-Gaussian’) distribution with an identity link function (for details, see the section titled ‘Distributions and prior predictive checks’ in the main text). Eyeball estimation is used to assess the outcomes of these checks (for background on predictive checks and for alternative estimation procedures, see Gelman et al., 1996; Moran et al., 2022; Schoot et al., 2021). One diagnostic not shown in this appendix is the \(\widehat R\), which is shown in Appendix E instead.

References

Gelman, A., Meng, X., & Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 733–807.
Moran, G. E., Cunningham, J. P., & Blei, D. M. (2022). The posterior predictive null. Bayesian Analysis, 1(1). https://doi.org/10.1214/22-BA1313
Schoot, R. van de, Depaoli, S., Gelman, A., King, R., Kramer, B., Märtens, K., Tadesse, M. G., Vannucci, M., Willemsen, J., & Yau, C. (2021). Bayesian statistics and modelling. Nature Reviews Methods Primers, 1, 3. https://doi.org/10.1038/s43586-020-00003-0

Pablo Bernabeu, 2022. Licence: CC BY 4.0.
Thesis: https://doi.org/10.17635/lancaster/thesis/1795.

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