Conceptually plausible Bayesian inference in interval timing

Abstract

In a world that is uncertain and noisy, perception makes use of optimization procedures that rely on the statistical properties of previous experiences. A well-known example of this phenomenon is the central tendency effect observed in many psychophysical modalities. For example, in interval timing tasks, previous experiences influence the current percept, pulling behavioural responses towards the mean. In Bayesian observer models, these previous experiences are typically modelled by unimodal statistical distributions, referred to as the prior. Here, we critically assess the validity of the assumptions underlying these models and propose a model that allows for more flexible, yet conceptually more plausible, modelling of empirical distributions. By representing previous experiences as a mixture of lognormal distributions, this model can be parametrized to mimic different unimodal distributions and thus extends previous instantiations of Bayesian observer models. We fit the mixture lognormal model to published interval timing data of healthy young adults and a clinical population of aged mild cognitive impairment patients and age-matched controls, and demonstrate that this model better explains behavioural data and provides new insights into the mechanisms that underlie the behaviour of a memory-affected clinical population.

The Bayesian Mutation Sampler explains distributions of causal judgments

“…A parameter recovery study (Appendix A) supported this suspicion, but revealed that using a parameter grid search (cf. Maaß et al, 2021;Mestdagh et al, 2019) resulted in correlations between true and estimated parameters consistently above .75 (see Method 2 Coarse grid in Appendix A), which is generally seen as good or excellent recovery (e.g. Anders et al, 2016;van Maanen et al, 2021;van Ravenzwaaij & Oberauer, 2009;White et al, 2015).…”

The Bayesian Mutation Sampler Explains Distributions of Causal Judgments

“…A parameter recovery study ( Appendix A ) supported this suspicion, but revealed that using a parameter grid search (cf. Maaß et al, 2021 ; Mestdagh et al, 2019 ) resulted in correlations between true and estimated parameters consistently above .75 (see Method 2 Coarse grid in Appendix A ), which is generally seen as good or excellent recovery (e.g., Anders et al, 2016 ; van Maanen et al, 2021 ; van Ravenzwaaij & Oberauer, 2009 ; White et al, 2018 ). Moreover, the parameter recovery study provided assurance regarding the identifiability of the BMS (van Maanen & Miletić, 2021 ).…”

Duration reproduction under memory pressure: Modeling the roles of visual memory load in duration encoding and reproduction

“…An alternative assumption holds that the internal representation is linearly scaled, but with the noise increasing linearly with the absolute magnitude according to Weber’s law. However, empirical justification of linear vs. logarithmic coding of the internal representation largely depends on the adopted experimental paradigms (Maaß et al, 2021; Matthews & Meck, 2016; Ren et al, 2021). Accordingly, we explored both logarithmic and linear encoding models and compared their predictions to determine which model performs better. In the logarithmic-encoding model, the duration is first transformed to the logarithmic scale.…”