Bayesian inference of population prevalence

Abstract

<jats:title>Abstract</jats:title><jats:p>Within neuroscience, psychology and neuroimaging, the most frequently used statistical approach is null-hypothesis significance testing (NHST) of the population mean. An interesting alternative is to perform NHST within individual participants and then infer, from the proportion of participants showing an effect, the prevalence of that effect in the population. We propose a novel Bayesian method to estimate such population prevalence which has several advantages over population mean NHST. First, it provides a population level inference currently missing for designs with small numbers of participants such as traditional psychophysics, animal electrophysiology and precision imaging. Second, it delivers a quantitative estimate with associated uncertainty instead of reducing an experiment to a binary inference on a population mean. Bayesian prevalence is widely applicable to a broad range of studies in neuroscience, psychology and neuroimaging. Its emphasis on detecting effects within individual participants could help address replicability issues. To facilitate the applicability of Bayesian prevalence, we provide code in Matlab, Python and R.</jats:p>

Different computations over the same inputs produce selective behavior in algorithmic brain networks

“…By treating each participant as an N-of-1 study, 10 participants per task provide 10 independent replications of the experiment. We replicated the four computational stages in at least 9/10 participants (and in two further replication experiments with similarly high prevalence), providing strong evidence that a majority of individuals in the population sampled and tested in the same way would show the same effects (25).…”

“…with left vs. right input projected in right vs. left occipital cortex; see Methods, Stimuli). Our analyses of the ensuing computation in the networks of individual participants systematically revealed four stages of computation that represent and transform the same inputs to produce different task-specific behavior (N = 10 participants per task, each analyzed separately to provide an independent replication; we further replicated the key results in different participants, using opposite-phase Gabor patches and also with sequentially presented inputs) (25)(26)(27)(28).…”

Facial expressions dynamically cascade emotion category and intensity information over time

“…This indicates the proportion of the population from which the sample of experimental participants was drawn that would be expected to show the same effect, if subjected to the same experimental procedure. Inferring a non-zero population prevalence 41,42 at P = 0.05, (Bonferroni corrected over emotions) corresponds to a significance threshold of N > 10 receivers showing a significant result in each culture (i.e., full details in Methods, under 'Characterizing the communicative function of face movements, Population prevalence'). That is, 10 out of our 60 receivers showing an effect provides enough evidence to reject a null hypothesis that the population prevalence proportion is 0 (i.e., no receiver in the population would show the effect).…”

“…Colour saturation represents the number of receivers with a significant effect (FWER P < 0.05 within receiver test; see colour bar to the right of Fig. 3a) above population prevalence 41,42 threshold (see Methods, under 'Characterizing the communicative function of face movements'). Fig.…”

“…Population prevalence. To obtain a population inference from the within-receiver results, we use population prevalence 41,42 . In this approach, we model the population from which our experimental participants are sampled with a binary property: each possible participant either would, or would not, show a true positive effect in the specific test considered (i.e., of a specific AU classifying an expression).…”