Within neuroscience, psychology, and neuroimaging, the most frequently used statistical approach is null hypothesis significance testing (NHST) of the population mean. An alternative approach 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 that offers several advantages over population mean NHST. This method provides a population-level inference that is currently missing from study designs with small participant numbers, such as in traditional psychophysics and in precision imaging. Bayesian prevalence delivers a quantitative population estimate with associated uncertainty instead of reducing an experiment to a binary inference. Bayesian prevalence is widely applicable to a broad range of studies in neuroscience, psychology, and neuroimaging. Its emphasis on detecting effects within individual participants can also help address replicability issues in these fields. [ABSTRACT FROM AUTHOR]