This application calculates the exact posterior distribution on prevalence given the results of an imperfect test, as described in the preprint Bayesian Beta-Binomial Prevalence Estimation Using an Imperfect Test by Jonathan Baxter.

Instructions

Enter your data into the form below and click Estimate Prevalence. Beta priors and Monte Carlo samples are optional. The default values correspond to scenario 3 in COVID-19 Antibody Seroprevalence in Santa Clara County.

To see the impact of a small change in the number of false positives in test calibration, try changing the false positives to 4 and then 8.

Once the posterior has been calculated, copy the page URL if you wish to share the result.

Field Tests

Total tests
Positive tests

Test Calibration

Known negatives
False positives
Known positives
True positives

Test Beta Priors (optional)

α_u
β_u
α_v
β_v

Algorithm/Stats Params (optional)

Monte Carlo samples
Grid size
Credible Interval(%)
Population Weighting

More Examples

1. COVID-19 Antibody Seroprevalence in Santa Clara County, Version 1:
   Prevalence Posteriors:
   • Scenario 1: unweighted | weighted
   • Scenario 2: unweighted | weighted
   • Scenario 3: unweighted | weighted
2. COVID-19 Antibody Seroprevalence in Santa Clara County, Version 2:
   • Prevalence Posterior: unweighted | weighted
3. Estimation of seroprevalence of novel coronavirus disease (COVID-19) using preserved serum at an outpatient setting in Kobe, Japan: A cross-sectional study.
   • Prevalence Posterior: unweighted | weighted
   • Test calibration data