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Calcimator

Bayesian Prior Calculator

Apply Bayes' theorem to update a prior probability given test sensitivity and false positive rate. Calculate the posterior probability after a positive or negative result.

Inputs

Results

Posterior P(A | positive test)

0.16

Posterior P(A | negative test)

0

Positive Likelihood Ratio19
Negative Likelihood Ratio0.05
Prior Odds0.01
Posterior Odds (after + test)0.19
Information Gain (bits)4.01
How to Use This Calculator
  1. Enter the Prior Probability — your belief that the condition is present before seeing the test result (e.g., disease prevalence).
  2. Enter the Sensitivity (true positive rate) — the probability the test is positive given the condition is present.
  3. Enter the False Positive Rate — the probability the test is positive when the condition is absent (1 − Specificity).
  4. Bayes' theorem updates the prior: P(condition | positive test) = (sensitivity × prior) / P(positive test).
  5. The Posterior Probability is the updated belief after a positive result; it depends heavily on the prior.
  6. Low prevalence dramatically reduces the positive predictive value even for highly sensitive tests — this is the base rate fallacy.

How the result changes with Prior Probability P(A)

Prior Probability P(A)Posterior P(A | positive test)Posterior P(A | negative test)
0.10.680.01
0.350.910.03
0.650.970.09
0.90.990.32

What each input means

Prior Probability P(A)
Your initial belief about the probability before seeing evidence. E.g., disease prevalence.
Sensitivity (True Positive Rate)
Probability of a positive test given the condition is present. Also called recall or TPR.
False Positive Rate
Probability of a positive test given the condition is absent. Equal to 1 - specificity.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    Prior Probability P(A) = 0.01, Sensitivity (True Positive Rate) = 0.95, False Positive Rate = 0.05 = 3 input(s) provided
  2. Calculate Posterior P
    Posterior P
    0.161 = 0.161
  3. Calculate Posterior P
    Posterior P
    0.0005 = 0.0005
  4. Calculate Positive Likelihood Ratio
    Positive Likelihood Ratio = Math
    19 = 19
  5. Calculate Negative Likelihood Ratio
    Negative Likelihood Ratio
    0.0526 = 0.0526

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators.

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