Skip to main content
Calcimator

Bayesian Inference Calculator

Calculate posterior probability, Bayes factor, likelihood ratio, and evidence strength using Bayes' theorem.

Inputs

Results

Posterior Probability P(H|E)

66.67%

Bayes Factor

2

Likelihood Ratio4
Prior Odds1
Posterior Odds2
Update Factor1.333
How to Use This Calculator
  1. Enter the prior probability P(H) for your hypothesis.
  2. Input the likelihood P(E|H): probability of the evidence given the hypothesis is true.
  3. Enter the evidence probability P(E), the overall probability of observing the evidence.
  4. Review the posterior probability P(H|E), calculated automatically using Bayes' theorem.
  5. Check the Bayes factor, likelihood ratio, prior odds, and posterior odds for additional measures of how strongly the evidence supports the hypothesis.

How the result changes with Evidence Probability P(E)

Evidence Probability P(E)Posterior Probability P(H|E)Bayes Factor
0.1400%-1.333
0.35114.29%-8
0.6561.54%1.6
0.944.44%0.8

What each input means

Prior Probability P(H)
Prior probability of hypothesis
Likelihood P(E|H)
Probability of evidence given hypothesis
Evidence Probability P(E)
Marginal probability of evidence

How this is calculated

Formula

P(H|E) = P(E|H) × P(H) / P(E)

Worked example, using the default values

  1. Identify Input Parameters
    Prior Probability P(H) = 0.5, Likelihood P(E|H) = 0.8, Evidence Probability P(E) = 0.6 = 3 input(s) provided
  2. Calculate Posterior Probability P
    Posterior Probability P
    66.67 = 66.67%
  3. Calculate Bayes Factor
    Bayes Factor
    2 = 2
  4. Calculate Likelihood Ratio
    Likelihood Ratio
    4 = 4
  5. Calculate Prior Odds
    Prior Odds
    1 = 1

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

Related Calculators

The questions that sit next to this one — chosen by subject, including calculators filed under a different category.

Math & Statistics

Probability Calculator

Calculate probability of single events, combined events (AND/OR), permutations, and combinations.

Machine Learning & AI

Model Performance Metrics Calculator

Calculate accuracy, precision, recall, F1 score, MCC, AUC, and other classification performance metrics.

Statistics

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.

MLOps & AI Costing

Inference Latency Calculator

Estimate model inference latency, throughput, and memory requirements across CPU, GPU, and edge hardware.

Machine Learning & AI

Neural Network Parameters Calculator

Calculate total parameters, weights, biases, and memory requirements for neural network architectures.

More in Technology & Computing.