Bayesian Inference Calculator
Bayesian Inference Calculator computes posterior probabilities using Bayes’ theorem \\( P(H|D) = \frac{P(D|H) \cdot P(H)}{P(D)} \\). Enter prior probabilities, likelihoods, and evidence for one or more hypotheses. Results are visualized as a bar chart with p5.js, and computational steps are displayed with MathJax.
Bayesian Inference Calculator
This calculator computes posterior probabilities using Bayes’ theorem \\( P(H|D) = \frac{P(D|H) \cdot P(H)}{P(D)} \\). Input prior probabilities \\( P(H) \\), likelihoods \\( P(D|H) \\), and evidence \\( P(D) \\) (optional). For multiple hypotheses, enter values as comma-separated lists (e.g., “0.4,0.6”). If evidence is not provided, it is computed as \\( P(D) = \sum_i P(D|H_i) \cdot P(H_i) \\). Results are visualized as a bar chart using p5.js, and steps are shown with MathJax. Share or embed results as needed.
Example 1: Single Hypothesis
Parameters: \\( P(H) = 0.5 \\), \\( P(D|H) = 0.8 \\), \\( P(D) = 0.6 \\).
Result: Posterior \\( P(H|D) = \frac{0.8 \cdot 0.5}{0.6} \approx 0.6667 \\).
Example 2: Two Hypotheses
Parameters: \\( P(H_1) = 0.4 \\), \\( P(H_2) = 0.6 \\), \\( P(D|H_1) = 0.8 \\), \\( P(D|H_2) = 0.3 \\), \\( P(D) \\) blank.
Step 1: Compute evidence \\( P(D) = 0.8 \cdot 0.4 + 0.3 \cdot 0.6 = 0.5 \\).
Result: Posteriors \\( P(H_1|D) \approx 0.64 \\), \\( P(H_2|D) \approx 0.36 \\).
Example 3: Medical Test
Parameters: \\( P(\text{Disease}) = 0.01 \\), \\( P(\text{Positive|Disease}) = 0.95 \\), \\( P(\text{Positive|No Disease}) = 0.05 \\), \\( P(\text{Positive}) \\) blank.
Result: Computes posterior probability of disease given a positive test.