This calculator is designed for any 3-by-3 Bayesian setup with row categories {X₁, X₂, X₃} and observed results {Y₁, Y₂, Y₃}. You enter the prior probabilities for the row categories and the conditional probabilities for each row. The app computes the joint table, evidence totals, a tree view, and any posterior such as P(X₂ | Y₂).
Inputs
Enter values as percentages like 30 or 12.5. The labels are fully generic, and you can work either from the table directly or from a tree-style interpretation of the same priors and row-conditionals.
| Row category | Prior P(Xᵢ) | |||
|---|---|---|---|---|
Row validation rule: enter percentages from 0 to 100. Each prior set and each conditional row should sum to 100%.
Same inputs, but written as a probability tree: first choose a row category, then a result branch. The leaf values below update automatically as joint probabilities.
P(Xᵢ|Yⱼ) = P(Xᵢ)·P(Yⱼ|Xᵢ) / Σₖ P(Xₖ)·P(Yⱼ|Xₖ)Computed joint table
These are the leaf probabilities after multiplying each prior by each row-conditional probability.
| Joint P(Xᵢ∩Yⱼ) | Y₁ | Y₂ | Y₃ | Row total |
|---|---|---|---|---|
| X₁ | ||||
| X₂ | ||||
| X₃ | ||||
| Column total |