Enter Network Inputs
This tool models a three-node binary chain: A → B → C. Enter percentages from 0 to 100.
Example Data Table
| Scenario | P(A) | P(B|A) | P(B|¬A) | P(C|B) | P(C|¬B) | Evidence | Posterior P(A) | Posterior P(C) |
|---|---|---|---|---|---|---|---|---|
| Strong positive chain | 40% | 75% | 20% | 85% | 15% | B=True, C=True | 71.43% | 100.00% |
| Observed final outcome only | 55% | 80% | 35% | 70% | 25% | C=True | 64.66% | 100.00% |
| Conflicting evidence | 30% | 90% | 10% | 60% | 20% | B=False, C=True | 4.55% | 100.00% |
Formula Used
1) Joint probability for the network
For any complete state,
P(A, B, C) = P(A) × P(B | A) × P(C | B).
This factorization follows the directed chain structure.
2) Evidence probability
P(E) = Σ P(A, B, C) across every state matching the observed evidence.
The tool sums valid states automatically.
3) Posterior update
P(X | E) = P(X, E) / P(E).
The calculator normalizes matching states to produce posterior probabilities for each node.
4) Entropy change
H(p) = -p log₂(p) - (1-p) log₂(1-p).
Lower posterior entropy means evidence reduced uncertainty.
How to Use This Calculator
- Enter custom labels for the three binary nodes.
- Provide the prior probability for the first node.
- Enter conditional percentages for the middle and final nodes.
- Choose observed evidence for node B, node C, or both.
- Click Calculate Network to update all probabilities.
- Review the prior versus posterior summary table.
- Inspect the full joint state table for exact enumeration.
- Download the results as CSV or PDF when needed.
8 FAQs
1) What does this tool calculate?
It computes prior, joint, and posterior probabilities for a three-node binary Bayesian network. It also shows evidence probability, entropy change, lift, and the most likely posterior state.
2) Why is the network arranged as A → B → C?
This structure keeps the model understandable while still showing dependency propagation. Evidence on later nodes can still update earlier beliefs through exact Bayesian normalization.
3) Can I leave evidence fields unknown?
Yes. Unknown evidence means the tool uses only the prior and conditional tables. Posterior results then match the original marginal probabilities.
4) What is evidence probability?
Evidence probability is the total probability of all states consistent with your observations. It tells you how likely the observed combination is under the current network.
5) What does lift mean in the summary table?
Lift compares posterior probability to prior probability. A value above 1 means evidence increased belief. A value below 1 means evidence reduced belief.
6) Why can evidence become impossible?
If your probabilities assign zero chance to every state matching the chosen evidence, normalization cannot occur. The tool warns you when that configuration is impossible.
7) Should I enter percentages or decimals?
Enter percentages from 0 to 100. The calculator converts them internally into probability values between 0 and 1 before performing Bayesian calculations.
8) What do the CSV and PDF exports include?
The exports include evidence details, the prior versus posterior summary, and the complete joint state table. This makes review, reporting, and sharing much easier.