What is a Bayesian network?

A Bayesian network is a directed acyclic graph (DAG) in which nodes represent random variables and edges represent direct probabilistic dependence. Each node stores a conditional probability table (CPT) giving the probability of that node's states given the states of its parents. The joint probability of every variable in the network factorises as the product of each node's CPT entry, which lets the full joint distribution be represented compactly instead of as one enormous table. This simulation uses a disease node with four mutually exclusive states (Flu, Common Cold, Allergic Rhinitis, Bacterial Sinusitis) as the parent of eight binary symptom nodes, each with its own real CPT of P(symptom present | disease).

How does the exact inference by enumeration work here?

Because every symptom node's only parent is the disease node, the joint probability of a disease state d together with a set of observed symptom values e1..ek is P(d) times the product of P(ei | d) for every observed symptom i, straight from Bayes' rule and the chain rule for this graph structure. The simulator computes that unnormalised product for all four disease states, then divides each by the sum across all four so the results sum to 1 — this is exact enumeration inference, not an approximation and not a heuristic weighted sum. Every time you toggle a symptom, the full enumeration is recomputed from the original priors and CPTs.

Why does toggling one symptom change the probability of several diseases at once?

Because all diseases compete for the same normalised probability mass. Observing itchy, watery eyes multiplies the allergy score by a high likelihood (0.75) and the flu score by a low likelihood (0.05); after renormalising, allergy's share rises and every other disease's share falls, even though their own individual CPT entries for that symptom did not change. This is Bayesian updating: evidence for one hypothesis is automatically evidence against its competitors, which is exactly what real diagnostic reasoning should do.

How is this different from a simple weighted-score heuristic?

A heuristic scoring system might just add up points for each matching symptom with no principled justification for the weights or the total. This simulator instead multiplies genuine conditional probabilities together according to the product rule of probability and normalises by the true marginal likelihood of the observed evidence, exactly as Bayes' rule requires: P(disease | evidence) = P(evidence | disease) P(disease) / P(evidence). The numbers are calibrated probabilities that sum to 1 and can be checked by hand for any single piece of evidence, not an arbitrary score.

What do the conditional probability tables (CPTs) represent?

Each symptom's CPT lists, for every disease state, the probability that a patient with that disease would exhibit the symptom, for example P(fever = present | Flu) = 0.80 versus P(fever = present | Allergic Rhinitis) = 0.02. These illustrative values reflect well-known clinical tendencies (fever and body aches are common in flu, itchy eyes and sneezing are common in allergies, facial pressure is common in sinusitis) but are simplified teaching numbers, not diagnostic statistics from a real clinical dataset.

Is this simulation medical advice?

No. This is an educational demonstration of Bayesian network inference using illustrative, simplified probability numbers. It is not a diagnostic tool, has not been validated on real patient data, and must never be used to make decisions about your health or anyone else's. If you have symptoms that concern you, contact a qualified healthcare professional or your local emergency services.

Symptom Checker — Bayesian Network Inference Live

⚠️ Educational simulation only — not medical advice. Illustrative probabilities used to teach Bayesian inference; never use this to make real health decisions. Consult a qualified healthcare professional for any medical concern.