Forward sampling is a way to generate a sample of every variable in a belief network so that each sample is generated in proportion to its probability. This enables us to estimate the prior probability of any variable.

Suppose $X_1,\mathrm{\dots },X_n$ is a total ordering of the variables so that the parents of each variable come before the variable in the total order. Forward sampling draws a sample of all of the variables by drawing a sample of each variable $X_1,\mathrm{\dots },X_n$ in order. First, it samples $X_1$ using the cumulative distribution, as described above. For each of the other variables, due to the total ordering of variables, when it comes time to sample $X_i$, it already has values for all of $X_i$’s parents. It now samples a value for $X_i$ from the distribution of $X_i$ given the values already assigned to the parents of $X_i$. Repeating this for every variable generates a sample containing values for all of the variables. The probability distribution of a query variable is estimated by considering the proportion of the samples that have assigned each value of the variable.