Perform Bayesian Learning on a Probabilistic Network of Project Risks.

This function is part of the probabilistic network module, whose API may still evolve in future versions.

Usage

prob_net_learn(network, observations = list(), num_samples = 1000)

Arguments

network: A prob_net object created by prob_net().
observations: A named list where names are node IDs and values are observed values.
num_samples: Number of samples to simulate for each node (default is 1000).

Value

A data frame with num_samples rows and one column per node containing the simulated posterior samples.

Details

This function updates a probabilistic network of project risks with observed values for certain nodes and then performs inference to generate posterior distributions for unobserved nodes. The function supports normal, uniform, lognormal, conditional continuous, conditional discrete, discrete, and aggregate (summation) node types.

Conditioning is performed by rejection sampling: the network is simulated forward from its priors (as in prob_net_sim()) and only the draws whose observed nodes equal the supplied values are retained, repeating until num_samples matching draws are collected. Because whole joint draws are filtered, evidence propagates to upstream (parent and confounding) nodes as well as downstream ones. This distinguishes observational conditioning ("seeing", the sense of [Pearl 2009]) from intervention ("doing"): only when the observed node is a root cause with no shared ancestry do prob_net_learn() and prob_net_update() induce the same distribution.

Because matches are exact, observations are supported on discrete (or discrete-conditional) nodes; observing a continuous node has probability zero of an exact match and will raise an error. Nodes not listed in observations retain their model distributions. If observations is empty the result is a plain forward simulation.

Examples

# Define nodes
nodes <- data.frame(
  id = c("A", "B", "C", "D"),
  label = c("Node A", "Node B", "Node C", "Node D"),
  stringsAsFactors = FALSE
)

# Define links
links <- data.frame(
  source = c("A", "B", "C"),
  target = c("C", "D", "D"),
  weight = c(1, 2, 3),
  stringsAsFactors = FALSE
)

# Define distributions for nodes
distributions <- list(
  A = list(type = "discrete", values = c(0, 1), probs = c(0.5, 0.5)),
  B = list(type = "normal", mean = 2, sd = 0.5),
  C = list(
    type = "conditional", condition = "A",
    true_dist = list(type = "normal", mean = 1, sd = 0.5),
    false_dist = list(type = "discrete", values = c(0, 1), probs = c(0.4, 0.6))
  ),
  D = list(type = "aggregate", nodes = c("B", "C"))
)

# Create the network graph
graph <- prob_net(nodes, links, distributions = distributions)

# Perform Bayesian updating with observations
observations <- list(A = 1)
updated_results <- prob_net_learn(graph, observations, num_samples = 1000)
head(updated_results)
#>   A        B        C        D
#> 1 1 2.103534 1.161956 3.265489
#> 2 1 1.053238 1.395591 2.448829
#> 3 1 2.355251 0.577767 2.933018
#> 4 1 1.899903 1.503502 3.403405
#> 5 1 1.966782 1.190242 3.157024
#> 6 1 1.869244 1.288280 3.157524