pra-bayesian-risk

name	pra-bayesian-risk
description	Compute and update the probability of a risk event from root causes, and turn risk probabilities into project cost distributions, using the PRA package. Use when a user has a risk register with root-cause probabilities and wants a prior risk probability, a Bayesian update after observing causes, or a cost-impact distribution.

When to use

Best when you have identifiable root causes with estimated probabilities and want to update estimates as the project progresses (i.e. a risk register). For task-level distributions and total project cost/schedule, prefer Monte Carlo (pra-monte-carlo). The two combine: estimate risk probabilities here, then feed cost impacts into a cost distribution.

Prior and posterior risk probability

risk_prob_tool(cause_probs_json, risks_given_causes_json, risks_given_not_causes_json) computes P(R) by the law of total probability over independent root causes. All three arrays are the same length:

• cause_probs_json: P(cause present), e.g. [0.3, 0.2]
• risks_given_causes_json: P(Risk | Cause), e.g. [0.8, 0.6]
• risks_given_not_causes_json: P(Risk | not Cause), e.g. [0.2, 0.4]

risk_post_prob_tool(..., observed_causes_json) updates P(R) after observing cause states. observed_causes_json uses 1 (occurred), 0 (did not occur), null (still unknown), e.g. [1, null].

Cost distributions

• cost_pdf_tool(num_sims, risk_probs_json, means_given_risks_json, sds_given_risks_json, base_cost) — prior cost distribution. Each simulation draws whether each risk occurs, then samples its cost impact.
• cost_post_pdf_tool(num_sims, observed_risks_json, means_given_risks_json, sds_given_risks_json, base_cost) — posterior after observing which risks occurred (observed_risks_json uses true/false/null).

Parameters: means_given_risks_json / sds_given_risks_json give the mean and SD of the additional cost if a risk occurs (one per risk); base_cost is the baseline before any risk impacts.

Workflow

risk_prob_tool → cost_pdf_tool → [observe causes/risks] → risk_post_prob_tool → cost_post_pdf_tool.

References

• NASA Risk-Informed Decision Making Handbook (SP-2010-576).
• NASA Bayesian Schedule and Cost Risk Analysis.