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Posterior Risk Probability.

Source: R/learning.R
risk_post_prob.Rd

This function calculates the posterior probability of a risk event 'R' occurring based on observations of multiple root causes and their associated conditional probabilities.

Usage

risk_post_prob(
  cause_probs,
  risks_given_causes,
  risks_given_not_causes,
  observed_causes
)

Arguments

cause_probs

A vector of prior probabilities for each root cause 'C_i'.

risks_given_causes

A vector of conditional probabilities of the risk event 'R' given each cause 'C_i'.

risks_given_not_causes

A vector of conditional probabilities of the risk event 'R' given not each cause 'C_i'.

observed_causes

A vector of observed values for each cause 'C_i' (1 if observed, 0 if not observed, NA if unobserved).

Value

A numeric value for the posterior probability of the risk event given the observed causes.

Details

Observed causes are fixed to their conditional probability (\(P(R \mid C_i)\) if present, \(P(R \mid \bar{C}_i)\) if absent) while unobserved causes (NA) keep their marginal contribution. The causes are then combined with the same noisy-OR as risk_prob(), so the posterior is on the same scale as the prior and observing an aggravating cause raises it.

References

Damnjanovic, Ivan, and Kenneth Reinschmidt. Data analytics for engineering and construction project risk management. No. 172534. Cham, Switzerland: Springer, 2020.

Examples

cause_probs <- c(0.3, 0.2)
risks_given_causes <- c(0.8, 0.6)
risks_given_not_causes <- c(0.2, 0.4)
observed_causes <- c(1, NA)
risk_post_prob <- risk_post_prob(
  cause_probs, risks_given_causes,
  risks_given_not_causes, observed_causes
)
print(risk_post_prob)
#> [1] 0.888