cpt_population: Population-Based Conditional Probability Table
In mispitools: Missing Person Identification Tools

cpt_population

R Documentation

Population-Based Conditional Probability Table

Description

Computes a conditional probability table (CPT) representing the joint probability distribution of sex, age group, and hair color in the reference population. This table represents P(D|H2), the probability of observing the evidence under the hypothesis that the unidentified person is NOT the missing person.

The function assumes a uniform age distribution across the population and computes the probability of falling within or outside the specified age range.

Usage

cpt_population(
  propS = c(0.5, 0.5),
  MPa = 40,
  MPr = 6,
  propC = c(0.3, 0.2, 0.25, 0.15, 0.1)
)

Arguments

`propS`	Numeric vector of length 2. Sex proportions in the population, specified as c(proportion_female, proportion_male). Must sum to 1. Default: c(0.5, 0.5) for equal proportions.
`MPa`	Numeric. Missing person's estimated age in years. Used to define the center of the age matching interval. Default: 40.
`MPr`	Numeric. Age range tolerance in years (plus/minus). The matching age interval is `(MPa - MPr)` to `(MPa + MPr)`. Individuals within this range are classified as T1 (age match), others as T0 (age mismatch). Default: 6.
`propC`	Numeric vector of length 5. Hair color proportions in the population for colors 1 through 5. Must sum to 1. Default values represent a typical distribution. Colors are: 1=Black, 2=Brown, 3=Blonde, 4=Red, 5=Gray/White.

Details

The probability of age match (T1) is calculated assuming a uniform distribution over ages 1-80:

P(T1) = (MPa + MPr - (MPa - MPr)) / 80 = 2 \times MPr / 80

The joint probability for each cell is:

P(Sex, Age, Color) = P(Sex) \times P(AgeGroup) \times P(Color)

Value

A 4x5 numeric matrix representing joint probabilities. Rows correspond to sex-age group combinations:

F-T1: Female, age within range
F-T0: Female, age outside range
M-T1: Male, age within range
M-T0: Male, age outside range

Columns correspond to hair colors 1-5. Each cell contains P(Sex, AgeGroup, HairColor | H2).

Deprecation

Soft-deprecated in mispitools 2.0. The per-feature H2 marginal it builds as an outer product is generalised by nongenetic_feature plus the unified per-feature engine (one feature per trait, combined downstream). The legacy function still works for the 2.0 release-candidate cycle and will be removed afterwards.

References

Marsico FL, et al. (2023). "Likelihood ratios for non-genetic evidence in missing person cases." Forensic Science International: Genetics, 66, 102891. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.fsigen.2023.102891")}

Examples

# Default parameters: equal sex proportions, MP age 40 +/- 6 years
cpt_h2 <- cpt_population()
print(cpt_h2)

# Custom population: 60% female, narrower age range, different hair colors
cpt_custom <- cpt_population(
  propS = c(0.6, 0.4),
  MPa = 35,
  MPr = 3,
  propC = c(0.4, 0.25, 0.2, 0.1, 0.05)
)

# Verify rows sum correctly (should sum to hair color proportions)
colSums(cpt_h2)

mispitools documentation built on Aug. 26, 2026, 1:08 a.m.