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Compute Bayesian Prior-Posterior and Information Gain Curves

Source: R/bayes_curves_functions.R
make_bayes_curves.Rd

Computes Bayesian updating curves showing how different lineup responses update beliefs about suspect guilt, following Wells, Yang, & Smalarz (2015).

Usage

make_bayes_curves(
  data,
  response_categories = c("simple", "confidence"),
  confidence_bins = NULL,
  prior_grid = seq(0.01, 0.99, 0.01),
  lineup_size = 6,
  innocent_suspect = "auto"
)

Arguments

data

A dataframe with the following columns:

  • target_present: Logical. TRUE if guilty suspect in lineup

  • identification: Character. "suspect", "filler", or "reject"

  • confidence: Numeric. Confidence rating (optional for response categories)

response_categories

Character vector specifying how to categorize responses. Options:

  • "simple": Three categories (suspect, filler, reject)

  • "confidence": Combines identification with confidence bins

confidence_bins

Numeric vector of bin edges if using confidence categories (e.g., c(0, 60, 80, 100)). Ignored if response_categories = "simple".

prior_grid

Numeric vector of prior probabilities to evaluate (default: seq(0.01, 0.99, 0.01))

lineup_size

Nominal lineup size, used when target-absent data have no designated innocent suspect.

innocent_suspect

How innocent-suspect identifications in target-absent lineups are obtained. "designated": the lineups had a designated innocent suspect, so target-absent "suspect" rows are counted directly, and zero such rows means a false-ID rate of zero. "estimated": there was no designated innocent suspect, so the innocent-suspect count is estimated as filler IDs divided by lineup_size. "auto" (the default) chooses "designated" when any target-absent row is a suspect ID or the data have a non-missing suspect_pos column, and "estimated" otherwise, with a message.

Value

A list containing:

  • curves: Dataframe with prior, posterior, and information gain for each response

  • likelihoods: Dataframe with p(x|guilty) and p(x|innocent) for each response

  • response_counts: Count of each response type by target presence

  • n_guilty: Number of target-present lineups

  • n_innocent: Number of target-absent lineups

Details

This function treats lineup outcomes as evidence for Bayesian updating. For each response type x (e.g., high-confidence suspect ID, rejection, etc.), it computes:

Likelihoods from observed data: $$p(x|guilty) = \frac{count(x | target\_present)}{N_{guilty}}$$ $$p(x|innocent) = \frac{count(x | target\_absent)}{N_{innocent}}$$

For each prior probability p(guilty): $$p(x) = p(guilty) \cdot p(x|guilty) + (1-p(guilty)) \cdot p(x|innocent)$$ $$p(guilty|x) = \frac{p(guilty) \cdot p(x|guilty)}{p(x)}$$

Information gain: $$IG(x) = H(prior) - H(posterior)$$

where H(p) is binary entropy.

The information gain quantifies how much uncertainty is reduced by observing response x. It is negative when the response moves belief towards 0.5, as a suspect identification does at a low prior; that is a correct update that leaves more uncertainty, not misleading evidence.

References

Wells, G. L., Yang, Y., & Smalarz, L. (2015). Eyewitness identification: Bayesian information gain, base-rate effect-equivalency curves, and reasonable suspicion. Law and Human Behavior, 39(2), 99-122.

Examples

data(lineup_example)
bayes <- make_bayes_curves(lineup_example)
bayes$likelihoods
#> # A tibble: 3 × 5
#>   response p_x_given_guilty p_x_given_innocent n_guilty n_innocent
#>   <chr>               <dbl>              <dbl>    <int>      <dbl>
#> 1 filler             0.311               0.587      218        411
#> 2 reject             0.0957              0.287       67        201
#> 3 suspect            0.593               0.126      415         88