get_expected_category_statistic_from_stanfit: Get expected category mean mu or covariance matrix sigma

In hlplab/MVBeliefUpdatr: Fitting, Summarizing, and Visualizing of Multivariate Gaussian Ideal Observers and Adaptors

Get expected category mean mu or covariance matrix sigma

Description

Returns the expected value of posterior marginal distribution over category means mu and/or category covariance matrix Sigma, marginalized over all MCMC samples.

Usage

get_expected_category_statistic_from_stanfit(
  x,
  categories = get_category_levels_from_stanfit(x),
  groups = get_group_levels_from_stanfit(x, include_prior = TRUE),
  statistic = c("mu", "Sigma"),
  untransform_cues = TRUE
)

get_expected_mu_from_stanfit(x, ...)

get_expected_sigma_from_stanfit(x, ...)

Arguments

x	An mv_ibbu_stanfit object.
categories	Character vector with categories for which category statistics are to be returned. (default: all categories)
groups	Character vector with groups for which category statistics are to be returned. (default: all groups)
statistic	Which category statistic should be returned? 'mu' for category mean or 'Sigma' for category covariance matrix, or 'c("mu", "Sigma")' for both. (default: both)
untransform_cues	Should m_0 and S_0 be transformed back into the original cue space? (default: 'TRUE')

Details

Each MCMC samples' expected value for the category mean E[mu] = m_n (i.e, the posterior/updated mean of the multivariate Normal over category means mu). Marginalizing across all MCMC samples (representing uncertainty in the true value of m_n), we get E[E[mu]] = mean(m_n).

Each MCMC samples' expected value for the category covariance matrix E[Sigma] = S_n / (nu_n - D - 1), where S_n is the posterior/updated scatter matrix, nu_n is the posterior/updated pseudocount representing the strength of the posterior/updated beliefs over category covariance matrices sigma (i.e., the inverse-Wishart), and D is the dimension of the multivariate Normal. Marginalizing across all MCMC samples (representing uncertainty in the true value of S_n), we get E[E[Sigma]] = mean(S_n / (nu_n - D - 1)).

Value

If just one group and category was requested, a vector (for the mean) or matrix (for the covariance matrix). If more than one group or category was requested, a tibble with one row for each unique combination of group and category.

References

\insertRef

murphy2012MVBeliefUpdatr

See Also

TBD

hlplab/MVBeliefUpdatr documentation built on March 29, 2025, 10:42 p.m.