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Fit BREAD summary-mode Bayesian model

Source: R/fit_summary.R
fit_bread_summary.Rd

v1 MVP fit. For each region, fits a Normal linear regression y ~ design with a conjugate Normal-Inverse-Gamma prior, yielding an analytical posterior — no MCMC. The marginal posterior of each coefficient is a location-scale Student-t, used downstream by posterior_summary().

Usage

fit_bread_summary(region_mat, coldata, design, contrast, prior = NULL)

Arguments

region_mat

Region-by-sample numeric matrix (from summarize_features()).

coldata

Sample metadata (S4Vectors::DataFrame or data.frame).

design

One-sided formula.

contrast

Character coefficient name of interest.

prior

A bread_prior() object (or NULL for defaults).

Value

A list with:

  • fits: per-region list of list(mu_n, Lambda_n_inv, a_n, b_n, n, error)

  • design_matrix: model matrix X actually used

  • coef_names: coefficient names

  • contrast, contrast_idx: contrast name and its column index in X

  • region_ids: rownames of region_mat

  • prior: the prior applied (with mu0/Lambda0 filled in)

Model

For region r and sample i: $$y_{ir} \sim \mathcal{N}(X_i \beta_r,\, \sigma_r^2),$$ $$\beta_r \mid \sigma_r^2 \sim \mathcal{N}(\mu_0,\, \sigma_r^2 \Lambda_0^{-1}),$$ $$\sigma_r^2 \sim \mathrm{Inv\text{-}Gamma}(a_0, b_0).$$ Posterior: $$\Lambda_n = X^\top X + \Lambda_0,\quad \mu_n = \Lambda_n^{-1}(X^\top y + \Lambda_0 \mu_0),$$ $$a_n = a_0 + n/2,\quad b_n = b_0 + \tfrac{1}{2}(y^\top y + \mu_0^\top \Lambda_0 \mu_0 - \mu_n^\top \Lambda_n \mu_n).$$