Maximum a posteriori purified profiles under a Gaussian convolution

For fixed plug-in \(\boldsymbol{\zeta}=(\boldsymbol{\mu},\{\boldsymbol{\Sigma}_j\})\) and a bulk vector \(\boldsymbol{y}\), returns cell-type-specific MAP estimates of the latent purified profiles \(\boldsymbol{x}_{\cdot j}\) in the additive Gaussian model of the article. This is the Bayesian counterpart to the frequentist plug-in that replaces \(\boldsymbol{x}_{\cdot j}\) by \(\boldsymbol{\mu}_{\cdot j}\) when estimating proportions alone.

Usage

.map_gaussian_convolution(y, mean_signature_matrix, Sigma)

Arguments

y

Bulk vector \(\boldsymbol{y}\in\mathbb{R}^{G}\).

mean_signature_matrix

Mean matrix \(\boldsymbol{\mu}\in\mathcal{M}_{G\times J}\) (prior / plug-in means).

Sigma

Array \((\boldsymbol{\Sigma}_j)_{j}\in\mathcal{M}_{G\times G\times J}\).

Value

List of length \(J\) with MAP vectors in \(\mathbb{R}^{G}\).