LMN-package {LMN}

Inference for Linear Models with Nuisance Parameters.

Description

Efficient profile likelihood and marginal posteriors when nuisance parameters are those of linear regression models.

Details

Consider a model p(\boldsymbol{Y} \mid \boldsymbol{B}, \boldsymbol{\Sigma}, \boldsymbol{\theta}) of the form

\boldsymbol{Y} \sim \textrm{Matrix-Normal}(\boldsymbol{X}(\boldsymbol{\theta})\boldsymbol{B}, \boldsymbol{V}(\boldsymbol{\theta}), \boldsymbol{\Sigma}),

where \boldsymbol{Y}_{n \times q} is the response matrix, \boldsymbol{X}(\theta)_{n \times p} is a covariate matrix which depends on \boldsymbol{\theta}, \boldsymbol{B}_{p \times q} is the coefficient matrix, \boldsymbol{V}(\boldsymbol{\theta})_{n \times n} and \boldsymbol{\Sigma}_{q \times q} are the between-row and between-column variance matrices, and (suppressing the dependence on \boldsymbol{\theta}) the Matrix-Normal distribution is defined by the multivariate normal distribution \textrm{vec}(\boldsymbol{Y}) \sim \mathcal{N}(\textrm{vec}(\boldsymbol{X}\boldsymbol{B}), \boldsymbol{\Sigma} \otimes \boldsymbol{V}), where \textrm{vec}(\boldsymbol{Y}) is a vector of length nq stacking the columns of of \boldsymbol{Y}, and \boldsymbol{\Sigma} \otimes \boldsymbol{V} is the Kronecker product.

The model above is referred to as a Linear Model with Nuisance parameters (LMN) (\boldsymbol{B}, \boldsymbol{\Sigma}), with parameters of interest \boldsymbol{\theta}. That is, the LMN package provides tools to efficiently conduct inference on \boldsymbol{\theta} first, and subsequently on (\boldsymbol{B}, \boldsymbol{\Sigma}), by Frequentist profile likelihood or Bayesian marginal inference with a Matrix-Normal Inverse-Wishart (MNIW) conjugate prior on (\boldsymbol{B}, \boldsymbol{\Sigma}).

Author(s)

Maintainer: Martin Lysy [e-mail]

Authors:

• Bryan Yates

See Also

Useful links:

• https://github.com/mlysy/LMN

• Report bugs at https://github.com/mlysy/LMN/issues