Sparse Matrix Computation in Mixed Effects Model

GDAGsim: Sparse matrix algorithms for Bayesian computation

GDAGsim is a software library which can be used to carry out conditional sampling of linear Gaussian directed acyclic graph models, and hence can be used for the implementation of efficient block MCMC samplers for such models. This paper examines the software library and its design, and how it can be applied to problems in Bayesian inference.

Data Sparse Matrix Computation - Lecture 11

2 Randomized algorithms 4 2.1 Randomized low-rank factorization . . . . . . . . . . . . . . . . . 4 2.2 How to find such a Q . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 How to construct Q with randomness . . . . . . . . . . . . . . . . 5 2.4 An adaptive randomized range finder algorithm . . . . . . . . . . 6 2.5 Example of implementation of the adaptive range approximation method . ...

Data Sparse Matrix Computation - Lecture 20

Sparse Matrix Representations of Linear Mixed Models

We describe a representation of linear mixed-effects models using a sparse semidefinite matrix. This representation provides for efficient evaluation of the profiled log-likelihood or profiled restricted loglikelihood of the model, given the relative precision parameters for the random effects. The evaluation is based upon the LDLT form of the Cholesky decomposition of the augmented sparse repr...

Efficient Hessian computation using sparse matrix derivatives in RAM notation.

This article proposes a new, more efficient method to compute the minus two log likelihood, its gradient, and the Hessian for structural equation models (SEMs) in reticular action model (RAM) notation. The method exploits the beneficial aspect of RAM notation that the matrix derivatives used in RAM are sparse. For an SEM with K variables, P parameters, and P' entries in the symmetrical or asymm...