density::GMRF_t< scalartype_ > Class Template Reference

Gaussian Markov Random Field. More...

#include <density.hpp>

Detailed Description

template<class scalartype_>
class density::GMRF_t< scalartype_ >

Gaussian Markov Random Field.

 Class to evaluate the negative log density of a mean zero multivariate 
 normal distribution with a sparse precision matrix. Let Q denote the 
 precision matrix. Then the density is proportional to
 |Q|^.5*exp(-.5*x'*Q*x)
 
 Three constructors are available:

 1. General case
 ===============
 The user supplies the precision matrix Q of class Eigen::SparseMatrix<Type> 
 
 2. Special case: GMRF on d-dimensional lattice.
 ===============================================
 The user supplies a d-dim lattice for which Q is automatically 
 constructed like this:
 First order Gaussian Markov Random Field on (subset of) d-dim grid.
 Grid is specified through the first array argument to constructor, 
 with individual nodes determined by the outdermost dimension 
 e.g. x= 1 1 2 2
         1 2 1 2
 corresponding to a 2x2 lattice with 4 nodes and d=2.

 Example of precision in 2D:

    -1
 -1 4+c -1
    -1

The precision Q is convolved with it self "order" times. This way
more smoothness can be obtained. The quadratic form contribution 
is .5*x'*Q^order*x

3. Vector of deltas
===================
The parameter "delta" describes the (inverse) correlation. It is
allowed to specify a vector of deltas so that different spatial 
regions can have different spatial correlation.

NOTE: The variance in the model depends on delta. In other words:
The model may be thought of as an arbitrary scaled correlation 
model and is thus not really meaningful without an additional scale
parameter (see SCALE_t and VECSCALE_t classes).

Definition at line 828 of file density.hpp.

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The documentation for this class was generated from the following file:

• density.hpp