# pymc.LKJCorr#

class pymc.LKJCorr(name, n, eta, *, return_matrix=False, **kwargs)[source]#

The LKJ (Lewandowski, Kurowicka and Joe) log-likelihood.

The LKJ distribution is a prior distribution for correlation matrices. If eta = 1 this corresponds to the uniform distribution over correlation matrices. For eta -> oo the LKJ prior approaches the identity matrix.

 Support Upper triangular matrix with values in [-1, 1]
Parameters:
n

Dimension of the covariance matrix (n > 1).

eta

The shape parameter (eta > 0) of the LKJ distribution. eta = 1 implies a uniform distribution of the correlation matrices; larger values put more weight on matrices with few correlations.

return_matrixbool, default=False

If True, returns the full correlation matrix. False only returns the values of the upper triangular matrix excluding diagonal in a single vector of length n(n-1)/2 for memory efficiency

Notes

This is mainly useful if you want the standard deviations to be fixed, as LKJCholsekyCov is optimized for the case where they come from a distribution.

References

[LKJ2009]

Lewandowski, D., Kurowicka, D. and Joe, H. (2009). “Generating random correlation matrices based on vines and extended onion method.” Journal of multivariate analysis, 100(9), pp.1989-2001.

Examples

```with pm.Model() as model:

# Define the vector of fixed standard deviations
sds = 3*np.ones(10)

corr = pm.LKJCorr(
'corr', eta=4, n=10, return_matrix=True
)

# Define a new MvNormal with the given correlation matrix
vals = sds*pm.MvNormal('vals', mu=np.zeros(10), cov=corr, shape=10)

# Or transform an uncorrelated normal distribution:
vals_raw = pm.Normal('vals_raw', shape=10)
chol = pt.linalg.cholesky(corr)
vals = sds*pt.dot(chol,vals_raw)

# The matrix is internally still sampled as a upper triangular vector
 `LKJCorr.dist`(n, eta, *[, return_matrix])