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pymc.MvNormal — PyMC 5.25.1 documentation

class pymc.MvNormal(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, default_transform=UNSET, **kwargs)[source]#

Multivariate normal distribution.

\[f(x \mid \pi, T) = \frac{|T|^{1/2}}{(2\pi)^{k/2}} \exp\left\{ -\frac{1}{2} (x-\mu)^{\prime} T (x-\mu) \right\}\]

Parameters:

mutensor_like of float

Vector of means.

covtensor_like of float, optional

Covariance matrix. Exactly one of cov, tau, or chol is needed.

tautensor_like of float, optional

Precision matrix. Exactly one of cov, tau, or chol is needed.

choltensor_like of float, optional

Cholesky decomposition of covariance matrix. Exactly one of cov, tau, or chol is needed.

lower: bool, default=True

Whether chol is the lower tridiagonal cholesky factor.

Examples

Define a multivariate normal variable for a given covariance matrix:

cov = np.array([[1.0, 0.5], [0.5, 2]])
mu = np.zeros(2)
vals = pm.MvNormal("vals", mu=mu, cov=cov, shape=(5, 2))

Most of the time it is preferable to specify the cholesky factor of the covariance instead. For example, we could fit a multivariate outcome like this (see the docstring of LKJCholeskyCov for more information about this):

mu = np.zeros(3)
true_cov = np.array(
    [
        [1.0, 0.5, 0.1],
        [0.5, 2.0, 0.2],
        [0.1, 0.2, 1.0],
    ],
)
data = np.random.multivariate_normal(mu, true_cov, 10)

sd_dist = pm.Exponential.dist(1.0, shape=3)
chol, corr, stds = pm.LKJCholeskyCov(
    "chol_cov", n=3, eta=2, sd_dist=sd_dist, compute_corr=True
)
vals = pm.MvNormal("vals", mu=mu, chol=chol, observed=data)

For unobserved values it can be better to use a non-centered parametrization:

sd_dist = pm.Exponential.dist(1.0, shape=3)
chol, _, _ = pm.LKJCholeskyCov("chol_cov", n=3, eta=2, sd_dist=sd_dist, compute_corr=True)
vals_raw = pm.Normal("vals_raw", mu=0, sigma=1, shape=(5, 3))
vals = pm.Deterministic("vals", pt.dot(chol, vals_raw.T).T)

Methods

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