particles.distributions.MvNormal

class MvNormal(loc=0.0, scale=1.0, cov=None)[source]

Multivariate Normal distribution.

Parameters:

  • loc (ndarray) – location parameter (default: 0.)

  • scale (ndarray) – scale parameter (default: 1.)

  • cov ((d, d) ndarray) – covariance matrix (default: identity, with dim determined by loc)

Notes

The dimension d is determined either by argument cov (if it is a dxd array), or by argument loc (if cov is not specified). In the latter case, the covariance matrix is set to the identity matrix.

If scale is set to 1. (default value), we use the standard parametrisation of a Gaussian, with mean loc and covariance matrix cov. Otherwise:

x = dists.MvNormal(loc=m, scale=s, cov=Sigma).rvs(size=30)

is equivalent to:

x = m + s * dists.MvNormal(cov=Sigma).rvs(size=30)

The idea is that they are cases when we may want to pass varying means and scales (but a fixed correlation matrix). Note that cov does not need to be a correlation matrix; e.g.:

MvNormal(loc=m, scale=s, cov=C)

corresponds to N(m, diag(s)*C*diag(s)).

In addition, note that m and s may be (N, d) vectors; i.e for each n=1…N we have a different mean, and a different scale.

To specify a Multivariate Normal distribution with a different covariance matrix for each particle, see VaryingCovNormal.

__init__(loc=0.0, scale=1.0, cov=None)[source]

Methods

__init__([loc, scale, cov])

linear_transform(z)

logpdf(x)

pdf(x)

posterior(x[, Sigma])

Posterior for model: X1, ..., Xn ~ N(theta, Sigma), theta ~ self.

ppf(u)

Note: if dim(u) < self.dim, the remaining columns are filled with 0.

rvs([size])

shape(size)

Attributes

dim

int([x]) -> integer int(x, base=10) -> integer