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Multivariate Normal from Bijector¤

distreqx.distributions.mvn_from_bijector.MultivariateNormalFromBijector (AbstractMultivariateNormalFromBijector) ¤

Multivariate normal distribution on R^k.

The multivariate normal over x is characterized by an invertible affine transformation x = f(z) = A @ z + b, where z is a random variable that follows a standard multivariate normal on R^k, i.e., p(z) = N(0, I_k), A is a k x k transformation matrix, and b is a k-dimensional vector.

The resulting PDF on x is a multivariate normal, p(x) = N(b, C), where C = A @ A.T is the covariance matrix.

The transformation x = f(z) must be specified by a linear scale bijector implementing the operation A @ z and a shift (or location) term b.

__init__(self, loc: Array, scale: AbstractLinearBijector) ¤

Initializes the distribution.

Arguments:

  • loc: The term b, i.e., the mean of the multivariate normal distribution.
  • scale: The bijector specifying the linear transformation A @ z, as described in the class docstring.