# bayespy.nodes.GaussianMarkovChain¶

class bayespy.nodes.GaussianMarkovChain(mu, Lambda, A, nu, n=None, inputs=None, **kwargs)[source]

Node for Gaussian Markov chain random variables.

In a simple case, the graphical model can be presented as:

where and are the mean and the precision matrix of the initial state, is the state dynamics matrix and is the precision of the innovation noise. It is possible that and/or are different for each transition instead of being constant.

The probability distribution is

where

Parameters: mu : Gaussian-like node or (…,D)-array , mean of , -dimensional with plates (…) Lambda : Wishart-like node or (…,D,D)-array , precision matrix of , -dimensional with plates (…) A : Gaussian-like node or (D,D)-array or (…,1,D,D)-array or (…,N-1,D,D)-array , state dynamics matrix, -dimensional with plates (D,) or (…,1,D) or (…,N-1,D) nu : gamma-like node or (D,)-array or (…,1,D)-array or (…,N-1,D)-array , diagonal elements of the precision of the innovation process, plates (D,) or (…,1,D) or (…,N-1,D) n : int, optional , the length of the chain. Must be given if and are constant over time.
__init__(mu, Lambda, A, nu, n=None, inputs=None, **kwargs)[source]

Create GaussianMarkovChain node.

Methods