approxSSM: Linear Gaussian Approximation for Non-Gaussian State Space...

In jrnold/KFAS: Kalman Filter and Smoother for Exponential Family State Space Models.

Description

Function approxSMM computes the linear Gaussian approximation of a state space model where the observations have a non-Gaussian exponential family distribution. Currently only Poisson and Binomial distributions are supported.

Usage

  approxSSM(object, theta = NULL, maxiter = 100)

Arguments

object	Non-Gaussian state space model object of class SSModel.
theta	Initial values for conditional mode theta. Default is log(mean(y/u)) for Poisson and log(mean(y/(u-y))) for Binomial distribution (or log(mean(y)) in case of u[t]-y[t] = 0 for some t).
maxiter	Maximum number of iterations used in linearisation. Default is 100.

Details

The linear Gaussian approximating model is a model defined by

ytilde[t] = Z[t]α[t] + ε[t], ε[t] ~ N(0,Htilde[t]),

α[t+1] = T[t]α[t] + R[t]η[t], η[t] ~ N(0,Q[t]),

and α[1] ~ N(a[1],P[1]), where ytilde and Htilde is chosen in a way that the linear Gaussian approximating model has the same conditional mode of θ=Zα given the observations y as the original non-Gaussian model. Models also have same curvature at the mode.

The linearization of the exponential family state space model is based on the first two derivatives of the observational logdensity.

The approximating Gaussian model is used in computation of the log-likelihood of the non-Gaussian model and in importance sampling of non-Gaussian model.

Value

An object which contains the approximating Gaussian state space model with additional components original.distribution, original.y, thetahat, and iterations (the number of iterations used).

See Also

Importance sampling of non-Gaussian state space models importanceSSM, construct a SSModel object SSModel.

jrnold/KFAS documentation built on May 19, 2019, 11:55 p.m.