Generates data from a specific linear Gaussian state space model of the form \( x_{t} = \phi x_{t-1} + \sigma_v v_t \) and \( y_t = x_t + \sigma_e e_t \), where \(v_t\) and \(e_t\) denote independent standard Gaussian random variables, i.e. \(N(0,1)\).
generateData(phi, sigmav, sigmae, T, x0)The parameter \(\phi\) that scales the current state in the state dynamics. It is restricted to [-1,1] to obtain a stable model.
The standard deviation of the state process noise. Must be positive.
The standard deviation of the observation process noise. Must be positive.
The number of time points to simulate.
The initial state.
The function returns a list with the elements:
x: The latent state for \(t=0,...,T\).
y: The observation for \(t=0,...,T\).
Dahlin, J. & Schoen, T. B. "Getting started with particle Metropolis-Hastings for inference in nonlinear dynamical models." pre-print, arXiv:1511.01707, 2015.