Description Usage Arguments Value Examples

Takes in a square precision matrix, which ideally should be sparse and using Choleski factorization simulates data from a mean 0 process where the inverse of the precision matrix represents the variance-covariance of the points in the process. The resulting simulants represent samples of a Gaussian Markov random field (GMRF).

1 | ```
sim.AR(n, Q)
``` |

`n` |
int > 0, number of observations to simulate from the GMRF. |

`Q` |
matrix, a square precision matrix. |

Matrix object, matrix where each row is a single obsrevation from a GMRF with covariance structure Q^-1.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
require("ggplot2")
# simulate 2D ar1 process
# pairwise correlation
rho <- .95
# pairwise variance
sigma <- .5
# 2 dimensions of simulations
years <- 20
ages <- 10
# kronnecker product to get joint covariance
Q2D <- kronecker(Q.AR1(M=years, sigma, rho), Q.AR1(M=ages, sigma, rho))
# simulate the data and place it in a data frame
Q2D.df <- data.frame(obs=c(sim.AR(1, Q2D)), age=rep(1:ages, years),
year=rep(1:years, each=ages))
# graph results
ggplot(data=Q2D.df, aes(year, obs, group=age, color=age)) + geom_line()
``` |

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