predict.fmou,fmou-method: Prediction and uncertainty quantification on the future...

In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

Prediction and uncertainty quantification on the future observations using a FMOU model.

Description

This function predicts the future observations using a FMOU model. Uncertainty quantification is available.

Usage

## S4 method for signature 'fmou'
predict.fmou(object, param_est, step=1, interval=FALSE, interval_data=TRUE)

Arguments

object	an objecft of class fmou.
param_est	estimated parameters in the FMOU model. Obtained by the results of fit.fmou().
step	a vector. Number of steps to be predicted. Default is 1.
interval	a bool value, default is FALSE. If TRUE, the 95% predictive intervals are computed.
interval_data	a bool value, default is TRUE. If TRUE, the 95% predictive intervals of the observations are computed. Otherwise, the 95% predictive intervals of the mean of the observation are computed.

Value

pred_mean	the predictive mean.
pred_interval_95lb	the 95% lower bound of the interval.
pred_interval_95ub	the 95% upper bound of the interval.

Author(s)

Mengyang Gu [aut, cre], Xinyi Fang [aut], Yizi Lin [aut]

Maintainer: Mengyang Gu <[e-mail]>

References

Lin, Y., Liu, X., Segall, P., & Gu, M. (2025). Fast data inversion for high-dimensional dynamical systems from noisy measurements. arXiv preprint arXiv:2501.01324.

Examples

## generate simulated data
library(FastGaSP)
library(rstiefel)

d = 5  # number of latent factors
k = 20 # length of observation at each time step
n = 500 # number time step
noise_level = 1 # variance of noise

U = rustiefel(k, k) # factor loading matrix
z = matrix(NA, d, n)
sigma_2 = runif(d, 0.5, 1)
rho = runif(d, 0.95, 1)
for(l in 1:d){
  R = matrix(NA, n, n)
  diag(R) = 1
  for(ir in 1:n){
    for(ic in 1:n){
      R[ir, ic] = rho[l]^(abs(ir-ic)) * R[ir, ir]
    }
  }
  R = (sigma_2[l]/(1-rho[l]^2) )* R
  z[l, ] = t(chol(R)) %*% rnorm(n)
}

signal = U[,1:d] %*% z
y = signal + matrix(rnorm(n*k,mean=0,sd=sqrt(noise_level)),k,n)

##constucting the fmou.model
fmou.model=fmou(output=y, d=d, est_U0=TRUE, est_sigma0_2=TRUE)

## estimate the parameters
em_alg <- fit.fmou(fmou.model, M=500)

## two-step-ahead prediction
pred_2step <- predict.fmou(fmou.model,em_alg, step=c(1:2))

FastGaSP documentation built on April 4, 2025, 5:16 a.m.