constrlogLikGrad: Numerical Gradient of the Log-Constrained-Likelihood of a...
In lineqGPR: Gaussian Process Regression Models with Linear Inequality Constraints

Description Usage Arguments Details Value Comments Author(s) References See Also

Compute the gradient numerically of the negative log-constrained-likelihood of a Gaussian Process conditionally to the inequality constraints (Lopez-Lopera et al., 2018).

constrlogLikGrad(
  par = model$kernParam$par,
  model,
  parfixed = rep(FALSE, length(par)),
  mcmc.opts = list(probe = "Genz", nb.mcmc = 1000),
  estim.varnoise = FALSE
)

`par`	the values of the covariance parameters.
`model`	an object with class `lineqGP`.
`parfixed`	indices of fixed parameters to do not be optimised.
`mcmc.opts`	mcmc options. `mcmc.opts$probe` A character string corresponding to the estimator for the orthant multinormal probabilities. Options: `"Genz"` (Genz, 1992), `"ExpT"` (Botev, 2017). If `probe == "ExpT"`, `mcmc.opts$nb.mcmc` is the number of MCMC samples used for the estimation.
`estim.varnoise`	If `true`, a noise variance is estimated.

Orthant multinormal probabilities are estimated via (Genz, 1992; Botev, 2017).

The gradient of the negative log-constrained-likelihood.

As orthant multinormal probabilities don't have explicit expressions, the gradient is implemented numerically based on nl.grad.

A. F. Lopez-Lopera.

Lopez-Lopera, A. F., Bachoc, F., Durrande, N., and Roustant, O. (2018), "Finite-dimensional Gaussian approximation with linear inequality constraints". SIAM/ASA Journal on Uncertainty Quantification, 6(3): 1224-1255. [link]

Bachoc, F., Lagnoux, A., and Lopez-Lopera, A. F. (2018), "Maximum likelihood estimation for Gaussian processes under inequality constraints". ArXiv e-prints [link]

Genz, A. (1992), "Numerical computation of multivariate normal probabilities". Journal of Computational and Graphical Statistics, 1:141-150. [link]

Botev, Z. I. (2017), "The normal law under linear restrictions: simulation and estimation via minimax tilting". Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79(1):125-148. [link]

constrlogLikFun, logLikFun, logLikGrad

lineqGPR documentation built on Jan. 11, 2020, 9:23 a.m.