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Priors for a GPMechanism's hyperparameters

Source: R/priors.R
gp_prior.Rd

Bundles the priors a GPMechanism places on its hyperparameters. All are on the standardised scale: before fitting, each parent and the node itself are centred and scaled to unit sd, so signal_sd = 1 means "functions vary about as much as the data", and a lengthscale of 1 means "the function changes over roughly one sd of the parent".

The defaults are log-uniform over exactly the box the type-II maximum likelihood search is bounded to. Maximising the likelihood inside that box is the same as finding the posterior mode under this prior, so the defaults make Kagu's implicit prior explicit without changing any fit. They are deliberately vague; see vignette("predictive_checks") for what they imply about the data and how to choose something more informative.

Root nodes (no parents) are modelled by a Normal; root_mean and root_sd are used for prior predictive simulation only - a root node's posterior uses a non-informative reference prior, which these weak priors barely differ from once there is any data.

Usage

gp_prior(
  lengthscale = prior_loguniform(exp(-3), exp(4)),
  signal_sd = prior_loguniform(exp(-2), exp(2)),
  noise_sd = prior_loguniform(exp(-3), exp(1)),
  root_mean = prior_normal(0, 1),
  root_sd = prior_lognormal(0, 0.5)
)

Arguments

lengthscale

Prior on each parent's kernel lengthscale.

signal_sd

Prior on the kernel signal sd (the function's scale).

noise_sd

Prior on the observation noise sd.

root_mean

Prior on a root node's (standardised) mean.

root_sd

Prior on a root node's (standardised) sd.

Value

A kagu_gp_prior object.

See also

prior_families, GPMechanism

Examples

gp_prior()   # the implicit default
#> <kagu_gp_prior> (standardised scale)
#>   lengthscale  loguniform(lower = 0.04979, upper = 54.6)
#>   signal_sd    loguniform(lower = 0.1353, upper = 7.389)
#>   noise_sd     loguniform(lower = 0.04979, upper = 2.718)
#>   root_mean    normal(mean = 0, sd = 1)
#>   root_sd      lognormal(meanlog = 0, sdlog = 0.5)

# Weakly informative: smooth functions, signal and noise on the data's scale
gp_prior(
  lengthscale = prior_lognormal(0, 0.5),
  signal_sd   = prior_halfnormal(1),
  noise_sd    = prior_halfnormal(1)
)
#> <kagu_gp_prior> (standardised scale)
#>   lengthscale  lognormal(meanlog = 0, sdlog = 0.5)
#>   signal_sd    halfnormal(scale = 1)
#>   noise_sd     halfnormal(scale = 1)
#>   root_mean    normal(mean = 0, sd = 1)
#>   root_sd      lognormal(meanlog = 0, sdlog = 0.5)