getting-started

library(greta.gp)
#> Loading required package: greta
#> 
#> Attaching package: 'greta'
#> The following objects are masked from 'package:stats':
#> 
#>     binomial, cov2cor, poisson
#> The following objects are masked from 'package:base':
#> 
#>     %*%, apply, backsolve, beta, chol2inv, colMeans, colSums, diag,
#>     eigen, forwardsolve, gamma, identity, rowMeans, rowSums, sweep,
#>     tapply

Gaussian processes in greta

greta.gp extends greta to let you define Gaussian processes as part of your model. It provides a syntax to create and combine GP kernels, and use them to define either full rank or sparse Gaussian processes.

Example

# simulate data
x <- runif(20, 0, 10)
y <- sin(x) + rnorm(20, 0, 0.5)
x_plot <- seq(-1, 11, length.out = 200)

library(greta)
library(greta.gp)

# hyperparameters
rbf_var <- lognormal(0, 1)
rbf_len <- lognormal(0, 1)
obs_sd <- lognormal(0, 1)

# kernel & GP
kernel <- rbf(rbf_len, rbf_var) + bias(1)
f <- gp(x, kernel)

# likelihood
distribution(y) <- normal(f, obs_sd)

# prediction
f_plot <- project(f, x_plot)

# fit the model by Hamiltonian Monte Carlo
m <- model(f_plot)
draws <- mcmc(m)

# plot 200 posterior samples
plot(
  y ~ x,
  pch = 16,
  col = grey(0.4),
  xlim = c(0, 10),
  ylim = c(-2.5, 2.5),
  las = 1,
  fg = grey(0.7),
)

for (i in 1:200) {
  lines(
    draws[[1]][i, ] ~ x_plot,
    lwd = 2,
    col = rgb(0.7, 0.1, 0.4, 0.1)
  )
}