Simulate an Entire Observed Dataset from a Randomly Generated Function

This function automates the process of generating a random underlying function (of various types) and then sampling noisy observations from it, returning a complete simulated dataset.

simulate_process(
  x = NULL,
  n_basis = 50,
  sd_fun = 1,
  sd = 0.1,
  sd_poly = 0.1,
  type = c("linear", "nonlinear", "quadratic", "nondynamic"),
  p = 1,
  pred_step = 16,
  normalize = FALSE
)

Arguments

x

A numeric vector specifying the grid points where the function is evaluated.

n_basis

An integer specifying the number of basis functions (for "nonlinear" type).

sd_fun

A numeric value controlling the smoothness of the function under the IWP prior.

sd

A numeric value or vector specifying the standard deviation(s) of observation noise.

sd_poly

A numeric value specifying the standard deviation for polynomial coefficients.

type

A character string specifying the type of function to simulate. One of "linear", "quadratic", "nonlinear", or "nondynamic".

p

An integer specifying the order of the polynomial trend in the nonlinear model.

pred_step

A numeric value representing the resolution parameter for scaling the IWP precision.

normalize

A logical value indicating whether to rescale the function to roughly zero mean and unit range.

Value

A data frame containing:

x

Grid points where the function is evaluated.

y

Noisy observed values.

truef

True underlying function values at each x.

sd

Noise standard deviation used at each point.

Examples

dat <- simulate_process(type = "nonlinear")
plot(dat$x, dat$y)