aleatory.processes.GPRBF#

class aleatory.processes.GPRBF(length_scale=1.0, sigma=1.0, T=1.0, rng=None)[source]#

Gaussian Process with Radial Basis Function (RBF) Kernel#

A Gaussian Process with RBF kernel is a centered Gaussian Process with covariance function given by

\[K(t, s) = \sigma^2 \exp\left(-\frac{(t - s)^2}{2l^2}\right)\]

where \(l\) is the length scale parameter and \(\sigma\) is the scale parameter.

Notes#

Examples#

from aleatory.processes import GPRBF
process = GPRBF(length_scale=0.3, sigma=1.0, T=1.0)
fig = process.plot_paths_and_kernel(n=100, N=5, matrix_shape=True)
fig.show()

from aleatory.processes import GPRBF
process = GPRBF(length_scale=0.3, sigma=1.0, T=1.0)
fig = process.draw(n=100, N=200, figsize=(12, 7))
fig.show()
__init__(length_scale=1.0, sigma=1.0, T=1.0, rng=None)[source]#
Parameters:

  • length_scale (double) – the length scale parameter \(l\) in the above covariance function

  • sigma (double) – the scale parameter \(\sigma\) in the above covariance function

  • T (double) – the endpoint of the time interval \([0,T]\) over which the process is defined

  • rng – random number generator for reproducibility

Methods

__init__([length_scale, sigma, T, rng])

param double length_scale:

the length scale parameter \(l\) in the above covariance function

covariance_function(times)

draw(n, N[, T, marginal, envelope, type, title])

Simulates and plots paths/trajectories from the instanced stochastic process.

estimate_covariances([times])

estimate_expectations()

estimate_quantiles(q)

estimate_stds()

estimate_variances()

get_marginal(time)

make_widget([cmap, matrix_shape])

marginal_expectation([times])

marginal_stds([times])

marginal_variance([times])

plot(n, N[, T, title, suptitle])

Simulates and plots paths/trajectories from the instanced stochastic process.

plot_covariance([times, colormap, ...])

plot_kernel([times, colormap, matrix_shape, ...])

plot_kernel3d([times, title])

plot_mean_function([T, n])

plot_mean_variance([times])

plot_paths_and_kernel(n, N[, T, cmap, ...])

Plots the paths of the process and the covariance kernel.

process_covariance([times])

process_expectation()

process_stds()

process_variance()

sample(n[, T])

sample_at(times)

simulate(n, N[, T])

Simulate paths/trajectories from the instanced stochastic process.

variance_function(times)

Attributes

T

End time of the process.

rng