aleatory.processes.GPMatern

class aleatory.processes.GPMatern(length_scale=1.0, sigma=1.0, nu=1.5, T=1.0, rng=None)

Gaussian Process with Matern Kernel

Notes

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

\[K(t, s) = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \sqrt{2\nu} \frac{|t - s|}{l} \right)^\nu K_\nu\left( \sqrt{2\nu} \frac{|t - s|}{l} \right)\]

where \(l\) is the length scale parameter, \(\sigma\) is the scale parameter, \(\nu\) is the smoothness parameter, and \(K_{\nu}\) is the modified Bessel function of the second kind.

__init__(length_scale=1.0, sigma=1.0, nu=1.5, T=1.0, rng=None)

Methods

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