Cluster-level inference (Gaussian)

Cluster-level inference refers to the probability that 1D Gaussian fields will produce an upcrossing with an extent of k when thresholded at a value u. This probability pertains to specific upcrossings. The basic procedure for RFT validations is outlined in Examples/Basic/Validating. Only code details are provided below.

See also ./rft1d/examples/val_upx_0_gauss_cluster.py

import numpy as np
from matplotlib import pyplot
import rft1d

eps        = np.finfo(float).eps   #smallest float

#(0) Test on one random field:
np.random.seed(0)
nResponses   = 2000
nNodes       = 101
FWHM         = 10.0
interp       = True
wrap         = True
heights      = [2.2, 2.4, 2.6, 2.8]
### generate data:
y            = rft1d.randn1d(nResponses, nNodes, FWHM)
calc         = rft1d.geom.ClusterMetricCalculator()
rftcalc      = rft1d.prob.RFTCalculator(STAT='Z', nodes=nNodes, FWHM=FWHM)

#(1) Maximum region size:
K0      = np.linspace(eps, 15, 21)
K       = np.array([[calc.max_cluster_extent(yy, h, interp, wrap)   for yy in y]  for h in heights])
P       = np.array([(K>=k0).mean(axis=1)  for k0 in K0]).T
P0      = np.array([[rftcalc.p.cluster(k0, h)  for k0 in K0/FWHM]  for h in heights])

#(2) Plot results:
pyplot.close('all')
colors  = ['b', 'g', 'r', 'orange']
labels  = ['u = %.1f'%h for h in heights]
ax      = pyplot.axes()
for color,p,p0,label in zip(colors,P,P0,labels):
        ax.plot(K0, p,  'o', color=color)
        ax.plot(K0, p0, '-', color=color, label=label)
ax.plot([0,1],[10,10], 'k-', label='Theoretical')
ax.plot([0,1],[10,10], 'ko-', label='Simulated')
ax.legend()
ax.set_xlabel('$x$', size=20)
ax.set_ylabel('$P(k_{max}) > x$', size=20)
ax.set_ylim(0, 0.25)
ax.set_title('Upcrossing extent validations (Gaussian fields)', size=20)
pyplot.show()

(Source code, png, hires.png, pdf)