France

In this notebook we demonstrate the use of the Debiased Spatial Whittle for a simulated random field on an incomplete grid, where the sampling region follows the shape of the territory of France.

Imports¶

In [1]:

import matplotlib.pyplot as plt
import debiased_spatial_whittle.grids as grids
from debiased_spatial_whittle.models.spectral import SpectralMatern
from debiased_spatial_whittle.grids.base import RectangularGrid
from debiased_spatial_whittle.sampling.simulation import SamplerOnRectangularGrid
from debiased_spatial_whittle.inference.periodogram import Periodogram, ExpectedPeriodogram
from debiased_spatial_whittle.inference.likelihood import Estimator, DebiasedWhittle
from debiased_spatial_whittle.grids.old import ImgGrid

import matplotlib.pyplot as plt import debiased_spatial_whittle.grids as grids from debiased_spatial_whittle.models.spectral import SpectralMatern from debiased_spatial_whittle.grids.base import RectangularGrid from debiased_spatial_whittle.sampling.simulation import SamplerOnRectangularGrid from debiased_spatial_whittle.inference.periodogram import Periodogram, ExpectedPeriodogram from debiased_spatial_whittle.inference.likelihood import Estimator, DebiasedWhittle from debiased_spatial_whittle.grids.old import ImgGrid

Model specification¶

In [2]:

model = SpectralMatern(rho=15, nu=2.0)

model = SpectralMatern(rho=15, nu=2.0)

Grid specification¶

In [3]:

shape = (512, 512)
mask_france = ImgGrid(shape).get_new()
grid_france = RectangularGrid(shape)
grid_france.mask = mask_france
sampler = SamplerOnRectangularGrid(model, grid_france)

shape = (512, 512) mask_france = ImgGrid(shape).get_new() grid_france = RectangularGrid(shape) grid_france.mask = mask_france sampler = SamplerOnRectangularGrid(model, grid_france)

Sample generation¶

In [4]:

z = sampler()
plt.figure()
plt.imshow(z, origin="lower", cmap="RdBu")
plt.show()

z = sampler() plt.figure() plt.imshow(z, origin="lower", cmap="RdBu") plt.show()

Inference¶

In [5]:

periodogram = Periodogram()
expected_periodogram = ExpectedPeriodogram(grid_france, periodogram)
debiased_whittle = DebiasedWhittle(periodogram, expected_periodogram)
estimator = Estimator(debiased_whittle)

periodogram = Periodogram() expected_periodogram = ExpectedPeriodogram(grid_france, periodogram) debiased_whittle = DebiasedWhittle(periodogram, expected_periodogram) estimator = Estimator(debiased_whittle)

In [6]:

model_est = SpectralMatern()
model_est.set_param_bounds(dict(rho=(3, 50), nu=(0.5, 5)))
estimate = estimator(model_est, z, opt_callback=lambda *args, **kwargs: print(*args))
print(estimate.rho)

model_est = SpectralMatern() model_est.set_param_bounds(dict(rho=(3, 50), nu=(0.5, 5))) estimate = estimator(model_est, z, opt_callback=lambda *args, **kwargs: print(*args)) print(estimate.rho)

[3.24592493 1.36757938]

[4.74157839 3.04834872]

[5.20055131 3.32504723]

[6.56919315 4.09007361]

[7.51437093 4.5659791 ]

[8.36777361 4.94441327]

[8.81423446 5.        ]

[9.22093231 4.97680015]

[9.42353583 4.87206681]

[9.9745532  4.39907896]

[10.01102647  4.38519129]

[10.11990392  4.33835129]

[11.5052515  2.7119285]

[12.44472509  2.63883863]

[13.68623083  2.03775649]

[14.40644008  1.90505653]

[14.8940292   1.92169151]

[15.21248266  1.86917589]

[15.48589249  1.82989631]

[15.4850677   1.83311326]
15.485067703949477