3d exponential model

We simulate from a 3d exponential covariance model and estimate its parameters from the simulation

In [1]:

# ##Imports
import matplotlib.pyplot as plt
from IPython.display import HTML
from debiased_spatial_whittle.grids.base import RectangularGrid
from debiased_spatial_whittle.inference.likelihood import DebiasedWhittle, Estimator
from debiased_spatial_whittle.models.univariate import (
    SquaredExponentialModel,
    NuggetModel,
)
from debiased_spatial_whittle.inference.periodogram import Periodogram, ExpectedPeriodogram
from debiased_spatial_whittle.sampling.simulation import SamplerOnRectangularGrid
from debiased_spatial_whittle.utils import video_plot_3d

# ##Imports import matplotlib.pyplot as plt from IPython.display import HTML from debiased_spatial_whittle.grids.base import RectangularGrid from debiased_spatial_whittle.inference.likelihood import DebiasedWhittle, Estimator from debiased_spatial_whittle.models.univariate import ( SquaredExponentialModel, NuggetModel, ) from debiased_spatial_whittle.inference.periodogram import Periodogram, ExpectedPeriodogram from debiased_spatial_whittle.sampling.simulation import SamplerOnRectangularGrid from debiased_spatial_whittle.utils import video_plot_3d

Grid and model specification¶

In [2]:

n = (32, 32, 256)
grid = RectangularGrid(n)

n = (32, 32, 256) grid = RectangularGrid(n)

In [3]:

model = SquaredExponentialModel(rho=8.0, sigma=0.8)
model = NuggetModel(model, nugget=0.0001)
# ##Sample generation

model = SquaredExponentialModel(rho=8.0, sigma=0.8) model = NuggetModel(model, nugget=0.0001) # ##Sample generation

In [4]:

sampler = SamplerOnRectangularGrid(model, grid)
z = sampler()

sampler = SamplerOnRectangularGrid(model, grid) z = sampler()

-0.016607062739554056 666.8735239303197
up-sampling

In [5]:

anim = video_plot_3d(z, get_title=lambda i: "", cmap="Spectral")
plt.close()
HTML(anim.to_jshtml())

anim = video_plot_3d(z, get_title=lambda i: "", cmap="Spectral") plt.close() HTML(anim.to_jshtml())

Out[5]:

Once Loop Reflect

Inference¶

In [6]:

p = Periodogram()
ep = ExpectedPeriodogram(grid, p)
d = DebiasedWhittle(p, ep)
e = Estimator(d, use_gradients=False)

p = Periodogram() ep = ExpectedPeriodogram(grid, p) d = DebiasedWhittle(p, ep) e = Estimator(d, use_gradients=False)

In [7]:

model = SquaredExponentialModel(rho=2.0, sigma=1)
model = NuggetModel(model, nugget=0.0001)
model.fix_parameter("nugget")

model = SquaredExponentialModel(rho=2.0, sigma=1) model = NuggetModel(model, nugget=0.0001) model.fix_parameter("nugget")

In [8]:

def opt_callback(*args, **kargs):
    print(*args)
    print(**kargs)

def opt_callback(*args, **kargs): print(*args) print(**kargs)

In [9]:

print("start estimation")
e(model, z, opt_callback=opt_callback)

print("start estimation") e(model, z, opt_callback=opt_callback)

start estimation

[2.84883191 0.47133716]

[2.88744541 0.7520595 ]

[3.08774994 0.700794  ]

[3.90869887 0.56387576]

[4.38223006 0.61877257]

[5.98810485 0.69755237]

[7.23010894 0.73764452]

[8.19117583 0.75722208]

[8.46434364 0.75751357]

[8.5074994  0.75504699]

[8.50348011 0.75266892]

[8.49517128 0.75180883]

[8.49040147 0.75164232]

[8.49040146 0.75164232]

Out[9]:

NuggetModel()

Name	Value	Type	Range
nugget	0.0001	ModelParameter	read-only (0, 1)

SquaredExponentialModel()

Name	Value	Type	Range
rho	8.490401462049036	ModelParameter	(0, inf)
sigma	0.7516423193467396	ModelParameter	(0, inf)