t = data.time
f = data.flux
d = 0.2
x = np.linspace(-6, 0, 10)
y = np.linspace(-1.0, 10, 12)
s2n = np.zeros((len(x), len(y)))
ll = np.zeros((len(x), len(y)))
delta_ll = np.zeros((len(x), len(y)))
for ix, a in enumerate(x):
for iy, l in enumerate(y):
gp = GaussianProcess([10 ** a, 10 ** l, 1e6])
gp.compute(data.time, data.ferr)
null = gp.lnlikelihood(f - 1.0)
results = []
for i, t0 in enumerate(t):
if np.abs(t0 - truth[2]) < 2*d:
continue
model = np.ones_like(f)
model[(t < t0+d) * (t > t0-d)] *= 1.0 - 0.0001
results.append((t0, gp.lnlikelihood(f - model)))
results = np.array(results)
model = np.ones_like(f)
model[(t < truth[2]+d) * (t > truth[2]-d)] *= 1.0 - 0.0001
ll_true = gp.lnlikelihood(f - model)
mu, std = np.mean(results[:, 1]), np.std(results[:, 1])
s2n[ix, iy] = (ll_true - mu) / std
ds.flux *= model
datasets.append(ds)
[pl.plot(ds.time, ds.flux, ".") for ds in datasets]
pl.savefig("data.png")
# Compute the Gaussian processes on the dataset.
gp = GaussianProcess([1e-3, 3.0, 10.])
gp.compute(dataset.time, dataset.ferr)
# Loop over true epochs.
d = 0.2
correct = []
incorrect = []
for t0, depth, duration, data in zip(t0s, depths, durations, datasets):
null = gp.lnlikelihood(data.flux - 1.0)
# Compute the correct model.
model = np.ones_like(data.time)
model[(data.time < t0+duration)*(data.time > t0-duration)] *= 1.0 - 0.0001
correct.append(gp.lnlikelihood(data.flux - model) - null)
for i, t in enumerate(data.time):
if np.abs(t0 - t) < 2*d:
continue
# Compute the test model.
model = np.ones_like(data.time)
model[(data.time < t+duration)*(data.time > t-duration)] *= 1-0.0001
incorrect.append(gp.lnlikelihood(data.flux - model) - null)
# Generate some fake data.
period = 0.956
x = 10 * np.sort(np.random.rand(75))
yerr = 0.1 + 0.1 * np.random.rand(len(x))
y = gp.sample_prior(x)
y += 0.8 * np.cos(2 * np.pi * x / period)
y += yerr * np.random.randn(len(yerr))
# Set up a periodic kernel.
pk = ExpSquaredKernel(np.sqrt(0.8), 1000.0) * CosineKernel(period)
kernel2 = kernel + pk
gp2 = GaussianProcess(kernel2)
# Condition on this data.
gp2.compute(x, yerr)
# Compute the log-likelihood.
print("Log likelihood = {0}".format(gp2.lnlikelihood(y)))
# Compute the conditional predictive distribution.
t = np.linspace(0, 10, 200)
f = gp2.sample_conditional(y, t, size=500)
mu = np.mean(f, axis=0)
std = np.std(f, axis=0)
pl.errorbar(x, y, yerr=yerr, fmt=".k")
pl.plot(t, mu, "k", lw=2, alpha=0.5)
pl.plot(t, mu+std, "k", alpha=0.5)
pl.plot(t, mu-std, "k", alpha=0.5)
pl.savefig("periodic.png")
