def test_calibrate_lrt_works_with_sampling(self):
m = 1
nfreq = 100
freq = np.linspace(1, 10, nfreq)
rng = np.random.RandomState(100)
noise = rng.exponential(size=nfreq)
model = models.Const1D()
model.amplitude = 2.0
p = model(freq)
power = noise * p
ps = Powerspectrum()
ps.freq = freq
ps.power = power
ps.m = m
ps.df = freq[1] - freq[0]
ps.norm = "leahy"
lpost = PSDPosterior(ps.freq, ps.power, model, m=1)
p_amplitude_1 = lambda amplitude: \
scipy.stats.norm(loc=2.0, scale=1.0).pdf(amplitude)
p_alpha_0 = lambda alpha: \
scipy.stats.uniform(0.0, 5.0).pdf(alpha)
p_amplitude_0 = lambda amplitude: \
scipy.stats.norm(loc=self.a2_mean, scale=self.a2_var).pdf(
amplitude)
priors = {"amplitude": p_amplitude_1}
priors2 = {
"amplitude_1": p_amplitude_1,
"amplitude_0": p_amplitude_0,
"alpha_0": p_alpha_0
}
lpost.logprior = set_logprior(lpost, priors)
model2 = models.PowerLaw1D() + models.Const1D()
model2.x_0_0.fixed = True
lpost2 = PSDPosterior(ps.freq, ps.power, model2, 1)
lpost2.logprior = set_logprior(lpost2, priors2)
pe = PSDParEst(ps)
with catch_warnings(RuntimeWarning):
pval = pe.calibrate_lrt(lpost, [2.0],
lpost2, [2.0, 1.0, 2.0],
sample=None,
max_post=True,
nsim=10,
nwalkers=10,
burnin=10,
niter=10,
seed=100)
assert pval > 0.001
def test_logprior_fails_without_prior(self):
lpost = PSDPosterior(self.ps.freq,
self.ps.power,
self.model,
m=self.ps.m)
with pytest.raises(AttributeError):
lpost.logprior([1])
def test_logprior(self):
t0 = [2.0]
lpost = PSDPosterior(self.ps, self.model)
lpost.logprior = set_logprior(lpost, self.priors)
lp_test = lpost.logprior(t0)
lp = np.log(scipy.stats.norm(2.0, 1.0).pdf(t0))
assert lp == lp_test
def test_logprior(self):
t0 = [2.0]
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
lp_test = lpost.logprior(t0)
lp = np.log(scipy.stats.norm(2.0, 1.0).pdf(t0))
assert lp == lp_test
def test_calibrate_lrt_works_with_sampling(self):
m = 1
nfreq = 10000
freq = np.linspace(1, 10, nfreq)
rng = np.random.RandomState(100)
noise = rng.exponential(size=nfreq)
model = models.Const1D()
model.amplitude = 2.0
p = model(freq)
power = noise * p
ps = Powerspectrum()
ps.freq = freq
ps.power = power
ps.m = m
ps.df = freq[1] - freq[0]
ps.norm = "leahy"
lpost = PSDPosterior(ps.freq, ps.power, model, m=1)
p_amplitude_1 = lambda amplitude: \
scipy.stats.norm(loc=2.0, scale=1.0).pdf(amplitude)
p_alpha_0 = lambda alpha: \
scipy.stats.uniform(0.0, 5.0).pdf(alpha)
p_amplitude_0 = lambda amplitude: \
scipy.stats.norm(loc=self.a2_mean, scale=self.a2_var).pdf(
amplitude)
priors = {"amplitude": p_amplitude_1}
priors2 = {"amplitude_1": p_amplitude_1,
"amplitude_0": p_amplitude_0,
"alpha_0": p_alpha_0}
lpost.logprior = set_logprior(lpost, priors)
model2 = models.PowerLaw1D() + models.Const1D()
model2.x_0_0.fixed = True
lpost2 = PSDPosterior(ps.freq, ps.power, model2, 1)
lpost2.logprior = set_logprior(lpost2, priors2)
pe = PSDParEst(ps)
pval = pe.calibrate_lrt(lpost, [2.0], lpost2,
[2.0, 1.0, 2.0], sample=None,
max_post=True, nsim=10, nwalkers=100,
burnin=100, niter=20,
seed=100)
assert pval > 0.001
def test_compute_highest_outlier_works(self):
mp_ind = 5
max_power = 1000.0
ps = Powerspectrum()
ps.freq = np.arange(10)
ps.power = np.ones_like(ps.freq)
ps.power[mp_ind] = max_power
ps.m = 1
ps.df = ps.freq[1]-ps.freq[0]
ps.norm = "leahy"
model = models.Const1D()
p_amplitude = lambda amplitude: \
scipy.stats.norm(loc=1.0, scale=1.0).pdf(
amplitude)
priors = {"amplitude": p_amplitude}
lpost = PSDPosterior(ps.freq, ps.power, model, 1)
lpost.logprior = set_logprior(lpost, priors)
pe = PSDParEst(ps)
res = pe.fit(lpost, [1.0])
res.mfit = np.ones_like(ps.freq)
max_y, max_x, max_ind = pe._compute_highest_outlier(lpost, res)
assert np.isclose(max_y[0], 2*max_power)
assert np.isclose(max_x[0], ps.freq[mp_ind])
assert max_ind == mp_ind
def test_making_posterior(self):
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
assert lpost.x.all() == self.ps.freq.all()
assert lpost.y.all() == self.ps.power.all()
def test_correct_number_of_parameters(self):
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
with pytest.raises(IncorrectParameterError):
lpost([2,3])
def test_correct_number_of_parameters(self):
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
with pytest.raises(IncorrectParameterError):
lpost([2,3])
def test_making_posterior(self):
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
assert lpost.x.all() == self.ps.freq.all()
assert lpost.y.all() == self.ps.power.all()
def test_compute_highest_outlier_works(self):
mp_ind = 5
max_power = 1000.0
ps = Powerspectrum()
ps.freq = np.arange(10)
ps.power = np.ones_like(ps.freq)
ps.power[mp_ind] = max_power
ps.m = 1
ps.df = ps.freq[1]-ps.freq[0]
ps.norm = "leahy"
model = models.Const1D()
p_amplitude = lambda amplitude: \
scipy.stats.norm(loc=1.0, scale=1.0).pdf(
amplitude)
priors = {"amplitude": p_amplitude}
lpost = PSDPosterior(ps.freq, ps.power, model, 1)
lpost.logprior = set_logprior(lpost, priors)
pe = PSDParEst(ps)
res = pe.fit(lpost, [1.0])
res.mfit = np.ones_like(ps.freq)
max_y, max_x, max_ind = pe._compute_highest_outlier(lpost, res)
assert np.isclose(max_y[0], 2*max_power)
assert np.isclose(max_x[0], ps.freq[mp_ind])
assert max_ind == mp_ind
def test_negative_loglikelihood(self):
t0 = [2.0]
m = self.model(self.ps.freq[1:], t0)
loglike = np.sum(self.ps.power[1:]/m + np.log(m))
lpost = PSDPosterior(self.ps, self.model)
lpost.logprior = set_logprior(lpost, self.priors)
loglike_test = lpost.loglikelihood(t0, neg=True)
assert np.isclose(loglike, loglike_test)
def test_counts_are_nan(self):
y = np.nan * np.ones_like(self.ps.freq)
ps_nan = copy.copy(self.ps)
ps_nan.power = np.nan*np.ones_like(self.ps.freq)
t0 = [2.0]
m = self.model(self.ps.freq[1:], t0)
lpost = PSDPosterior(ps_nan.freq, ps_nan.power, self.model)
lpost.logprior = set_logprior(lpost, self.priors)
assert np.isclose(lpost(t0), logmin, 1e-5)
def test_counts_are_nan(self):
y = np.nan * np.ones_like(self.ps.freq)
ps_nan = copy.copy(self.ps)
ps_nan.power = np.nan * np.ones_like(self.ps.freq)
t0 = [2.0]
m = self.model(self.ps.freq[1:], t0)
lpost = PSDPosterior(ps_nan.freq, ps_nan.power, self.model)
lpost.logprior = set_logprior(lpost, self.priors)
assert np.isclose(lpost(t0), logmin, 1e-5)
def test_negative_loglikelihood(self):
t0 = [2.0]
m = self.model(self.ps.freq[1:], t0)
loglike = np.sum(self.ps.power[1:]/m + np.log(m))
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
loglike_test = lpost.loglikelihood(t0, neg=True)
assert np.isclose(loglike, loglike_test)
def test_loglikelihood(self):
t0 = [2.0]
self.model.amplitude = t0[0]
mean_model = self.model(self.ps.freq)
loglike = -np.sum(np.log(mean_model)) - np.sum(self.ps.power/mean_model)
lpost = PSDPosterior(self.ps, self.model)
lpost.logprior = set_logprior(lpost, self.priors)
loglike_test = lpost.loglikelihood(t0, neg=False)
assert np.isclose(loglike, loglike_test)
def test_negative_posterior(self):
t0 = [2.0]
m = self.model(self.ps.freq[1:], t0)
lpost = PSDPosterior(self.ps, self.model)
lpost.logprior = set_logprior(lpost, self.priors)
post_test = lpost(t0, neg=True)
loglike = -np.sum(self.ps.power[1:]/m + np.log(m))
logprior = np.log(scipy.stats.norm(2.0, 1.0).pdf(t0))
post = -loglike - logprior
assert np.isclose(post_test, post, atol=1.e-10)
def test_negative_posterior(self):
t0 = [2.0]
m = self.model(self.ps.freq[1:], t0)
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
post_test = lpost(t0, neg=True)
loglike = -np.sum(self.ps.power[1:]/m + np.log(m))
logprior = np.log(scipy.stats.norm(2.0, 1.0).pdf(t0))
post = -loglike - logprior
assert np.isclose(post_test, post, atol=1.e-10)
def test_loglikelihood(self):
t0 = [2.0]
self.model.amplitude = t0[0]
mean_model = self.model(self.ps.freq)
loglike = -np.sum(np.log(mean_model)) - np.sum(self.ps.power/mean_model)
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
loglike_test = lpost.loglikelihood(t0, neg=False)
assert np.isclose(loglike, loglike_test)
def test_posterior(self):
t0 = [2.0]
self.model.amplitude = t0[0]
m = self.model(self.ps.freq[1:])
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
post_test = lpost(t0, neg=False)
loglike = -np.sum(self.ps.power[1:]/m + np.log(m))
logprior = np.log(scipy.stats.norm(2.0, 1.0).pdf(t0))
post = loglike + logprior
assert np.isclose(post_test, post, atol=1.e-10)
def test_negative_loglikelihood(self):
t0 = [2.0]
self.model.amplitude = t0[0]
mean_model = self.model(self.ps.freq)
loglike = 2.0 * self.m * (np.sum(np.log(mean_model)) + np.sum(
self.ps.power / mean_model) + np.sum(
(2.0 / (2. * self.m) - 1.0) * np.log(self.ps.power)))
lpost = PSDPosterior(self.ps, self.model)
lpost.logprior = set_logprior(lpost, self.priors)
loglike_test = lpost.loglikelihood(t0, neg=True)
assert np.isclose(loglike, loglike_test)
def test_negative_posterior(self):
t0 = [2.0]
self.model.amplitude = t0[0]
mean_model = self.model(self.ps.freq)
lpost = PSDPosterior(self.ps, self.model)
lpost.logprior = set_logprior(lpost, self.priors)
post_test = lpost(t0, neg=True)
loglike = -2.0 * self.m * (np.sum(np.log(mean_model)) + np.sum(
self.ps.power / mean_model) + np.sum(
(2.0 / (2. * self.m) - 1.0) * np.log(self.ps.power)))
logprior = np.log(scipy.stats.norm(2.0, 1.0).pdf(t0))
post = -loglike - logprior
assert np.isclose(post_test, post, atol=1.e-10)
def test_negative_loglikelihood(self):
t0 = [2.0]
self.model.amplitude = t0[0]
mean_model = self.model(self.ps.freq)
loglike = 2.0*self.m*(np.sum(np.log(mean_model)) +
np.sum(self.ps.power/mean_model) +
np.sum((2.0 / (2. * self.m) - 1.0) *
np.log(self.ps.power)))
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
loglike_test = lpost.loglikelihood(t0, neg=True)
assert np.isclose(loglike, loglike_test)
def test_calibrate_highest_outlier_works_with_sampling(self):
m = 1
nfreq = 100
seed = 100
freq = np.linspace(1, 10, nfreq)
rng = np.random.RandomState(seed)
noise = rng.exponential(size=nfreq)
model = models.Const1D()
model.amplitude = 2.0
p = model(freq)
power = noise * p
ps = Powerspectrum()
ps.freq = freq
ps.power = power
ps.m = m
ps.df = freq[1] - freq[0]
ps.norm = "leahy"
nsim = 5
lpost = PSDPosterior(ps.freq, ps.power, model, m=1)
p_amplitude = lambda amplitude: \
scipy.stats.norm(loc=1.0, scale=1.0).pdf(
amplitude)
priors = {"amplitude": p_amplitude}
lpost.logprior = set_logprior(lpost, priors)
pe = PSDParEst(ps)
with catch_warnings(RuntimeWarning):
pval = pe.calibrate_highest_outlier(lpost, [2.0],
sample=None,
max_post=True,
seed=seed,
nsim=nsim,
niter=10,
nwalkers=20,
burnin=10)
assert pval > 0.001
def test_negative_posterior(self):
t0 = [2.0]
self.model.amplitude = t0[0]
mean_model = self.model(self.ps.freq)
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
lpost.logprior = set_logprior(lpost, self.priors)
post_test = lpost(t0, neg=True)
loglike = -2.0*self.m*(np.sum(np.log(mean_model)) +
np.sum(self.ps.power/mean_model) +
np.sum((2.0 / (2. * self.m) - 1.0) *
np.log(self.ps.power)))
logprior = np.log(scipy.stats.norm(2.0, 1.0).pdf(t0))
post = -loglike - logprior
assert np.isclose(post_test, post, atol=1.e-10)
def test_calibrate_highest_outlier_works_with_sampling(self):
m = 1
nfreq = 100000
seed = 100
freq = np.linspace(1, 10, nfreq)
rng = np.random.RandomState(seed)
noise = rng.exponential(size=nfreq)
model = models.Const1D()
model.amplitude = 2.0
p = model(freq)
power = noise * p
ps = Powerspectrum()
ps.freq = freq
ps.power = power
ps.m = m
ps.df = freq[1] - freq[0]
ps.norm = "leahy"
nsim = 10
lpost = PSDPosterior(ps.freq, ps.power, model, m=1)
p_amplitude = lambda amplitude: \
scipy.stats.norm(loc=1.0, scale=1.0).pdf(
amplitude)
priors = {"amplitude": p_amplitude}
lpost.logprior = set_logprior(lpost, priors)
pe = PSDParEst(ps)
pval = pe.calibrate_highest_outlier(lpost, [2.0], sample=None,
max_post=True, seed=seed,
nsim=nsim, niter=20, nwalkers=100,
burnin=100)
assert pval > 0.001
def test_logprior_fails_without_prior(self):
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, m=self.ps.m)
with pytest.raises(AttributeError):
lpost.logprior([1])
def test_logprior_fails_without_prior(self):
lpost = PSDPosterior(self.ps, self.model)
with pytest.raises(AttributeError):
lpost.logprior([1])