def exact_likelihood(self, theta, x):
kappa, mu, sigma = theta
e = exp( - kappa * self.h )
c = 2 * kappa / sigma ** 2 / (1 - e)
q = 2 * kappa * mu / sigma ** 2 - 1
v = 2 * c * x[1:]
df = 2 * (q + 1)
nc = 2 * c * x[:-1] * e
l = ncx2.logpdf(v, df, nc) + log(2 * c)
return - l[np.isfinite(l)].mean()
def mle_cir(params):
global rates, dt
K, theta, sigma = params
r0_vector = rates[0:rates.shape[0] - 1]
r1_vector = rates[1:]
c = 2 * K / ((1 - np.exp(-K * dt)) * sigma**2)
nc = 2 * c * r0_vector.values * np.exp(-K * dt)
df = 4 * theta / (K * sigma**2)
lik = ncx2.logpdf(2 * r1_vector.values * c, df, nc) + np.log(2 * c)
likelihood = pd.Series(lik).sum()
return -likelihood
def signalData_lnpdf(x, alpha=__alpha, beta=__beta, num_mc=__num_mc, **kwargs):
"""
evaluate the signal probability density function at x
this is done by monte carlo sampling from p(y|alpha, beta) and approximating the integral of ncx2.pdf(x, __noise_df, y)
"""
y = np.outer(__draw_truncatedPareto(Nsamp=num_mc, alpha=alpha, beta=beta), np.ones_like(x)) ### draw monte carlo samples from p(y|alpha, beta)
x = np.outer(np.ones(num_mc), x)
ans = ncx2.logpdf(x, __noise_df, y)
### FIXME:
### there is a wrapping problem with calls to scipy.stats.ncx2 when the parameters get really big
### pragmatically, this seems to happen when y >> x, but it also happens when x~y>>1
### until we can find a better solution, we will simply set any positive values to -infty so they are negligible within __logaddexp
### this should be the correct thing when y>>x, which we think is mostly what happens
ans[ans>0] = -np.infty
return __logaddexp(ans) - np.log(num_mc)
def lnlike(theta, data, psd):
"""
The log-likelihood. Non-central chiquared with 2 dof, noncentrality given
by the template
"""
inband = (pca_result.sample_frequencies>1000)*(pca_result<4000)
# Construct the template (non-centrality), normalised by the noise variance
template = PCtemplatePSD(theta)[inband] / psd[inband]
# Normalise by the noise variance
data_normed = data[inband] / psd[inband]
# likelihood of each frequency
lnlikelihoods = ncx2.logpdf(data_normed, 2, template)
return sum(lnlikelihoods)
loss = float(loss / len(p_dists))
mds_stress = (stress(debug_D_squareform, mu)
if debug_D_squareform is not None else 0.0)
all_loss.append(loss)
mlflow.log_metric("loss", loss)
mlflow.log_metric("stress", mds_stress)
print(
f"[DEBUG] epoch {epoch}, loss: {loss:.2f}, stress: {mds_stress:,.2f}"
# f" mu in [{float(jnp.min(mu)):.3f}, {float(jnp.max(mu)):.3f}], "
# f" ss_unc in [{float(jnp.min(ss_unc)):.3f}, {float(jnp.max(ss_unc)):.3f}]"
)
ss = EPSILON + jax.nn.softplus(SCALE * ss_unc)
print("[DEBUG] mean ss: ", float(jnp.mean(ss)))
mlflow.log_metric("mean_ss", float(jnp.mean(ss)))
return mu, ss, all_loss
if __name__ == "__main__":
from scipy.stats import ncx2
# compare jax ncx2_log_pdf with scipy
df, nc = 2, 1.06
x = np.array([20.0])
v1 = ncx2.logpdf(x, df, nc)
v2 = _ncx2_log_pdf(x, nc)
print(f"scipy: {v1[0]:.5f}")
print(f"jax : {v2[0]:.5f}")