def deriv(Q, R, dR=None, width=5, degree=2):
from bumps.wsolve import wpolyfit
d = numpy.empty_like(Q)
if dR is None: dR = numpy.ones_like(Q)
k = (width - 1) / 2
p = wpolyfit(Q[:width], R[:width], dy=dR[:width], degree=degree)
d[:k + 1] = p.der(Q[:k + 1])
for i in range(k + 1, len(Q) - k - 1):
idx = slice(i - k, i + k + 1)
p = wpolyfit(Q[idx], R[idx], dy=dR[idx], degree=degree)
d[i] = p.der(Q[i])
p = wpolyfit(Q[-width:], R[-width:], dy=dR[-width:], degree=degree)
d[-k - 1:] = p.der(Q[-k - 1:])
return d
def deriv(Q, R, dR=None, width=5, degree=2):
from bumps.wsolve import wpolyfit
d = np.empty_like(Q)
if dR is None:
dR = np.ones_like(Q)
k = (width-1)/2
p = wpolyfit(Q[:width], R[:width], dy=dR[:width], degree=degree)
d[:k+1] = p.der(Q[:k+1])
for i in range(k+1, len(Q)-k-1):
idx = slice(i-k, i+k+1)
p = wpolyfit(Q[idx], R[idx], dy=dR[idx], degree=degree)
d[i] = p.der(Q[i])
p = wpolyfit(Q[-width:], R[-width:], dy=dR[-width:], degree=degree)
d[-k-1:] = p.der(Q[-k-1:])
return d
def plot_logp(state, portion=None):
from pylab import axes, title
from scipy.stats import chi2, kstest
from matplotlib.ticker import NullFormatter
# Plot log likelihoods
draw, logp = state.logp()
start = int((1 - portion) * len(draw)) if portion else 0
genid = arange(state.generation - len(draw) + start, state.generation) + 1
width, height, margin, delta = 0.7, 0.75, 0.1, 0.01
trace = axes([margin, 0.1, width, height])
trace.plot(genid, logp[start:], ',', markersize=1)
trace.set_xlabel('Generation number')
trace.set_ylabel('Log likelihood at x[k]')
title('Log Likelihood History')
# Plot log likelihood trend line
from bumps.wsolve import wpolyfit
from .formatnum import format_uncertainty
x = np.arange(start, logp.shape[0]) + state.generation - state.Ngen + 1
y = np.mean(logp[start:], axis=1)
dy = np.std(logp[start:], axis=1, ddof=1)
p = wpolyfit(x, y, dy=dy, degree=1)
px, dpx = p.ci(x, 1.)
trace.plot(x, px, 'k-', x, px + dpx, 'k-.', x, px - dpx, 'k-.')
trace.text(x[0],
y[0],
"slope=" + format_uncertainty(p.coeff[0], p.std[0]),
va='top',
ha='left')
# Plot long likelihood histogram
data = logp[start:].flatten()
hist = axes(
[margin + width + delta, 0.1, 1 - 2 * margin - width - delta, height])
hist.hist(data, bins=40, orientation='horizontal', density=True)
hist.set_ylim(trace.get_ylim())
null_formatter = NullFormatter()
hist.xaxis.set_major_formatter(null_formatter)
hist.yaxis.set_major_formatter(null_formatter)
# Plot chisq fit to log likelihood histogram
float_df, loc, scale = chi2.fit(-data, f0=state.Nvar)
df = int(float_df + 0.5)
pval = kstest(-data, lambda x: chi2.cdf(x, df, loc, scale))
#with open("/tmp/chi", "a") as fd:
# print("chi2 pars for llf", float_df, loc, scale, pval, file=fd)
xmin, xmax = trace.get_ylim()
x = np.linspace(xmin, xmax, 200)
hist.plot(chi2.pdf(-x, df, loc, scale), x, 'r')
bounds = (-20, -inf), (40, inf)
sigma = 1
data = fn((1, 1)) + randn(*x.shape) * sigma # Fake data
# Sample from the posterior density function
n = 2
model = Simulation(
f=fn, data=data, sigma=sigma, bounds=bounds, labels=["x", "y"])
sampler = Dream(
model=model,
population=randn(5 * n, 4, n),
thinning=1,
draws=20000,
)
mc = sampler.sample()
mc.title = 'Strong anti-correlation'
# Create a derived parameter without the correlation
mc.derive_vars(lambda p: (p[0] + p[1]), labels=['x+y'])
# Compare the MCMC estimate for the derived parameter to a least squares fit
from bumps.wsolve import wpolyfit
poly = wpolyfit(x, data, degree=1, origin=True)
print("x+y from linear fit", poly.coeff[0], poly.std[0])
points, logp = mc.sample(portion=0.5)
print("x+y from MCMC", mean(points[:, 2]), std(points[:, 2], ddof=1))
# Plot the samples
plot_all(mc, portion=0.5)
show()
# Sample from the posterior density function
n = 2
model = Simulation(f=fn,
data=data,
sigma=sigma,
bounds=bounds,
labels=["x", "y"])
sampler = Dream(
model=model,
population=randn(5 * n, 4, n),
thinning=1,
draws=20000,
)
mc = sampler.sample()
mc.title = 'Strong anti-correlation'
# Create a derived parameter without the correlation
mc.derive_vars(lambda p: (p[0] + p[1]), labels=['x+y'])
# Compare the MCMC estimate for the derived parameter to a least squares fit
from bumps.wsolve import wpolyfit
poly = wpolyfit(x, data, degree=1, origin=True)
print("x+y from linear fit", poly.coeff[0], poly.std[0])
points, logp = mc.sample(portion=0.5)
print("x+y from MCMC", mean(points[:, 2]), std(points[:, 2], ddof=1))
# Plot the samples
plot_all(mc, portion=0.5)
show()
