def test_logsumexpinf():
np.random.seed(0)
a = np.random.rand(10)
b = np.random.rand(10)
assert logsumexp(-np.inf, b=[-np.inf]) == -np.inf
assert logsumexp(a, b=b) == sp.logsumexp(a, b=b)
a[0] = -np.inf
assert logsumexp(a, b=b) == sp.logsumexp(a, b=b)
b[0] = -np.inf
with warnings.catch_warnings():
warnings.filterwarnings('ignore',
'invalid value encountered in multiply',
RuntimeWarning)
assert np.isnan(sp.logsumexp(a, b=b))
assert np.isfinite(logsumexp(a, b=b))
def dlogX(self, nsamples=None):
"""Compute volume of shell of loglikelihood.
Parameters
----------
nsamples: int, optional
Number of samples to generate. optional. If None, then compute the
statistical average. If integer, generate samples from the
distribution. (Default: None)
"""
if np.ndim(nsamples) > 0:
return nsamples
elif nsamples is None:
t = np.log(self.nlive / (self.nlive + 1)).to_frame()
else:
r = np.log(np.random.rand(len(self), nsamples))
t = pandas.DataFrame(r, self.index).divide(self.nlive, axis=0)
logX = t.cumsum()
logXp = logX.shift(1, fill_value=0)
logXm = logX.shift(-1, fill_value=-np.inf)
dlogX = logsumexp(
[logXp.to_numpy(), logXm.to_numpy()],
b=[np.ones_like(logXp), -np.ones_like(logXm)],
axis=0) - np.log(2)
if nsamples is None:
dlogX = np.squeeze(dlogX)
return WeightedSeries(dlogX, self.index, weights=self.weights)
else:
return WeightedDataFrame(dlogX, self.index, weights=self.weights)
def logZ(self, nsamples=None):
"""Log-Evidence.
- If nsamples is not supplied, return mean log evidence
- If nsamples is integer, return nsamples from the distribution
- If nsamples is array, use nsamples as volumes of evidence shells
"""
dlogX = self.dlogX(nsamples)
logw = dlogX.add(self.beta * self.logL, axis=0)
return logsumexp(logw, axis=0)
def merge_samples_weighted(samples, weights=None):
r"""Merge sets of samples with weights.
Combine two (or more) samples so the new PDF is
P(x|new) = weight_A P(x|A) + weight_B P(x|B).
The number of samples and internal weights do not affect the result.
Parameters
----------
samples: list(NestedSamples) or list(MCMCSamples)
List or array-like of one or more MCMC or nested sampling runs.
weights: list(double) or None
Weight for each run in samples (normalized internally).
Can be omitted if samples are NestedSamples,
then exp(logZ) is used as weight.
Returns
-------
new_samples: MCMCSamples
Merged (weighted) run.
"""
if not isinstance(samples, Sequence):
raise TypeError("samples must be a Sequence (list of samples).")
mcmc_samples = copy.deepcopy([MCMCSamples(s) for s in samples])
if weights is None:
try:
logZs = np.array(copy.deepcopy([s.logZ() for s in samples]))
except AttributeError:
raise ValueError("If samples includes MCMCSamples "
"then weights must be given.")
# Subtract logsumexp to avoid numerical issues (similar to max(logZs))
logZs -= logsumexp(logZs)
weights = np.exp(logZs)
else:
if len(weights) != len(samples):
raise ValueError(
"samples and weights must have the same length,"
"each weight is for a whole sample. Currently", len(samples),
len(weights))
new_samples = MCMCSamples()
for s, w in zip(mcmc_samples, weights):
# Normalize the given weights
new_weights = s.weights / s.weights.sum() * w / np.sum(weights)
s = MCMCSamples(s, weights=new_weights)
new_samples = new_samples.append(s)
new_samples.weights /= new_samples.weights.max()
return new_samples
def D(self, nsamples=None):
"""Kullback-Leibler divergence.
- If nsamples is not supplied, return mean KL divergence
- If nsamples is integer, return nsamples from the distribution
- If nsamples is array, use nsamples as volumes of evidence shells
"""
dlogX = self.dlogX(nsamples)
logZ = self.logZ(dlogX)
logw = dlogX.add(self.beta * self.logL, axis=0) - logZ
S = (dlogX * 0).add(self.beta * self.logL, axis=0) - logZ
return np.exp(logsumexp(logw, b=S, axis=0))
def ns_output(self, nsamples=200):
"""Compute Bayesian global quantities.
Using nested sampling we can compute the evidence (logZ),
Kullback-Leibler divergence (D) and Bayesian model dimensionality (d).
More precisely, we can infer these quantities via their probability
distribution.
Parameters
----------
nsamples: int, optional
number of samples to generate (Default: 100)
Returns
-------
pandas.DataFrame
Samples from the P(logZ, D, d) distribution
"""
dlogX = self.dlogX(nsamples)
samples = MCMCSamples(index=dlogX.columns)
samples['logZ'] = self.logZ(dlogX)
logw = dlogX.add(self.beta * self.logL, axis=0)
logw -= samples.logZ
S = (dlogX * 0).add(self.beta * self.logL, axis=0) - samples.logZ
samples['D'] = np.exp(logsumexp(logw, b=S, axis=0))
samples['d'] = np.exp(logsumexp(logw, b=(S - samples.D)**2,
axis=0)) * 2
samples.tex = {
'logZ': r'$\log\mathcal{Z}$',
'D': r'$\mathcal{D}$',
'd': r'$d$'
}
samples.label = self.label
return samples
def d(self, nsamples=None):
"""Bayesian model dimensionality.
- If nsamples is not supplied, return mean BMD
- If nsamples is integer, return nsamples from the distribution
- If nsamples is array, use nsamples as volumes of evidence shells
"""
dlogX = self.dlogX(nsamples)
logZ = self.logZ(dlogX)
D = self.D(dlogX)
logw = dlogX.add(self.beta * self.logL, axis=0) - logZ
S = (dlogX * 0).add(self.beta * self.logL, axis=0) - logZ
return np.exp(logsumexp(logw, b=(S - D)**2, axis=0)) * 2
def dlogX(self, nsamples=None):
"""Compute volume of shell of loglikelihood.
Parameters
----------
nsamples: int, optional
Number of samples to generate. optional. If None, then compute the
statistical average. If integer, generate samples from the
distribution. (Default: None)
"""
logX = self.logX(nsamples)
logXp = logX.shift(1, fill_value=0)
logXm = logX.shift(-1, fill_value=-np.inf)
dlogX = logsumexp([logXp.values, logXm.values],
b=[np.ones_like(logXp), -np.ones_like(logXm)],
axis=0) - np.log(2)
if nsamples is None:
dlogX = np.squeeze(dlogX)
return WeightedSeries(dlogX, self.index, weights=self.weights)
else:
return WeightedDataFrame(dlogX, self.index, weights=self.weights)
