def dic(self):
r""" Returns the corrected Deviance Information Criterion (DIC) for all chains loaded into ChainConsumer.
If a chain does not have a posterior, this method will return `None` for that chain. **Note that
the DIC metric is only valid on posterior surfaces which closely resemble multivariate normals!**
Formally, we follow Liddle (2007) and first define *Bayesian complexity* as
.. math::
p_D = \bar{D}(\theta) - D(\bar{\theta}),
where :math:`D(\theta) = -2\ln(P(\theta)) + C` is the deviance, where :math:`P` is the posterior
and :math:`C` a constant. From here the DIC is defined as
.. math::
DIC \equiv D(\bar{\theta}) + 2p_D = \bar{D}(\theta) + p_D.
Returns
-------
list[float]
A list of all the DIC values - one per chain, in the order in which the chains were added.
References
----------
[1] Andrew R. Liddle, "Information criteria for astrophysical model selection", MNRAS (2007)
"""
dics = []
dics_bool = []
for i, chain in enumerate(self.parent.chains):
p = chain.posterior
if p is None:
dics_bool.append(False)
self._logger.warn("You need to set the posterior for chain %s to get the DIC" % chain.name)
else:
dics_bool.append(True)
num_params = chain.chain.shape[1]
means = np.array([np.average(chain.chain[:, ii], weights=chain.weights) for ii in range(num_params)])
d = -2 * p
d_of_mean = griddata(chain.chain, d, means, method='nearest')[0]
mean_d = np.average(d, weights=chain.weights)
p_d = mean_d - d_of_mean
dic = mean_d + p_d
dics.append(dic)
if len(dics) > 0:
dics -= np.min(dics)
dics_fin = []
i = 0
for b in dics_bool:
if not b:
dics_fin.append(None)
else:
dics_fin.append(dics[i])
i += 1
return dics_fin
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