"""
Sampling history for MCMC.
MCMC keeps track of a number of things during sampling.
The results may be queried as follows::
draws, generation, thinning
sample(condition) returns draws, points, logp
logp() returns draws, logp
acceptance_rate() returns draws, AR
chains() returns draws, chains, logp
R_stat() returns draws, R
CR_weight() returns draws, CR_weight
best() returns best_x, best_logp
outliers() returns outliers
show()/save(file)/load(file)
Data is stored in circular arrays, which keeps the last N generations and
throws the rest away.
draws is the total number of draws from the sampler.
generation is the total number of generations.
thinning is the number of generations per stored sample.
draws[i] is the number of draws including those required to produce the
information in the corresponding return vector. Note that draw numbers
need not be linearly spaced, since techniques like delayed rejection
will result in a varying number of samples per generation.
logp[i] is the set of log likelihoods, one for each member of the population.
The logp() method returns the complete set, and the sample() method returns
a thinned set, with on element of logp[i] for each vector point[i, :].
AR[i] is the acceptance rate at generation i, showing the proportion of
proposed points which are accepted into the population.
chains[i, :, :] is the set of points in the differential evolution population
at thinned generation i. Ideally, the thinning rate of the MCMC process
is chosen so that thinned generations i and i+1 are independent samples
from the posterior distribution, though there is a chance that this may
not be the case, and indeed, some points in generation i+1 may be identical
to those in generation i. Actual generation number is i*thinning.
points[i, :] is the ith point in a returned sample. The i is just a place
holder; there is no inherent ordering to the sample once they have been
extracted from the chains. Note that the sample may be from a marginal
distribution.
R[i] is the Gelman R statistic measuring convergence of the Markov chain.
CR_weight[i] is the set of weights used for selecting between the crossover
ratios available to the candidate generation process of differential
evolution. These will be fixed early in the sampling, even when adaptive
differential evolution is selected.
outliers[i] is a vector containing the thinned generation number at which
an outlier chain was removed, the id of the chain that was removed and
the id of the chain that replaced it. We leave it to the reader to decide
if the cloned samples, point[:generation, :, removed_id], should be included
in further analysis.
best_logp is the highest log likelihood observed during the analysis and
best_x is the corresponding point at which it was observed.
generation is the last generation number
"""
#TODO: state should be collected in files as we go
from __future__ import division, print_function
__all__ = ['MCMCDraw', 'load_state', 'save_state']
import re
import gzip
import numpy as np
from numpy import empty, sum, asarray, inf, argmax, hstack, dstack
from numpy import savetxt, reshape
from .outliers import identify_outliers
from .util import draw, rng
#EXT = ".mc.gz"
#CREATE = gzip.open
EXT = ".mc"
CREATE = open
# CRUFT: python 2.x needs to convert unicode to bytes when writing to file
try:
# python 2.x
unicode
def write(fid, s):
fid.write(s)
except NameError:
# python 3.x
def write(fid, s):
fid.write(s.encode('utf-8') if isinstance(s, str) else s)
class NoTrace:
def write(self, data):
pass
def flush(self):
pass
def close(self):
pass
[docs]def save_state(state, filename):
trace = NoTrace()
#trace = open(filename+"-trace.mc", "w")
write(trace, "starting trace\n")
# Build 2-D data structures
write(trace, "extracting draws, logp\n")
draws, logp = state.logp(full=True)
write(trace, "extracting acceptance rate\n")
_, AR = state.acceptance_rate()
write(trace, "building chain from draws, AR and logp\n")
chain = hstack((draws[:, None], AR[:, None], logp))
write(trace, "extracting point, logp\n")
_, point, logp = state.chains()
Nthin, Npop, Nvar = point.shape
write(trace, "shape is %d,%d,%d\n" % (Nthin, Npop, Nvar))
write(trace, "adding logp to point\n")
point = dstack((logp[:, :, None], point))
write(trace, "collapsing to draws x point\n")
point = reshape(point, (point.shape[0]*point.shape[1], point.shape[2]))
write(trace, "extracting R_stat\n")
draws, R_stat = state.R_stat()
write(trace, "extracting CR_weight\n")
_, CR_weight = state.CR_weight()
_, Ncr = CR_weight.shape
write(trace, "building stats\n")
stats = hstack((draws[:, None], R_stat, CR_weight))
#TODO: missing _outliers from save_state
# Write convergence info
write(trace, "writing chain\n")
fid = CREATE(filename+'-chain'+EXT, 'wb')
write(fid, '# draws acceptance_rate %d*logp\n' % Npop)
savetxt(fid, chain)
fid.close()
# Write point info
write(trace, "writing point\n")
fid = CREATE(filename+'-point'+EXT, 'wb')
write(fid, '# logp point (Nthin x Npop x Nvar = [%d,%d,%d])\n'
% (Nthin, Npop, Nvar))
savetxt(fid, point)
fid.close()
# Write stats
write(trace, "writing stats\n")
fid = CREATE(filename+'-stats'+EXT, 'wb')
write(fid, '# draws %d*R-stat %d*CR_weight\n' % (Nvar, Ncr))
savetxt(fid, stats)
fid.close()
write(trace, "done state save\n")
trace.close()
IND_PAT = re.compile('-1#IND')
INF_PAT = re.compile('1#INF')
def loadtxt(file, report=0):
"""
Like numpy loadtxt, but adapted for windows non-finite numbers.
"""
if not hasattr(file, 'readline'):
if file.endswith('.gz'):
#print("opening with gzip")
fh = gzip.open(file, 'r')
else:
fh = open(file, 'r')
else:
fh = file
res = []
section = 0
lineno = 0
for line in fh:
lineno += 1
if report and lineno%report == 0:
print("read", section*report)
section += 1
IND_PAT.sub('nan', line)
INF_PAT.sub('inf', line)
line = line.split('#')[0].strip()
values = line.split()
if len(values) > 0:
try:
res.append([float(v) for v in values])
except ValueError:
print("Parse error:", values)
if fh != file:
fh.close()
return asarray(res)
[docs]def load_state(filename, skip=0, report=0, derived_vars=0):
# Read chain file
chain = loadtxt(filename+'-chain'+EXT)
# Read point file
fid = open(filename+'-point'+EXT, 'r')
line = fid.readline()
point_dims = line[line.find('[')+1:line.find(']')]
Nthin, Npop, Nvar = eval(point_dims)
for _ in range(skip*Npop):
fid.readline()
point = loadtxt(fid, report=report*Npop)
fid.close()
# Read stats file
stats = loadtxt(filename+'-stats'+EXT)
# Guess dimensions
Ngen = chain.shape[0]
thinning = 1
Nthin -= skip
Nupdate = stats.shape[0]
#Ncr = stats.shape[1] - Nvar - 1
# Create empty draw and fill it with loaded data
state = MCMCDraw(0, 0, 0, 0, 0, 0, thinning)
#print("gen, var, pop", Ngen, Nvar, Npop)
state.draws = Ngen * Npop
state.generation = Ngen
state._gen_index = 0
state._gen_draws = chain[:, 0]
state._gen_acceptance_rate = chain[:, 1]
state._gen_logp = chain[:, 2:]
state.thinning = thinning
state._thin_count = Ngen//thinning
state._thin_index = 0
state._thin_draws = state._gen_draws[(skip+1)*thinning-1::thinning]
state._thin_logp = point[:, 0].reshape((Nthin, Npop))
state._thin_point = reshape(point[:, 1:Nvar+1-derived_vars], (Nthin, Npop, -1))
state._gen_current = state._thin_point[-1].copy()
state._update_count = Nupdate
state._update_index = 0
state._update_draws = stats[:, 0]
state._update_R_stat = stats[:, 1:Nvar+1-derived_vars]
state._update_CR_weight = stats[:, Nvar+1-derived_vars:]
state._outliers = []
bestidx = np.argmax(point[:, 0])
state._best_logp = point[bestidx, 0]
state._best_x = point[bestidx, 1:Nvar+1-derived_vars]
return state
[docs]class MCMCDraw(object):
"""
"""
_labels = None
_integer_vars = None # boolean array of integer variables, or None
title = None
def __init__(self, Ngen, Nthin, Nupdate, Nvar, Npop, Ncr, thinning):
# Total number of draws so far
self.draws = 0
# Maximum observed likelihood
self._best_x = None
self._best_logp = -inf
# Per generation iteration
self.generation = 0
self._gen_index = 0
self._gen_draws = empty(Ngen, 'i')
self._gen_logp = empty((Ngen, Npop))
self._gen_acceptance_rate = empty(Ngen)
# If we are thinning, we need to keep the current generation
# separately. [Note: don't remember why we need both the _gen_*
# and _thin_*] [Note: the caller x vector is assigned to
# _gen_current; this may lead to unexpected behaviour if x is
# changed by the caller.
self._gen_current = None
# Per thinned generation iteration
self.thinning = thinning
self._thin_index = 0
self._thin_count = 0
self._thin_timer = 0
self._thin_draws = empty(Nthin, 'i')
self._thin_point = empty((Nthin, Npop, Nvar))
self._thin_logp = empty((Nthin, Npop))
# Per update iteration
self._update_index = 0
self._update_count = 0
self._update_draws = empty(Nupdate, 'i')
self._update_R_stat = empty((Nupdate, Nvar))
self._update_CR_weight = empty((Nupdate, Ncr))
self._outliers = []
# Query functions will not return outlier chains; initially, all
# chains are marked as good. Call mark_outliers to remove
# outlier chains from the set.
self._good_chains = slice(None, None)
@property
def Ngen(self):
return self._gen_draws.shape[0]
@property
def Nthin(self):
return self._thin_draws.shape[0]
@property
def Nupdate(self):
return self._update_draws.shape[0]
@property
def Nvar(self):
"""Number of parameters in the fit"""
return self._thin_point.shape[2]
@property
def Npop(self):
return self._gen_logp.shape[1]
@property
def Ncr(self):
return self._update_CR_weight.shape[1]
[docs] def resize(self, Ngen, Nthin, Nupdate, Nvar, Npop, Ncr, thinning):
if self.Nvar != Nvar or self.Npop != Npop or self.Ncr != Ncr:
raise ValueError("Cannot change Nvar, Npop or Ncr on resize")
# For now, only handle the case where the we have one complete
# frame of data, such as on reloading the state vector
assert (self._gen_index == 0
and self._update_index == 0
and self._thin_index == 0)
assert (self.generation == self.Ngen
and self._update_count == self.Nupdate
and self._thin_count == self.Nthin)
self.thinning = thinning
if Ngen > self.Ngen:
self._gen_index = self.Ngen # must happen before resize!!
self._gen_draws = np.resize(self._gen_draws, Ngen)
self._gen_logp = np.resize(self._gen_logp, (Ngen, Npop))
self._gen_acceptance_rate \
= np.resize(self._gen_acceptance_rate, Ngen)
elif Ngen < self.Ngen:
self._gen_draws = self._gen_draws[-Ngen:].copy()
self._gen_logp = self._gen_logp[-Ngen:, :].copy()
self._gen_acceptance_rate \
= self._gen_acceptance_rate[-Ngen:].copy()
if Nthin > self.Nthin:
self._thin_index = self.Nthin # must happen before resize!!
self._thin_draws = np.resize(self._thin_draws, Nthin)
self._thin_point = np.resize(self._thin_point, (Nthin, Npop, Nvar))
self._thin_logp = np.resize(self._thin_logp, (Nthin, Npop))
elif Nthin < self.Nthin:
self._thin_draws = self._thin_draws[-Nthin:].copy()
self._thin_point = self._thin_point[-Nthin:, :, :].copy()
self._thin_logp = self._thin_logp[-Nthin:, :].copy()
if Nupdate > self.Nupdate:
self._update_count = self.Nupdate # must happen before resize!!
self._update_draws = np.resize(self._update_draws, Nupdate)
self._update_R_stat \
= np.resize(self._update_R_stat, (Nupdate, Nvar))
self._update_CR_weight \
= np.resize(self._update_CR_weight, (Nupdate, Ncr))
elif Nupdate < self.Nupdate:
self._update_draws = self._update_draws[-Nupdate:].copy()
self._update_R_stat = self._update_R_stat[-Nupdate:, :].copy()
self._update_CR_weight = self._update_CR_weight[-Nupdate:, :].copy()
[docs] def save(self, filename):
save_state(self, filename)
[docs] def show(self, portion=1.0, figfile=None):
from .views import plot_all
plot_all(self, portion=portion, figfile=figfile)
def _last_gen(self):
"""
Returns x, logp for most recent generation to dream.py.
"""
# Note: if generation number has wrapped and _gen_index is 0
# (the usual case when this function is called to resume an
# existing chain), then this returns the last row in the array.
return (self._thin_point[self._thin_index-1],
self._thin_logp[self._thin_index-1])
def _generation(self, new_draws, x, logp, accept, force_keep=False):
"""
Called from dream.py after each generation is completed with
a set of accepted points and their values.
"""
# Keep track of the total number of draws
# Note: this is first so that we tag the record with the number of
# draws taken so far, including the current draw.
self.draws += new_draws
self.generation += 1
# Record if this is the best so far
maxid = argmax(logp)
if logp[maxid] > self._best_logp:
self._best_logp = logp[maxid]
self._best_x = x[maxid, :]+0 # Force a copy
# Record acceptance rate and cost
i = self._gen_index
#print("generation", i, self.draws, "\n x", x, "\n logp", logp, "\n accept", accept)
self._gen_draws[i] = self.draws
self._gen_acceptance_rate[i] = 100*sum(accept)/new_draws
self._gen_logp[i] = logp
i = i+1
if i == len(self._gen_draws):
i = 0
self._gen_index = i
# Keep every nth iteration
self._thin_timer += 1
if self._thin_timer == self.thinning or force_keep:
self._thin_timer = 0
self._thin_count += 1
i = self._thin_index
self._thin_draws[i] = self.draws
self._thin_point[i] = x
self._thin_logp[i] = logp
i = i+1
if i == len(self._thin_draws):
i = 0
self._thin_index = i
self._gen_current = x+0 # force a copy
else:
self._gen_current = x+0 # force a copy
def _update(self, R_stat, CR_weight):
"""
Called from dream.py when a series of DE steps is completed and
summary statistics/adaptations are ready to be stored.
"""
self._update_count += 1
i = self._update_index
#print("update", i, self.draws, "\n Rstat", R_stat, "\n CR weight", CR_weight)
self._update_draws[i] = self.draws
self._update_R_stat[i] = R_stat
self._update_CR_weight[i] = CR_weight
i = i+1
if i == len(self._update_draws): i = 0
self._update_index = i
def _replace_outlier(self, old, new):
"""
Called from outliers.py when a chain is replaced by the
clone of another.
"""
self._outliers.append((self._thin_index, old, new))
self._gen_logp[:, old] = self._gen_logp[:, new]
self._thin_logp[:, old] = self._thin_logp[:, new]
self._thin_point[:, old, :] = self._thin_point[:, new, :]
# PAK: shouldn't we reduce the total number of draws since we
# are throwing way an entire chain?
@property
def labels(self):
if self._labels is None:
return ["P%d"%i for i in range(self._thin_point.shape[2])]
else:
return self._labels
@labels.setter
def labels(self, v):
self._labels = v
def _draw_pop(self):
"""
Return the current population.
"""
return self._gen_current
def _draw_large_pop(self, Npop):
_, chains, _ = self.chains()
Ngen, Nchain, Nvar = chains.shape
points = reshape(chains, (Ngen*Nchain, Nvar))
# There are two complications with the history buffer:
# (1) due to thinning, not every generation is stored
# (2) because it is circular, the cursor may be in the middle
# If the current generation isn't in the buffer (but is instead
# stored separately as _gen_current), then the entire buffer
# becomes the history pool.
# otherwise we need to exclude the current generation from
# the pool. If (2) happens, we need to increment everything
# above the cursor by the number of chains.
if self._gen_current is not None:
pool_size = Ngen*Nchain
cursor = pool_size # infinite
else:
pool_size = (Ngen-1)*Nchain
k = len(self._thin_draws)
cursor = Nchain*((k+self._thin_index-1)%k)
# Make a return population and fill it with the current generation
pop = empty((Npop, Nvar), 'd')
if self._gen_current is not None:
pop[:Nchain] = self._gen_current
else:
#print(pop.shape, points.shape, chains.shape)
pop[:Nchain] = points[cursor:cursor+Nchain]
if Npop > Nchain:
# Find the remainder with unique ancestors.
# Again, because this is a circular buffer, their may be random
# numbers generated at or above the cursor. All of these must
# be shifted by Nchains to avoid the cursor.
perm = draw(Npop-Nchain, pool_size)
perm[perm >= cursor] += Nchain
#print("perm", perm; raw_input('wait'))
pop[Nchain:] = points[perm]
return pop
def _unroll(self):
"""
Unroll the circular queue so that data access can be done inplace.
Call this when done stepping, and before plotting. Calls to
logp, sample, etc. assume the data is already unrolled.
"""
if self.generation > self._gen_index > 0:
self._gen_draws[:] = np.roll(self._gen_draws,
-self._gen_index, axis=0)
self._gen_logp[:] = np.roll(self._gen_logp,
-self._gen_index, axis=0)
self._gen_acceptance_rate[:] = np.roll(self._gen_acceptance_rate,
-self._gen_index, axis=0)
self._gen_index = 0
if self._thin_count > self._thin_index > 0:
self._thin_draws[:] = np.roll(self._thin_draws,
-self._thin_index, axis=0)
self._thin_point[:] = np.roll(self._thin_point,
-self._thin_index, axis=0)
self._thin_logp[:] = np.roll(self._thin_logp,
-self._thin_index, axis=0)
self._thin_index = 0
if self._update_count > self._update_index > 0:
self._update_draws[:] = np.roll(self._update_draws,
-self._update_index, axis=0)
self._update_R_stat[:] = np.roll(self._update_R_stat,
-self._update_index, axis=0)
self._update_CR_weight[:] = np.roll(self._update_CR_weight,
-self._update_index, axis=0)
self._update_index = 0
[docs] def remove_outliers(self, x, logp, test='IQR', portion=0.5):
"""
Replace outlier chains with clones of good ones. This should happen
early in the sampling processes so the clones have an opportunity
to evolve their own identity.
*state* contains the chains, with log likelihood for each point.
*x*, *logp* are the current population and the corresponding
log likelihoods
*test* is the name of the test to use (one of IQR, Grubbs, Mahal
or none).
*portion* in (0, 1] is the amount of the chain to use
Updates *state*, *x* and *logp* to reflect the changes.
See :mod:`outliers` for details.
"""
# Grab the last part of the chain histories
_, chains = self.logp()
chain_len, Nchains = chains.shape
outliers = identify_outliers(test, chains[-chain_len:], x)
# Loop over each outlier chain, replacing each with another
for old in outliers:
# Draw another chain at random, with replacement
while True:
new = rng.randint(Nchains)
if new not in outliers:
break
# Update the saved state and current population
self._replace_outlier(old=old, new=new)
x[old, :] = x[new, :]
logp[old] = logp[new]
[docs] def mark_outliers(self, test='IQR', portion=1.0):
"""
Mark some chains as outliers but don't remove them. This can happen
after drawing is complete, so that chains that did not converge are
not included in the statistics.
*test* is 'IQR', 'Mahol' or 'none'.
*portion* indicates what portion of the samples should be included
in the outlier test. The default is to include all of them.
"""
_, chains, logp = self.chains()
if test == 'none':
self._good_chains = slice(None, None)
else:
Ngen = chains.shape[0]
start = int(Ngen*(1-portion)) if portion else 0
outliers = identify_outliers(test, logp[start:], chains[-1])
#print("outliers", outliers)
#print(logp.shape, chains.shape)
if len(outliers) > 0:
self._good_chains = np.array([i
for i in range(logp.shape[1])
if i not in outliers])
else:
self._good_chains = slice(None, None)
#print(self._good_chains)
[docs] def logp(self, full=False):
"""
Return the iteration number and the log likelihood for each point in
the individual sequences in that iteration.
For example, to plot the convergence of each sequence::
draw, logp = state.logp()
plot(draw, logp)
Note that draw[i] represents the total number of samples taken,
including those for the samples in logp[i].
If full is True, then return all chains, not just good chains.
"""
self._unroll()
retval = self._gen_draws, self._gen_logp
if self.generation == self._gen_index:
retval = [v[:self.generation] for v in retval]
draws, logp = retval
return draws, (logp if full else logp[:, self._good_chains])
[docs] def acceptance_rate(self):
"""
Return the iteration number and the acceptance rate for that iteration.
For example, to plot the acceptance rate over time::
draw, AR = state.acceptance_rate()
plot(draw, AR)
"""
retval = self._gen_draws, self._gen_acceptance_rate
if self.generation == self._gen_index:
retval = [v[:self.generation] for v in retval]
elif self._gen_index > 0:
retval = [np.roll(v, -self._gen_index, axis=0) for v in retval]
return retval
[docs] def chains(self):
"""
Returns the observed Markov chains and the corresponding likelihoods.
The return value is a tuple (*draws*, *chains*, *logp*).
*draws* is the number of samples taken up to and including the samples
for the current generation.
*chains* is a three dimensional array of generations X chains X vars
giving the set of points observed for each chain in every generation.
Only the thinned samples are returned.
*logp* is a two dimensional array of generation X population giving
the log likelihood of observing the set of variable values given in
chains.
"""
self._unroll()
retval = self._thin_draws, self._thin_point, self._thin_logp
if self._thin_count == self._thin_index:
retval = [v[:self._thin_count] for v in retval]
return retval
[docs] def R_stat(self):
"""
Return the R-statistics convergence statistic for each variable.
For example, to plot the convergence of all variables over time::
draw, R = state.R_stat()
plot(draw, R)
See :mod:`dream.gelman` and references detailed therein.
"""
self._unroll()
retval = self._update_draws, self._update_R_stat
if self._update_count == self._update_index:
retval = [v[:self._update_count] for v in retval]
return retval
[docs] def CR_weight(self):
"""
Return the crossover ratio weights to be used in the next generation.
For example, to see if the adaptive CR is stable use::
draw, weight = state.CR_weight()
plot(draw, weight)
See :mod:`dream.crossover` for details.
"""
self._unroll()
retval = self._update_draws, self._update_CR_weight
if self._update_count == self._update_index:
retval = [v[:self._update_count] for v in retval]
return retval
[docs] def outliers(self):
"""
Return a list of outlier removal operations.
Each outlier operation is a tuple giving the thinned generation
in which it occurred, the old chain id and the new chain id.
The chains themselves have already been updated to reflect the
removal.
Curiously, it is possible for the maximum likelihood seen so far
to be removed by this operation.
"""
return asarray(self._outliers, 'i')
[docs] def best(self):
"""
Return the best point seen and its log likelihood.
"""
return self._best_x, self._best_logp
[docs] def keep_best(self):
"""
Place the best point at the end of the chain final good chain.
Good chains are defined by mark_outliers.
Because the Markov chain is designed to wander the parameter
space, the best individual seen during the random walk may have
been observed during the burn-in period, and may no longer be
present in the chain. If this is the case, replace the final
point with the best, otherwise swap the positions of the final
and the best.
"""
# Get state as a 1D array
_, chains, logp = self.chains()
Ngen, Npop, Nvar = chains.shape
points = reshape(chains, (Ngen*Npop, Nvar))
logp = reshape(logp, Ngen*Npop)
# Set the final position to the end of the last good chain. If
# mark_outliers has not been called, then _good_chains will
# just be slice(None, None)
if isinstance(self._good_chains, slice):
final = -1
else:
final = self._good_chains[-1] - Npop
# Find the location of the best point if it exists and swap with
# the final position
idx = np.where(logp == self._best_logp)[0]
if len(idx) == 0:
logp[final] = self._best_logp
points[final, :] = self._best_x
else:
idx = idx[0]
logp[final], logp[idx] = logp[idx], logp[final]
points[final, :], points[idx, :] = points[idx, :], points[final, :]
# For multiple minima, arbitrarily choose one of them
# TODO: this will lead to possible confusion when the best value
# spontaneously changes when the fit is complete.
self._best_p = points[final]
self._best_logp = logp[final]
[docs] def sample(self, **kw):
"""
Return a sample from the posterior distribution.
**Deprecated** use :meth:`draw` instead.
"""
drawn = self.draw(**kw)
return drawn.points, drawn.logp
[docs] def entropy(self, **kw):
"""
Return entropy estimate and uncertainty from an MCMC draw.
See :func:`entropy.entropy` for details.
"""
from .entropy import entropy, MVNEntropy
# Get the sample from the state
drawn = self.draw()
M = MVNEntropy(drawn.points)
print("Entropy from MVN: %s"%str(M))
# Always return entropy from draw, even if the sample is approximately
# normal
return entropy(drawn.points, drawn.logp, **kw)
#return entropy(drawn.points, drawn.logp, **kw) if M.reject_normal else (M.entropy, 0)
[docs] def draw(self, portion=1, vars=None, selection=None):
"""
Return a sample from the posterior distribution.
*portion* is the portion of each chain to use
*vars* is a list of variables to return for each point
*selection* sets the range for the returned marginal distribution
*selection* is a dictionary of {variable: (low, high)} to set the
range on each variable. Missing variables default to the full
range.
To plot the distribution for parameter p1::
draw = state.draw()
hist(draw.points[:, 0])
To plot the interdependence of p1 and p2::
draw = state.sample()
plot(draw.points[:, 0], draw.points[:, 1], '.')
"""
vars = vars if vars is not None else getattr(self, '_shown', None)
return Draw(self, portion=portion, vars=vars, selection=selection)
[docs] def set_visible_vars(self, labels):
self._shown = [self.labels.index(v) for v in labels]
#print("\n".join(str(pair) for pair in enumerate(self.labels)))
#print(labels)
#print(self._shown)
[docs] def set_integer_vars(self, labels):
"""
Indicate tha variables should be considered integer variables when
computing statistics.
"""
self._integer_vars = np.array([var in labels for var in self.labels])
[docs] def derive_vars(self, fn, labels=None):
"""
Generate derived variables from the current sample, adding columns
for the derived variables to each sample of every chain.
The new columns are treated as part of the sample.
*fn* is a function taking points p[:, k] for k in 0 ... samples and
returning a set of derived variables pj[k] for each sample k. The
variables can be returned as any kind of sequence including an
array or a tuple with one entry per variable. The caller uses
asarray to convert the returned variables into a vars X samples array.
For convenience, a single variable can be returned by itself.
*labels* are the labels to use for the derived variables.
The following example adds the new variable x+y = P[0] + P[1]::
state.derive_vars(lambda p: p[0]+p[1], labels=["x+y"])
"""
# Grab all samples as a set of points
_, chains, _ = self.chains()
Ngen, Npop, Nvar = chains.shape
points = reshape(chains, (Ngen*Npop, Nvar))
# Compute new variables from the points
newvars = asarray(fn(points.T)).T
Nnew = newvars.shape[1] if len(newvars.shape) == 2 else 1
newvars.reshape((Ngen, Npop, Nnew))
# Extend new variables to be the same length as the stored selection
Nthin = self._thin_point.shape[0]
newvars = np.resize(newvars, (Nthin, Npop, Nnew))
# Add new variables to the points
self._thin_point = dstack((self._thin_point, newvars))
# Add labels for the new variables, if available.
if labels is not None:
self.labels = self.labels + labels
elif self._labels is not None:
labels = ["P%d" % i for i in range(Nvar, Nvar+Nnew)]
self.labels = self.labels + labels
else: # no labels specified, old or new
pass
class Draw(object):
def __init__(self, state, vars=None, portion=None, selection=None):
self.state = state
self.vars = vars
self.portion = portion
self.selection = selection
self.points, self.logp \
= _sample(state, portion=portion, vars=vars, selection=selection)
self.labels \
= state.labels if vars is None else [state.labels[v] for v in vars]
self._stats = None
self.weights = None
self.num_vars = len(self.labels)
if state._integer_vars is not None:
self.integers = state._integer_vars[vars] if vars else None
else:
self.integers = None
def _sample(state, portion, vars, selection):
"""
Return a sample from a set of chains.
"""
draw, chains, logp = state.chains()
start = int((1-portion)*len(draw)) if portion else 0
# Collect the subset we are interested in
chains = chains[start:, state._good_chains, :]
logp = logp[start:, state._good_chains]
Ngen, Npop, Nvar = chains.shape
points = reshape(chains, (Ngen*Npop, Nvar))
logp = reshape(logp, (Ngen*Npop))
if selection not in [None, {}]:
idx = True
for v, r in selection.items():
if v == 'logp':
idx = idx & (logp >= r[0]) & (logp <= r[1])
else:
idx = idx & (points[:, v] >= r[0]) & (points[:, v] <= r[1])
points = points[idx, :]
logp = logp[idx]
if vars is not None:
points = points[:, vars]
return points, logp
def test():
from numpy.linalg import norm
from numpy.random import rand
from numpy import arange
# Make some fake data
Nupdate, Nstep = 3, 5
Ngen = Nupdate*Nstep
Nvar, Npop, Ncr = 3, 6, 2
xin = rand(Ngen, Npop, Nvar)
pin = rand(Ngen, Npop)
accept = rand(Ngen, Npop) < 0.8
CRin = rand(Nupdate, Ncr)
Rin = rand(Nupdate, 1)
#thinning = 2
#Nthin = int(Ngen/thinning)
# Put it into a state
thinning = 2
Nthin = int(Ngen/thinning)
state = MCMCDraw(Ngen=Ngen, Nthin=Nthin, Nupdate=Nupdate,
Nvar=Nvar, Npop=Npop, Ncr=Ncr, thinning=thinning)
for i in range(Nupdate):
state._update(R_stat=Rin[i], CR_weight=CRin[i])
for j in range(Nstep):
gen = i*Nstep+j
state._generation(new_draws=Npop, x=xin[gen],
logp=pin[gen], accept=accept[gen])
# Check that it got there
draws, logp = state.logp()
assert norm(draws - Npop*arange(1, Ngen+1)) == 0
assert norm(logp - pin) == 0
draws, AR = state.acceptance_rate()
assert norm(draws - Npop*arange(1, Ngen+1)) == 0
assert norm(AR - 100*sum(accept, axis=1)/Npop) == 0
draws, logp = state.sample()
#assert norm(draws - thinning*Npop*arange(1, Nthin+1)) == 0
#assert norm(sample - xin[thinning-1::thinning]) == 0
#assert norm(logp - pin[thinning-1::thinning]) == 0
draws, R = state.R_stat()
assert norm(draws - Npop*Nstep*arange(Nupdate)) == 0
assert norm(R-Rin) == 0
draws, CR = state.CR_weight()
assert norm(draws - Npop*Nstep*arange(Nupdate)) == 0
assert norm(CR - CRin) == 0
x, p = state.best()
bestid = argmax(pin)
i, j = bestid//Npop, bestid%Npop
assert pin[i, j] == p
assert norm(xin[i, j, :]-x) == 0
# Check that outlier updates properly
state._replace_outlier(1, 2)
outliers = state.outliers()
draws, logp = state.sample()
assert norm(outliers - asarray([[state._thin_index, 1, 2]])) == 0
#assert norm(sample[:, 1, :] - xin[thinning-1::thinning, 2, :]) == 0
#assert norm(sample[:, 2, :] - xin[thinning-1::thinning, 2, :]) == 0
#assert norm(logp[:, 1] - pin[thinning-1::thinning, 2]) == 0
#assert norm(logp[:, 2] - pin[thinning-1::thinning, 2]) == 0
from .stats import var_stats, format_vars
vstats = var_stats(state.draw())
print (format_vars(vstats))
if __name__ == "__main__":
test()
