def reject(self):
self.rejected += 1
if self.verbose:
print_(self._id + ' rejecting')
# Revert the field evaluation and the rest of the field.
self.f_eval.revert()
self.f.revert()
def plot_envelope(M,C,mesh):
"""
plot_envelope(M,C,mesh)
plots the pointwise mean +/- sd envelope defined by M and C
along their base mesh.
:Arguments:
- `M`: A Gaussian process mean.
- `C`: A Gaussian process covariance
- `mesh`: The mesh on which to evaluate the mean and cov.
"""
try:
from pylab import fill, plot, clf, axis
x=concatenate((mesh, mesh[::-1]))
mean, var = point_eval(M,C,mesh)
sig = sqrt(var)
mean = M(mesh)
y=concatenate((mean-sig, (mean+sig)[::-1]))
# clf()
fill(x,y,facecolor='.8',edgecolor='1.')
plot(mesh, mean, 'k-.')
except ImportError:
print_("Matplotlib is not installed; plotting is disabled.")
def plot_envelope(M, C, mesh):
"""
plot_envelope(M,C,mesh)
plots the pointwise mean +/- sd envelope defined by M and C
along their base mesh.
:Arguments:
- `M`: A Gaussian process mean.
- `C`: A Gaussian process covariance
- `mesh`: The mesh on which to evaluate the mean and cov.
"""
try:
from pylab import fill, plot, clf, axis
x = concatenate((mesh, mesh[::-1]))
mean, var = point_eval(M, C, mesh)
sig = sqrt(var)
mean = M(mesh)
y = concatenate((mean - sig, (mean + sig)[::-1]))
# clf()
fill(x, y, facecolor='.8', edgecolor='1.')
plot(mesh, mean, 'k-.')
except ImportError:
print_("Matplotlib is not installed; plotting is disabled.")
def reject(self):
self.rejected += 1
if self.verbose:
print_(self._id + ' rejecting')
# Revert the field evaluation and the rest of the field.
self.f_eval.revert()
self.f.revert()
def wrapped_f(pymc_obj, *args, **kwargs):
# Figure out what type of object it is
try:
values = {}
# First try Model type
for variable in pymc_obj._variables_to_tally:
if self.all_chains:
k = pymc_obj.db.chains
data = [variable.trace(chain=i) for i in range(k)]
else:
data = variable.trace()
name = variable.__name__
if kwargs.get('verbose'):
print_("\nDiagnostic for %s ..." % name)
values[name] = f(data, *args, **kwargs)
return values
except AttributeError:
pass
try:
# Then try Node type
if self.all_chains:
k = pymc_obj.trace.db.chains
data = [pymc_obj.trace(chain=i) for i in range(k)]
else:
data = pymc_obj.trace()
name = pymc_obj.__name__
return f(data, *args, **kwargs)
except (AttributeError, ValueError):
pass
# If others fail, assume that raw data is passed
return f(pymc_obj, *args, **kwargs)
def wrapped_f(pymc_obj, *args, **kwargs):
# Figure out what type of object it is
try:
values = {}
# First try Model type
for variable in pymc_obj._variables_to_tally:
if self.all_chains:
k = pymc_obj.db.chains
data = [variable.trace(chain=i) for i in range(k)]
else:
data = variable.trace()
name = variable.__name__
if kwargs.get('verbose'):
print_("\nDiagnostic for %s ..." % name)
values[name] = f(data, *args, **kwargs)
return values
except AttributeError:
pass
try:
# Then try Node type
if self.all_chains:
k = pymc_obj.trace.db.chains
data = [pymc_obj.trace(chain=i) for i in range(k)]
else:
data = pymc_obj.trace()
name = pymc_obj.__name__
return f(data, *args, **kwargs)
except (AttributeError,ValueError):
pass
# If others fail, assume that raw data is passed
return f(pymc_obj, *args, **kwargs)
def discrepancy(observed, simulated, expected):
"""Calculates Freeman-Tukey statistics (Freeman and Tukey 1950) as
a measure of discrepancy between observed and r replicates of simulated data. This
is a convenient method for assessing goodness-of-fit (see Brooks et al. 2000).
D(x|\theta) = \sum_j (\sqrt{x_j} - \sqrt{e_j})^2
:Parameters:
observed : Iterable of observed values (length n)
simulated : Iterable of simulated values (length rxn)
expected : Iterable of expected values (length rxn)
:Returns:
D_obs : Discrepancy of observed values
D_sim : Discrepancy of simulated values
"""
try:
simulated = simulated.astype(float)
except AttributeError:
simulated = simulated.trace().astype(float)
try:
expected = expected.astype(float)
except AttributeError:
expected = expected.trace().astype(float)
D_obs = np.sum([(np.sqrt(observed)-np.sqrt(e))**2 for e in expected], 1)
D_sim = np.sum([(np.sqrt(s)-np.sqrt(e))**2 for s,e in zip(simulated, expected)], 1)
# Print p-value
count = sum(s>o for o,s in zip(D_obs,D_sim))
print_('Bayesian p-value: p=%.3f' % (1.*count/len(D_obs)))
return D_obs, D_sim
def propose_first(self):
"""
This method proposes values for stochastics based on the empirical
covariance of the values sampled so far.
The proposal jumps are drawn from a multivariate normal distribution.
"""
arrayjump = np.dot(
self.proposal_sd,
np.random.normal(size=self.proposal_sd.shape[0]),
)
# save in case needed for calculating second proposal probability
self.arrayjump1 = arrayjump.copy() # is a copy needed?
if self.verbose > 2: print_('First jump:', arrayjump)
# Update each stochastic individually.
for stochastic in self.stochastics:
jump = arrayjump[self._slices[stochastic]].squeeze()
if np.iterable(stochastic.value):
jump = np.reshape(
arrayjump[self._slices[stochastic]],
np.shape(stochastic.value),
)
if self.isdiscrete[stochastic]:
jump = round_array(jump)
stochastic.value = stochastic.value + jump
def stats(self,
alpha=0.05,
start=0,
batches=100,
chain=None,
quantiles=(2.5, 25, 50, 75, 97.5)):
"""
Generate posterior statistics for node.
:Parameters:
name : string
The name of the tallyable object.
alpha : float
The alpha level for generating posterior intervals. Defaults to
0.05.
start : int
The starting index from which to summarize (each) chain. Defaults
to zero.
batches : int
Batch size for calculating standard deviation for non-independent
samples. Defaults to 100.
chain : int
The index for which chain to summarize. Defaults to None (all
chains).
quantiles : tuple or list
The desired quantiles to be calculated. Defaults to (2.5, 25, 50, 75, 97.5).
"""
try:
trace = np.squeeze(
np.array(self.db.trace(self.name)(chain=chain), float))[start:]
n = len(trace)
if not n:
print_('Cannot generate statistics for zero-length trace in',
self.__name__)
return
return {
'n':
n,
'standard deviation':
trace.std(0),
'mean':
trace.mean(0),
'%s%s HPD interval' % (int(100 * (1 - alpha)), '%'):
utils.hpd(trace, alpha),
'mc error':
batchsd(trace, batches),
'quantiles':
utils.quantiles(trace, qlist=quantiles)
}
except:
print_('Could not generate output statistics for', self.name)
return
def plot_GP_envelopes(f, x, HPD=[
.25, .5, .95], transx=None, transy=None):
"""
plot_GP_envelopes(f, x[, HPD, transx, transy])
Plots centered posterior probability envelopes for f, which is a GP instance,
which is a function of one variable.
:Arguments:
- `f`: A GaussianProcess object.
- `x`: The mesh on which to plot the envelopes.
- `HPD`: A list of values between 0 and 1 giving the probability mass
contained in each envelope.
- `transx`: Any transformation of the x-axis.
- `transy`: Any transformation of the y-axis.
"""
try:
from pymc.Matplot import centered_envelope
f_trace = f.trace()
x = x.ravel()
N = len(f_trace)
func_stacks = np.zeros((N, len(x)), dtype=float)
def identity(y):
return y
if transy is None:
transy = identity
if transx is None:
transx = identity
# Get evaluations
for i in range(N):
f = copy(f_trace[i])
func_stacks[i, :] = transy(f(transx(x)))
# Plot envelopes
HPD = np.sort(HPD)
sorted_func_stack = np.sort(func_stacks, 0)
for m in HPD[::-1]:
env = centered_envelope(sorted_func_stack, m)
# from IPython.Debugger import Pdb
# Pdb(color_scheme='LightBG').set_trace()
env.display(x, alpha=1. - m * .5, new=False)
centered_envelope(
sorted_func_stack,
0.).display(x,
alpha=1.,
new=False)
except ImportError:
six.print_('Plotter could not be imported; plotting disabled')
def savestate(self, state):
"""Save the sampler's state in a state.txt file."""
oldstate = np.get_printoptions()
np.set_printoptions(threshold=1e6)
try:
with open(os.path.join(self._directory, 'state.txt'), 'w') as f:
print_(state, file=f)
finally:
np.set_printoptions(**oldstate)
def savestate(self, state):
"""Save the sampler's state in a state.txt file."""
oldstate = np.get_printoptions()
np.set_printoptions(threshold=1e6)
try:
with open(os.path.join(self._directory, 'state.txt'), 'w') as f:
print_(state, file=f)
finally:
np.set_printoptions(**oldstate)
def propose(self):
if self.verbose:
print_(self._id + " proposing")
fc = pm.gp.fast_matrix_copy
eps_p_f = pm.utils.value(self.eps_p_f)
f = pm.utils.value(self.f_eval)
for i in xrange(len(self.scratch3)):
self.scratch3[i] = np.sum(eps_p_f[self.ti[i]] - f[i])
# Compute Cholesky factor of covariance of eps_p_f, C(x,x) + V
C_eval_value = pm.utils.value(self.C_eval)
C_eval_shape = C_eval_value.shape
# Get the Cholesky factor of C_eval, plus the nugget.
# I don't think you can use S_eval for speed, unfortunately.
in_chol = fc(C_eval_value, self.scratch1)
v_val = pm.utils.value(self.V)
for i in xrange(pm.utils.value(C_eval_shape)[0]):
in_chol[i, i] += v_val[i] / np.alen(self.ti[i])
info = pm.gp.linalg_utils.dpotrf_wrap(in_chol)
if info > 0:
raise np.linalg.LinAlgError
# Compute covariance of f conditional on eps_p_f.
offdiag = fc(C_eval_value, self.scratch2)
offdiag = pm.gp.trisolve(in_chol, offdiag, uplo="U", transa="T", inplace=True)
C_step = offdiag.T * offdiag
C_step *= -1
C_step += C_eval_value
# Compute mean of f conditional on eps_p_f.
for i in xrange(len(self.scratch3)):
self.scratch3[i] = np.mean(eps_p_f[self.ti[i]])
m_step = (
pm.utils.value(self.M_eval)
+ np.dot(offdiag.T, pm.gp.trisolve(in_chol, (self.scratch3 - self.M_eval.value), uplo="U", transa="T"))
.view(np.ndarray)
.ravel()
)
sig_step = C_step
info = pm.gp.linalg_utils.dpotrf_wrap(C_step.T)
if info > 0:
warnings.warn("Full conditional covariance was not positive definite.")
return
# Update value of f.
self.f_eval.value = m_step + np.dot(sig_step, np.random.normal(size=sig_step.shape[1])).view(np.ndarray).ravel()
# Propose the rest of the field from its conditional prior.
self.f.rand()
def plot_GP_envelopes(f, x, HPD=[.25, .5, .95], transx=None, transy=None):
"""
plot_GP_envelopes(f, x[, HPD, transx, transy])
Plots centered posterior probability envelopes for f, which is a GP instance,
which is a function of one variable.
:Arguments:
- `f`: A GaussianProcess object.
- `x`: The mesh on which to plot the envelopes.
- `HPD`: A list of values between 0 and 1 giving the probability mass
contained in each envelope.
- `transx`: Any transformation of the x-axis.
- `transy`: Any transformation of the y-axis.
"""
try:
from pymc.Matplot import centered_envelope
f_trace = f.trace()
x = x.ravel()
N = len(f_trace)
func_stacks = np.zeros((N, len(x)), dtype=float)
def identity(y):
return y
if transy is None:
transy = identity
if transx is None:
transx = identity
# Get evaluations
for i in range(N):
f = copy(f_trace[i])
func_stacks[i, :] = transy(f(transx(x)))
# Plot envelopes
HPD = np.sort(HPD)
sorted_func_stack = np.sort(func_stacks, 0)
for m in HPD[::-1]:
env = centered_envelope(sorted_func_stack, m)
# from IPython.Debugger import Pdb
# Pdb(color_scheme='LightBG').set_trace()
env.display(x, alpha=1. - m * .5, new=False)
centered_envelope(sorted_func_stack, 0.).display(x,
alpha=1.,
new=False)
except ImportError:
six.print_('Plotter could not be imported; plotting disabled')
def stats(self, alpha=0.05, start=0, batches=100,
chain=None, quantiles=(2.5, 25, 50, 75, 97.5)):
"""
Generate posterior statistics for node.
:Parameters:
name : string
The name of the tallyable object.
alpha : float
The alpha level for generating posterior intervals. Defaults to
0.05.
start : int
The starting index from which to summarize (each) chain. Defaults
to zero.
batches : int
Batch size for calculating standard deviation for non-independent
samples. Defaults to 100.
chain : int
The index for which chain to summarize. Defaults to None (all
chains).
quantiles : tuple or list
The desired quantiles to be calculated. Defaults to (2.5, 25, 50, 75, 97.5).
"""
try:
trace = np.squeeze(
np.array(
self.db.trace(
self.name)(
chain=chain),
float))[
start:]
n = len(trace)
if not n:
print_(
'Cannot generate statistics for zero-length trace in',
self.__name__)
return
return {
'n': n,
'standard deviation': trace.std(0),
'mean': trace.mean(0),
'%s%s HPD interval' % (int(100 * (1 - alpha)), '%'): utils.hpd(trace, alpha),
'mc error': batchsd(trace, min(n, batches)),
'quantiles': utils.quantiles(trace, qlist=quantiles)
}
except:
print_('Could not generate output statistics for', self.name)
return
def hastings_factor(self):
tau = 1./(self.adaptive_scale_factor * self.proposal_sd)**2
cur_val = self.stochastic.value
last_val = self.stochastic.last_value
lp_for = pm.truncnorm_like(cur_val, last_val, tau, self.low_bound, self.up_bound)
lp_bak = pm.truncnorm_like(last_val, cur_val, tau, self.low_bound, self.up_bound)
if self.verbose > 1:
six.print_(self._id + ': Hastings factor %f'%(lp_bak - lp_for))
return lp_bak - lp_for
def hastings_factor(self):
tau = 1. / (self.adaptive_scale_factor * self.proposal_sd)**2
cur_val = self.stochastic.value
last_val = self.stochastic.last_value
lp_for = pm.truncnorm_like(cur_val, last_val, tau, self.low_bound,
self.up_bound)
lp_bak = pm.truncnorm_like(last_val, cur_val, tau, self.low_bound,
self.up_bound)
if self.verbose > 1:
six.print_(self._id + ': Hastings factor %f' % (lp_bak - lp_for))
return lp_bak - lp_for
def iat(x, maxlag=None):
"""Calculate the integrated autocorrelation time (IAT), given the trace from a Stochastic."""
if not maxlag:
# Calculate maximum lag to which autocorrelation is calculated
maxlag = _find_max_lag(x)
acr = [autocorr(x, lag) for lag in range(1, maxlag + 1)]
# Calculate gamma values
gammas = [(acr[2 * i] + acr[2 * i + 1]) for i in range(maxlag // 2)]
cut = _cut_time(gammas)
if cut + 1 == len(gammas):
print_("Not enough lag to calculate IAT")
return np.sum(2 * gammas[:cut + 1]) - 1.0
def iat(x, maxlag=None):
"""Calculate the integrated autocorrelation time (IAT), given the trace from a Stochastic."""
if not maxlag:
# Calculate maximum lag to which autocorrelation is calculated
maxlag = _find_max_lag(x)
acr = [autocorr(x, lag) for lag in range(1, maxlag+1)]
# Calculate gamma values
gammas = [(acr[2*i]+acr[2*i+1]) for i in range(maxlag//2)]
cut = _cut_time(gammas)
if cut+1 == len(gammas):
print_("Not enough lag to calculate IAT")
return np.sum(2*gammas[:cut+1]) - 1.0
def _find_max_lag(x, rho_limit=0.05, maxmaxlag=20000, verbose=0):
"""Automatically find an appropriate maximum lag to calculate IAT"""
# Fetch autocovariance matrix
acv = autocov(x)
# Calculate rho
rho = acv[0,1]/acv[0,0]
lam = -1./np.log(abs(rho))
# Initial guess at 1.5 times lambda (i.e. 3 times mean life)
maxlag = int(np.floor(3.*lam)) + 1
# Jump forward 1% of lambda to look for rholimit threshold
jump = int(np.ceil(0.01*lam)) + 1
T = len(x)
while ((abs(rho) > rho_limit) & (maxlag < min(T/2, maxmaxlag))):
acv = autocov(x, maxlag)
rho = acv[0,1]/acv[0,0]
maxlag += jump
# Add 30% for good measure
maxlag = int(np.floor(1.3*maxlag))
if maxlag >= min(T/2, maxmaxlag):
maxlag = min(min(T/2, maxlag), maxmaxlag)
"maxlag fixed to %d" % maxlag
return maxlag
if maxlag <= 1:
print_("maxlag = %d, fixing value to 10" % maxlag)
return 10
if verbose:
print_("maxlag = %d" % maxlag)
return maxlag
def _find_max_lag(x, rho_limit=0.05, maxmaxlag=20000, verbose=0):
"""Automatically find an appropriate maximum lag to calculate IAT"""
# Fetch autocovariance matrix
acv = autocov(x)
# Calculate rho
rho = acv[0, 1] / acv[0, 0]
lam = -1. / np.log(abs(rho))
# Initial guess at 1.5 times lambda (i.e. 3 times mean life)
maxlag = int(np.floor(3. * lam)) + 1
# Jump forward 1% of lambda to look for rholimit threshold
jump = int(np.ceil(0.01 * lam)) + 1
T = len(x)
while ((abs(rho) > rho_limit) & (maxlag < min(T / 2, maxmaxlag))):
acv = autocov(x, maxlag)
rho = acv[0, 1] / acv[0, 0]
maxlag += jump
# Add 30% for good measure
maxlag = int(np.floor(1.3 * maxlag))
if maxlag >= min(T / 2, maxmaxlag):
maxlag = min(min(T / 2, maxlag), maxmaxlag)
"maxlag fixed to %d" % maxlag
return maxlag
if maxlag <= 1:
print_("maxlag = %d, fixing value to 10" % maxlag)
return 10
if verbose:
print_("maxlag = %d" % maxlag)
return maxlag
def propose_second(self):
"""
This method proposes values for stochastics based on the empirical
covariance of the values sampled so far.
The proposal jumps are drawn from a multivariate normal distribution.
"""
arrayjump = self.drscale * np.dot(
self.proposal_sd,
np.random.normal(size=self.proposal_sd.shape[0]),
)
if self.verbose > 2: print_('Second jump:', arrayjump)
# Update each stochastic individually.
for stochastic in self.stochastics:
jump = arrayjump[self._slices[stochastic]].squeeze()
if np.iterable(stochastic.value):
jump = np.reshape(
arrayjump[self._slices[stochastic]],
np.shape(stochastic.value),
)
if self.isdiscrete[stochastic]:
jump = round_array(jump)
stochastic.value = stochastic.value + jump
arrayjump1 = self.arrayjump1
arrayjump2 = arrayjump
self.q = np.exp(
-0.5 * (
np.linalg.norm(np.dot(arrayjump2 - arrayjump1, self.proposal_sd_inv), ord=2) ** 2 \
- np.linalg.norm(np.dot(-arrayjump1, self.proposal_sd_inv), ord=2) ** 2
)
)
def discrepancy(observed, simulated, expected):
"""Calculates Freeman-Tukey statistics (Freeman and Tukey 1950) as
a measure of discrepancy between observed and r replicates of simulated data. This
is a convenient method for assessing goodness-of-fit (see Brooks et al. 2000).
D(x|\theta) = \sum_j (\sqrt{x_j} - \sqrt{e_j})^2
:Parameters:
observed : Iterable of observed values (size=(n,))
simulated : Iterable of simulated values (size=(r,n))
expected : Iterable of expected values (size=(r,) or (r,n))
:Returns:
D_obs : Discrepancy of observed values
D_sim : Discrepancy of simulated values
"""
try:
simulated = simulated.astype(float)
except AttributeError:
simulated = simulated.trace().astype(float)
try:
expected = expected.astype(float)
except AttributeError:
expected = expected.trace().astype(float)
# Ensure expected values are rxn
expected = np.resize(expected, simulated.shape)
D_obs = np.sum([(np.sqrt(observed) - np.sqrt(e))**2 for e in expected], 1)
D_sim = np.sum([(np.sqrt(s) - np.sqrt(e))**2
for s, e in zip(simulated, expected)], 1)
# Print p-value
count = sum(s > o for o, s in zip(D_obs, D_sim))
print_('Bayesian p-value: p=%.3f' % (1. * count / len(D_obs)))
return D_obs, D_sim
def callback(p):
try:
print_('Current log-probability : %f' % self.logp)
except ZeroProbability:
print_('Current log-probability : %f' % -Inf)
import pymc
from pymc import six
from . import simple_von_mises
model=pymc.MCMC(simple_von_mises)
model.sample(iter=1000, burn=500, thin=2)
six.print_('mu',model.mu.value)
six.print_('kappa',model.kappa.value)
except:
pass
try:
import scipy.stats
from scipy import integrate, special
from scipy.misc import factorial, comb
from scipy.stats import genextreme, exponweib
from scipy.optimize import fmin
SP = True
except:
SP = False
try:
import pylab as P
except:
six.print_('Plotting disabled')
PLOT = False
# Some python densities for comparison
def cauchy(x, x0, gamma):
return 1/pi * gamma/((x-x0)**2 + gamma**2)
def gamma(x, alpha, beta):
return x**(alpha-1) * exp(-x/beta)/(special.gamma(alpha) * beta**alpha)
def multinomial_beta(alpha):
nom = (special.gamma(alpha)).prod(0)
den = special.gamma(alpha.sum(0))
return nom/den
except:
pass
try:
import scipy.stats
from scipy import integrate, special
from scipy.misc import factorial, comb
from scipy.stats import genextreme, exponweib
from scipy.optimize import fmin
SP = True
except:
SP = False
try:
import pylab as P
except:
six.print_('Plotting disabled')
PLOT = False
# Some python densities for comparison
def cauchy(x, x0, gamma):
return 1 / pi * gamma / ((x - x0)**2 + gamma**2)
def gamma(x, alpha, beta):
return x**(alpha - 1) * exp(
-x / beta) / (special.gamma(alpha) * beta**alpha)
def multinomial_beta(alpha):
nom = (special.gamma(alpha)).prod(0)
def propose(self):
if self.verbose:
print_(self._id + ' proposing')
fc = pm.gp.fast_matrix_copy
eps_p_f = pm.utils.value(self.eps_p_f)
f = pm.utils.value(self.f_eval)
for i in xrange(len(self.scratch3)):
self.scratch3[i] = np.sum(eps_p_f[self.ti[i]] - f[i])
# Compute Cholesky factor of covariance of eps_p_f, C(x,x) + V
C_eval_value = pm.utils.value(self.C_eval)
C_eval_shape = C_eval_value.shape
# Get the Cholesky factor of C_eval, plus the nugget.
# I don't think you can use S_eval for speed, unfortunately.
in_chol = fc(C_eval_value, self.scratch1)
v_val = pm.utils.value(self.V)
for i in xrange(pm.utils.value(C_eval_shape)[0]):
in_chol[i, i] += v_val[i] / np.alen(self.ti[i])
info = pm.gp.linalg_utils.dpotrf_wrap(in_chol)
if info > 0:
raise np.linalg.LinAlgError
# Compute covariance of f conditional on eps_p_f.
offdiag = fc(C_eval_value, self.scratch2)
offdiag = pm.gp.trisolve(in_chol,
offdiag,
uplo='U',
transa='T',
inplace=True)
C_step = offdiag.T * offdiag
C_step *= -1
C_step += C_eval_value
# Compute mean of f conditional on eps_p_f.
for i in xrange(len(self.scratch3)):
self.scratch3[i] = np.mean(eps_p_f[self.ti[i]])
m_step = pm.utils.value(self.M_eval) + np.dot(
offdiag.T,
pm.gp.trisolve(in_chol, (self.scratch3 - self.M_eval.value),
uplo='U',
transa='T')).view(np.ndarray).ravel()
sig_step = C_step
info = pm.gp.linalg_utils.dpotrf_wrap(C_step.T)
if info > 0:
warnings.warn(
'Full conditional covariance was not positive definite.')
return
# Update value of f.
self.f_eval.value = m_step + np.dot(
sig_step, np.random.normal(size=sig_step.shape[1])).view(
np.ndarray).ravel()
# Propose the rest of the field from its conditional prior.
self.f.rand()
def step(self):
"""
Perform the Robust Metropolis step.
"""
self._current_iter += 1
# Probability and likelihood for s's current value:
if self.verbose > 2:
print_()
print_(self._id + ' getting initial logp.')
logp = self.logp_plus_loglike
if self.verbose > 2:
print_(self._id + ' proposing.')
# Sample a candidate value
unit_proposal = self.unit_proposal(
) # First get unit proposal from a normal or t distribution.
# Now scale this unit proposal
if self._dim == 1:
centered_proposal = self._cholesky_factor * unit_proposal
else:
centered_proposal = np.transpose(
self._cholesky_factor).dot(unit_proposal)
self.stochastic.value = self.stochastic.value + centered_proposal
# Probability and likelihood for s's proposed value:
try:
logp_p = self.logp_plus_loglike
except ZeroProbability:
# Reject proposal
if self.verbose > 2:
print_(self._id + ' rejecting due to ZeroProbability.')
self.reject()
# Increment rejected count
self._rejected += 1
if self.verbose > 2:
print_(self._id + ' returning.')
return
if self.verbose > 2:
print_('logp_p - logp: ', logp_p - logp)
# Evaluate acceptance ratio
alpha = min(1.0, np.exp(logp_p - logp))
unif = np.random.uniform()
if unif > alpha:
# Revert s if fail
self.reject()
# Increment rejected count
self._rejected += 1
if self.verbose > 2:
print_(self._id + ' rejecting')
else:
# Increment accepted count
self._accepted += 1
if self.verbose > 2:
print_(self._id + ' accepting')
if (self._current_iter < self._stop_adapting) & (np.isfinite(alpha)):
# Update the scale matrix of the proposals
self.update_covar(alpha, unit_proposal, centered_proposal)
if self.verbose > 2:
print_(self._id + ' returning.')
def step(self):
"""
Perform the Robust Metropolis step.
"""
self._current_iter += 1
# Probability and likelihood for s's current value:
if self.verbose > 2:
print_()
print_(self._id + ' getting initial logp.')
logp = self.logp_plus_loglike
if self.verbose > 2:
print_(self._id + ' proposing.')
# Sample a candidate value
unit_proposal = self.unit_proposal() # First get unit proposal from a normal or t distribution.
# Now scale this unit proposal
if self._dim == 1:
centered_proposal = self._cholesky_factor * unit_proposal
else:
centered_proposal = np.transpose(self._cholesky_factor).dot(unit_proposal)
self.stochastic.value = self.stochastic.value + centered_proposal
# Probability and likelihood for s's proposed value:
try:
logp_p = self.logp_plus_loglike
except ZeroProbability:
# Reject proposal
if self.verbose > 2:
print_(self._id + ' rejecting due to ZeroProbability.')
self.reject()
# Increment rejected count
self._rejected += 1
if self.verbose > 2:
print_(self._id + ' returning.')
return
if self.verbose > 2:
print_('logp_p - logp: ', logp_p - logp)
# Evaluate acceptance ratio
alpha = min(1.0, np.exp(logp_p - logp))
unif = np.random.uniform()
if unif > alpha:
# Revert s if fail
self.reject()
# Increment rejected count
self._rejected += 1
if self.verbose > 2:
print_(self._id + ' rejecting')
else:
# Increment accepted count
self._accepted += 1
if self.verbose > 2:
print_(self._id + ' accepting')
if (self._current_iter < self._stop_adapting) & (np.isfinite(alpha)):
# Update the scale matrix of the proposals
self.update_covar(alpha, unit_proposal, centered_proposal)
if self.verbose > 2:
print_(self._id + ' returning.')
def validate(sampler,
replicates=20,
iterations=10000,
burn=5000,
thin=1,
deterministic=False,
db='ram',
plot=True,
verbose=0):
"""
Model validation method, following Cook et al. (Journal of Computational and
Graphical Statistics, 2006, DOI: 10.1198/106186006X136976).
Generates posterior samples based on 'true' parameter values and data simulated
from the priors. The quantiles of the parameter values are calculated, based on
the samples. If the model is valid, the quantiles should be uniformly distributed
over [0,1].
Since this relies on the generation of simulated data, all data stochastics
must have a valid random() method for validation to proceed.
Parameters
----------
sampler : Sampler
An MCMC sampler object.
replicates (optional) : int
The number of validation replicates (i.e. number of quantiles to be simulated).
Defaults to 100.
iterations (optional) : int
The number of MCMC iterations to be run per replicate. Defaults to 2000.
burn (optional) : int
The number of burn-in iterations to be run per replicate. Defaults to 1000.
thin (optional) : int
The thinning factor to be applied to posterior sample. Defaults to 1 (no thinning)
deterministic (optional) : bool
Flag for inclusion of deterministic nodes in validation procedure. Defaults
to False.
db (optional) : string
The database backend to use for the validation runs. Defaults to 'ram'.
plot (optional) : bool
Flag for validation plots. Defaults to True.
Returns
-------
stats : dict
Return a dictionary containing tuples with the chi-square statistic and
associated p-value for each data stochastic.
Notes
-----
This function requires SciPy.
"""
import scipy as sp
# Set verbosity for models to zero
sampler.verbose = 0
# Specify parameters to be evaluated
parameters = sampler.stochastics
if deterministic:
# Add deterministics to the mix, if requested
parameters = parameters | sampler.deterministics
# Assign database backend
original_backend = sampler.db.__name__
sampler._assign_database_backend(db)
# Empty lists for quantiles
quantiles = {}
if verbose:
print_("\nExecuting Cook et al. (2006) validation procedure ...\n")
# Loop over replicates
for i in range(replicates):
# Sample from priors
for p in sampler.stochastics:
if not p.extended_parents:
p.random()
# Sample "true" data values
for o in sampler.observed_stochastics:
# Generate simuated data for data stochastic
o.set_value(o.random(), force=True)
if verbose:
print_("Data for %s is %s" % (o.__name__, o.value))
param_values = {}
# Record data-generating parameter values
for s in parameters:
param_values[s] = s.value
try:
# Fit models given parameter values
sampler.sample(iterations, burn=burn, thin=thin)
for s in param_values:
if not i:
# Initialize dict
quantiles[s.__name__] = []
trace = s.trace()
q = sum(trace < param_values[s], 0) / float(len(trace))
quantiles[s.__name__].append(open01(q))
# Replace data values
for o in sampler.observed_stochastics:
o.revert()
finally:
# Replace data values
for o in sampler.observed_stochastics:
o.revert()
# Replace backend
sampler._assign_database_backend(original_backend)
if not i % 10 and i and verbose:
print_("\tCompleted validation replicate", i)
# Replace backend
sampler._assign_database_backend(original_backend)
stats = {}
# Calculate chi-square statistics
for param in quantiles:
q = quantiles[param]
# Calculate chi-square statistics
X2 = sum(sp.special.ndtri(q)**2)
# Calculate p-value
p = sp.special.chdtrc(replicates, X2)
stats[param] = (X2, p)
if plot:
# Convert p-values to z-scores
p = copy(stats)
for i in p:
p[i] = p[i][1]
pymc.Matplot.zplot(p, verbose=verbose)
return stats
def __init__(
self,
stochastic,
cov=None,
delay=1000,
interval=200,
greedy=True,
drscale=0.1,
shrink_if_necessary=False,
scales=None,
verbose=-1,
tally=False,
):
# Verbosity flag
self.verbose = verbose
self.accepted = 0
self.rejected = 0 # Just a dummy variable for compatibility with the superclass
self.rejected_then_accepted = 0
self.rejected_twice = 0
if not np.iterable(stochastic) or isinstance(stochastic,
pymc.Variable):
stochastic = [stochastic]
# Initialize superclass
pymc.StepMethod.__init__(self, stochastic, verbose, tally)
self._id = 'DelayedRejectionAdaptiveMetropolis_' + '_'.join(
[p.__name__ for p in self.stochastics])
# State variables used to restore the state in a latter session.
self._state += [
'accepted', 'rejected_then_accepted', 'rejected_twice',
'_trace_count', '_current_iter', 'C', 'proposal_sd',
'_proposal_deviate', '_trace', 'shrink_if_necessary'
]
self._tuning_info = ['C']
self.proposal_sd = None
self.shrink_if_necessary = shrink_if_necessary
# Number of successful steps before the empirical covariance is
# computed
self.delay = delay
# Interval between covariance updates
self.interval = interval
# Flag for tallying only accepted jumps until delay reached
self.greedy = greedy
# Scale for second attempt
self.drscale = drscale
# Initialization methods
self.check_type()
self.dimension()
# Set the initial covariance using cov, or the following fallback mechanisms:
# 1. If scales is provided, use it.
# 2. If a trace is present, compute the covariance matrix empirically from it.
# 3. Use the stochastics value as a guess of the variance.
if cov is not None:
self.C = cov
elif scales:
self.C = self.cov_from_scales(scales)
else:
try:
self.C = self.cov_from_trace()
except AttributeError:
self.C = self.cov_from_value(100.)
self.updateproposal_sd()
# Keep track of the internal trace length
# It may be different from the iteration count since greedy
# sampling can be done during warm-up period.
self._trace_count = 0
self._current_iter = 0
self._proposal_deviate = np.zeros(self.dim)
self.chain_mean = np.asmatrix(np.zeros(self.dim))
self._trace = []
if self.verbose >= 2:
print_("Initialization...")
print_('Dimension: ', self.dim)
print_("C_0: ", self.C)
print_("Sigma: ", self.proposal_sd)
from . import PyMCmodel
import pymc as pm
from pymc import six
import numpy as np
import matplotlib.pyplot as pl
import matplotlib
matplotlib.rcParams['axes.facecolor'] = 'w'
import time
n_iter = 10000
rej = []
times = []
mesh_sizes = [0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512]
for mesh_size in [0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512]:
six.print_(mesh_size)
m = PyMCmodel.make_model(mesh_size, False)
if mesh_size == 0:
sm = pm.gp.MeshlessGPMetropolis(m['sm'].f)
else:
sm = pm.gp.GPEvaluationMetropolis(m['sm'].f_eval, proposal_sd=.01)
t1 = time.time()
for i in xrange(n_iter):
sm.step()
times.append((time.time() - t1) / float(n_iter))
rej.append(sm.rejected / float(sm.rejected + sm.accepted))
m = PyMCmodel.make_model(0, True)
sm = pm.gp.GPEvaluationMetropolis(m['sm'].f_eval, proposal_sd=.01)
t1 = time.time()
for i in xrange(n_iter):
def raftery_lewis(x, q, r, s=.95, epsilon=.001, verbose=1):
"""
Return the number of iterations needed to achieve a given
precision.
:Parameters:
x : sequence
Sampled series.
q : float
Quantile.
r : float
Accuracy requested for quantile.
s (optional) : float
Probability of attaining the requested accuracy (defaults to 0.95).
epsilon (optional) : float
Half width of the tolerance interval required for the q-quantile (defaults to 0.001).
verbose (optional) : int
Verbosity level for output (defaults to 1).
:Return:
nmin : int
Minimum number of independent iterates required to achieve
the specified accuracy for the q-quantile.
kthin : int
Skip parameter sufficient to produce a first-order Markov
chain.
nburn : int
Number of iterations to be discarded at the beginning of the
simulation, i.e. the number of burn-in iterations.
nprec : int
Number of iterations not including the burn-in iterations which
need to be obtained in order to attain the precision specified
by the values of the q, r and s input parameters.
kmind : int
Minimum skip parameter sufficient to produce an independence
chain.
:Example:
>>> raftery_lewis(x, q=.025, r=.005)
:Reference:
Raftery, A.E. and Lewis, S.M. (1995). The number of iterations,
convergence diagnostics and generic Metropolis algorithms. In
Practical Markov Chain Monte Carlo (W.R. Gilks, D.J. Spiegelhalter
and S. Richardson, eds.). London, U.K.: Chapman and Hall.
See the fortran source file `gibbsit.f` for more details and references.
"""
if np.rank(x) > 1:
return [
raftery_lewis(y, q, r, s, epsilon, verbose)
for y in np.transpose(x)
]
output = nmin, kthin, nburn, nprec, kmind = pymc.flib.gibbmain(
x, q, r, s, epsilon)
if verbose:
print_("\n========================")
print_("Raftery-Lewis Diagnostic")
print_("========================")
print_()
print_(
"%s iterations required (assuming independence) to achieve %s accuracy with %i percent probability."
% (nmin, r, 100 * s))
print_()
print_(
"Thinning factor of %i required to produce a first-order Markov chain."
% kthin)
print_()
print_(
"%i iterations to be discarded at the beginning of the simulation (burn-in)."
% nburn)
print_()
print_("%s subsequent iterations required." % nprec)
print_()
print_(
"Thinning factor of %i required to produce an independence chain."
% kmind)
return output
def raftery_lewis(x, q, r, s=.95, epsilon=.001, verbose=1):
"""
Return the number of iterations needed to achieve a given
precision.
:Parameters:
x : sequence
Sampled series.
q : float
Quantile.
r : float
Accuracy requested for quantile.
s (optional) : float
Probability of attaining the requested accuracy (defaults to 0.95).
epsilon (optional) : float
Half width of the tolerance interval required for the q-quantile (defaults to 0.001).
verbose (optional) : int
Verbosity level for output (defaults to 1).
:Return:
nmin : int
Minimum number of independent iterates required to achieve
the specified accuracy for the q-quantile.
kthin : int
Skip parameter sufficient to produce a first-order Markov
chain.
nburn : int
Number of iterations to be discarded at the beginning of the
simulation, i.e. the number of burn-in iterations.
nprec : int
Number of iterations not including the burn-in iterations which
need to be obtained in order to attain the precision specified
by the values of the q, r and s input parameters.
kmind : int
Minimum skip parameter sufficient to produce an independence
chain.
:Example:
>>> raftery_lewis(x, q=.025, r=.005)
:Reference:
Raftery, A.E. and Lewis, S.M. (1995). The number of iterations,
convergence diagnostics and generic Metropolis algorithms. In
Practical Markov Chain Monte Carlo (W.R. Gilks, D.J. Spiegelhalter
and S. Richardson, eds.). London, U.K.: Chapman and Hall.
See the fortran source file `gibbsit.f` for more details and references.
"""
if np.rank(x)>1:
return [raftery_lewis(y, q, r, s, epsilon, verbose) for y in np.transpose(x)]
output = nmin, kthin, nburn, nprec, kmind = pymc.flib.gibbmain(x, q, r, s, epsilon)
if verbose:
print_("\n========================")
print_("Raftery-Lewis Diagnostic")
print_("========================")
print_()
print_("%s iterations required (assuming independence) to achieve %s accuracy with %i percent probability." % (nmin, r, 100*s))
print_()
print_("Thinning factor of %i required to produce a first-order Markov chain." % kthin)
print_()
print_("%i iterations to be discarded at the beginning of the simulation (burn-in)." % nburn)
print_()
print_("%s subsequent iterations required." % nprec)
print_()
print_("Thinning factor of %i required to produce an independence chain." % kmind)
return output
def __init__(self, input=None, eps=.001, diff_order = 5, verbose=-1):
if not scipy_imported:
raise ImportError('Scipy must be installed to use NormApprox and MAP.')
Model.__init__(self, input, verbose=verbose)
# Allocate memory for internal traces and get stochastic slices
self._slices = {}
self.len = 0
self.stochastic_len = {}
self.fitted = False
self.stochastic_list = list(self.stochastics)
self.N_stochastics = len(self.stochastic_list)
self.stochastic_indices = []
self.stochastic_types = []
self.stochastic_type_dict = {}
for i in xrange(len(self.stochastic_list)):
stochastic = self.stochastic_list[i]
# Check types of all stochastics.
type_now = check_type(stochastic)[0]
self.stochastic_type_dict[stochastic] = type_now
if not type_now is float:
print_("Warning: Stochastic " + stochastic.__name__ + "'s value is neither numerical nor array with " + \
"floating-point dtype. Recommend fitting method fmin (default).")
# Inspect shapes of all stochastics and create stochastic slices.
if isinstance(stochastic.value, ndarray):
self.stochastic_len[stochastic] = len(ravel(stochastic.value))
else:
self.stochastic_len[stochastic] = 1
self._slices[stochastic] = slice(self.len, self.len + self.stochastic_len[stochastic])
self.len += self.stochastic_len[stochastic]
# Record indices that correspond to each stochastic.
for j in range(len(ravel(stochastic.value))):
self.stochastic_indices.append((stochastic, j))
self.stochastic_types.append(type_now)
self.data_len = 0
for datum in self.observed_stochastics:
self.data_len += len(ravel(datum.value))
# Unpack step
self.eps = zeros(self.len,dtype=float)
if isinstance(eps,dict):
for stochastic in self.stochastics:
self.eps[self._slices[stochastic]] = eps[stochastic]
else:
self.eps[:] = eps
self.diff_order = diff_order
self._len_range = arange(self.len)
# Initialize gradient and Hessian matrix.
self.grad = zeros(self.len, dtype=float)
self.hess = asmatrix(zeros((self.len, self.len), dtype=float))
self._mu = None
# Initialize NormApproxMu object.
self.mu = NormApproxMu(self)
def func_for_diff(val, index):
"""
The function that gets passed to the derivatives.
"""
self[index] = val
return self.i_logp(index)
self.func_for_diff = func_for_diff
def step(self):
"""
Perform a Metropolis step.
Stochastic parameters are block-updated using a multivariate normal
distribution whose covariance is updated every self.interval once
self.delay steps have been performed.
The AM instance keeps a local copy of the stochastic parameter's trace.
This trace is used to computed the empirical covariance, and is
completely independent from the Database backend.
If self.greedy is True and the number of iterations is smaller than
self.delay, only accepted jumps are stored in the internal
trace to avoid computing singular covariance matrices.
"""
# Probability and likelihood for stochastic's current value:
# PROBLEM: I am using logp plus loglike everywhere... and I shouldn't be!! TODO
logp = self.logp_plus_loglike
if self.verbose > 1:
print_('Current value: ', self.stoch2array())
print_('Current likelihood: ', logp)
# Sample a candidate value
self.propose_first()
# Metropolis acception/rejection test
accept = False
try:
# Probability and likelihood for stochastic's 1st proposed value:
self.logp_p1 = self.logp_plus_loglike
logp_p1 = float(self.logp_p1)
self.logalpha01 = min(0, logp_p1 - logp)
logalpha01 = self.logalpha01
if self.verbose > 2:
print_('First proposed value: ', self.stoch2array())
print_('First proposed likelihood: ', logp_p1)
if np.log(np.random.random()) < logalpha01:
accept = True
self.accepted += 1
if self.verbose > 2:
print_('Accepted')
logp_p = logp_p1
else:
if self.verbose > 2:
print_('Delaying rejection...')
for stochastic in self.stochastics:
stochastic.revert()
self.propose_second()
try:
# Probability and likelihood for stochastic's 2nd proposed value:
# CHECK THAT THIS IS RECALCULATED WITH PROPOSE_SECODN
# CHECK THAT logp_p1 iS NOT CHANGED WHEN THIS IS RECALCD
logp_p2 = self.logp_plus_loglike
logalpha21 = min(0, logp_p1 - logp_p2)
l = logp_p2 - logp
q = self.q
logalpha_02 = np.log(
l * q * (1 - np.exp(logalpha21)) \
/ (1 - np.exp(logalpha01))
)
if self.verbose > 2:
print_('Second proposed value: ', self.stoch2array())
print_('Second proposed likelihood: ', logp_p2)
if np.log(np.random.random()) < logalpha_02:
accept = True
self.rejected_then_accepted += 1
logp_p = logp_p2
if self.verbose > 2:
print_('Accepted after one rejection')
else:
self.rejected_twice += 1
logp_p = None
if self.verbose > 2:
print_('Rejected twice')
except pymc.ZeroProbability:
self.rejected_twice += 1
logp_p = None
if self.verbose > 2:
print_('Rejected twice')
except pymc.ZeroProbability:
if self.verbose > 2:
print_('Delaying rejection...')
for stochastic in self.stochastics:
stochastic.revert()
self.propose_second()
try:
# Probability and likelihood for stochastic's proposed value:
logp_p2 = self.logp_plus_loglike
logp_p1 = -np.inf
logalpha01 = -np.inf
logalpha21 = min(0, logp_p1 - logp_p2)
l = np.exp(logp_p2 - logp)
q = self.q
logalpha_02 = np.log(
l * q * (1 - np.exp(logalpha21)) \
/ (1 - np.exp(logalpha01))
)
if self.verbose > 2:
print_('Second proposed value: ', self.stoch2array())
print_('Second proposed likelihood: ', logp_p2)
if np.log(np.random.random()) < logalpha_02:
accept = True
self.rejected_then_accepted += 1
logp_p = logp_p2
if self.verbose > 2:
print_(
'Accepted after one rejection with ZeroProbability'
)
else:
self.rejected_twice += 1
logp_p = None
if self.verbose > 2:
print_('Rejected twice')
except pymc.ZeroProbability:
self.rejected_twice += 1
logp_p = None
if self.verbose > 2:
print_('Rejected twice with ZeroProbability Error.')
#print_('\n\nRejected then accepted number of times: ',self.rejected_then_accepted)
#print_('Rejected twice number of times: ',self.rejected_twice)
if (not self._current_iter % self.interval) and self.verbose > 1:
print_("Step ", self._current_iter)
print_("\tLogprobability (current, proposed): ", logp, logp_p)
for stochastic in self.stochastics:
print_(
"\t",
stochastic.__name__,
stochastic.last_value,
stochastic.value,
)
if accept:
print_("\tAccepted\t*******\n")
else:
print_("\tRejected\n")
print_("\tAcceptance ratio: ",
(self.accepted + self.rejected_then_accepted) /
(self.accepted + 2. * self.rejected_then_accepted +
2. * self.rejected_twice))
if self._current_iter == self.delay:
self.greedy = False
if not accept:
self.reject()
if accept or not self.greedy:
self.internal_tally()
if self._current_iter > self.delay and self._current_iter % self.interval == 0:
self.update_cov()
self._current_iter += 1
from . import PyMCmodel
import pymc as pm
from pymc import six
import numpy as np
import matplotlib.pyplot as pl
import matplotlib
matplotlib.rcParams['axes.facecolor']='w'
import time
n_iter = 10000
rej = []
times = []
mesh_sizes = [0,1,2,4,8,16,32,64,128,256,512]
for mesh_size in [0,1,2,4,8,16,32,64,128,256,512]:
six.print_(mesh_size)
m = PyMCmodel.make_model(mesh_size, False)
if mesh_size==0:
sm = pm.gp.MeshlessGPMetropolis(m['sm'].f)
else:
sm = pm.gp.GPEvaluationMetropolis(m['sm'].f_eval, proposal_sd=.01)
t1 = time.time()
for i in xrange(n_iter):
sm.step()
times.append((time.time()-t1)/float(n_iter))
rej.append(sm.rejected/float(sm.rejected + sm.accepted))
m = PyMCmodel.make_model(0, True)
sm = pm.gp.GPEvaluationMetropolis(m['sm'].f_eval, proposal_sd=.01)
t1 = time.time()
for i in xrange(n_iter):
def callback(p):
try:
print_('Current log-probability : %f' % self.logp)
except ZeroProbability:
print_('Current log-probability : %f' % -Inf)
def validate(sampler, replicates=20, iterations=10000, burn=5000, thin=1, deterministic=False, db='ram', plot=True, verbose=0):
"""
Model validation method, following Cook et al. (Journal of Computational and
Graphical Statistics, 2006, DOI: 10.1198/106186006X136976).
Generates posterior samples based on 'true' parameter values and data simulated
from the priors. The quantiles of the parameter values are calculated, based on
the samples. If the model is valid, the quantiles should be uniformly distributed
over [0,1].
Since this relies on the generation of simulated data, all data stochastics
must have a valid random() method for validation to proceed.
Parameters
----------
sampler : Sampler
An MCMC sampler object.
replicates (optional) : int
The number of validation replicates (i.e. number of quantiles to be simulated).
Defaults to 100.
iterations (optional) : int
The number of MCMC iterations to be run per replicate. Defaults to 2000.
burn (optional) : int
The number of burn-in iterations to be run per replicate. Defaults to 1000.
thin (optional) : int
The thinning factor to be applied to posterior sample. Defaults to 1 (no thinning)
deterministic (optional) : bool
Flag for inclusion of deterministic nodes in validation procedure. Defaults
to False.
db (optional) : string
The database backend to use for the validation runs. Defaults to 'ram'.
plot (optional) : bool
Flag for validation plots. Defaults to True.
Returns
-------
stats : dict
Return a dictionary containing tuples with the chi-square statistic and
associated p-value for each data stochastic.
Notes
-----
This function requires SciPy.
"""
import scipy as sp
# Set verbosity for models to zero
sampler.verbose = 0
# Specify parameters to be evaluated
parameters = sampler.stochastics
if deterministic:
# Add deterministics to the mix, if requested
parameters = parameters | sampler.deterministics
# Assign database backend
original_backend = sampler.db.__name__
sampler._assign_database_backend(db)
# Empty lists for quantiles
quantiles = {}
if verbose:
print_("\nExecuting Cook et al. (2006) validation procedure ...\n")
# Loop over replicates
for i in range(replicates):
# Sample from priors
for p in sampler.stochastics:
if not p.extended_parents:
p.random()
# Sample "true" data values
for o in sampler.observed_stochastics:
# Generate simuated data for data stochastic
o.set_value(o.random(), force=True)
if verbose:
print_("Data for %s is %s" % (o.__name__, o.value))
param_values = {}
# Record data-generating parameter values
for s in parameters:
param_values[s] = s.value
try:
# Fit models given parameter values
sampler.sample(iterations, burn=burn, thin=thin)
for s in param_values:
if not i:
# Initialize dict
quantiles[s.__name__] = []
trace = s.trace()
q = sum(trace<param_values[s], 0)/float(len(trace))
quantiles[s.__name__].append(open01(q))
# Replace data values
for o in sampler.observed_stochastics:
o.revert()
finally:
# Replace data values
for o in sampler.observed_stochastics:
o.revert()
# Replace backend
sampler._assign_database_backend(original_backend)
if not i % 10 and i and verbose:
print_("\tCompleted validation replicate", i)
# Replace backend
sampler._assign_database_backend(original_backend)
stats = {}
# Calculate chi-square statistics
for param in quantiles:
q = quantiles[param]
# Calculate chi-square statistics
X2 = sum(sp.special.ndtri(q)**2)
# Calculate p-value
p = sp.special.chdtrc(replicates, X2)
stats[param] = (X2, p)
if plot:
# Convert p-values to z-scores
p = copy(stats)
for i in p:
p[i] = p[i][1]
pymc.Matplot.zplot(p, verbose=verbose)
return stats
def __init__(self, input=None, eps=.001, diff_order=5, verbose=-1):
if not scipy_imported:
raise ImportError(
'Scipy must be installed to use NormApprox and MAP.')
Model.__init__(self, input, verbose=verbose)
# Allocate memory for internal traces and get stochastic slices
self._slices = {}
self.len = 0
self.stochastic_len = {}
self.fitted = False
self.stochastic_list = list(self.stochastics)
self.N_stochastics = len(self.stochastic_list)
self.stochastic_indices = []
self.stochastic_types = []
self.stochastic_type_dict = {}
for i in xrange(len(self.stochastic_list)):
stochastic = self.stochastic_list[i]
# Check types of all stochastics.
type_now = check_type(stochastic)[0]
self.stochastic_type_dict[stochastic] = type_now
if not type_now is float:
print_("Warning: Stochastic " + stochastic.__name__ + "'s value is neither numerical nor array with " + \
"floating-point dtype. Recommend fitting method fmin (default).")
# Inspect shapes of all stochastics and create stochastic slices.
if isinstance(stochastic.value, ndarray):
self.stochastic_len[stochastic] = len(ravel(stochastic.value))
else:
self.stochastic_len[stochastic] = 1
self._slices[stochastic] = slice(
self.len, self.len + self.stochastic_len[stochastic])
self.len += self.stochastic_len[stochastic]
# Record indices that correspond to each stochastic.
for j in range(len(ravel(stochastic.value))):
self.stochastic_indices.append((stochastic, j))
self.stochastic_types.append(type_now)
self.data_len = 0
for datum in self.observed_stochastics:
self.data_len += len(ravel(datum.value))
# Unpack step
self.eps = zeros(self.len, dtype=float)
if isinstance(eps, dict):
for stochastic in self.stochastics:
self.eps[self._slices[stochastic]] = eps[stochastic]
else:
self.eps[:] = eps
self.diff_order = diff_order
self._len_range = arange(self.len)
# Initialize gradient and Hessian matrix.
self.grad = zeros(self.len, dtype=float)
self.hess = asmatrix(zeros((self.len, self.len), dtype=float))
self._mu = None
# Initialize NormApproxMu object.
self.mu = NormApproxMu(self)
def func_for_diff(val, index):
"""
The function that gets passed to the derivatives.
"""
self[index] = val
return self.i_logp(index)
self.func_for_diff = func_for_diff