def CauchyModel(size, snratio, g, g_true):
###
shearcal_m = pymc.Uniform('shearcal_m', -1, 1)
shearcal_c = pymc.Uniform('shearcal_c', -0.05, 0.05)
@pymc.deterministic
def alpha(m=shearcal_m, c=shearcal_c):
return (1 + m) * g_true + c
###
logbeta = pymc.Uniform('logbeta', -7, 2.5)
@pymc.deterministic
def beta(logbeta=logbeta):
return np.exp(logbeta)
###
data = pymc.Cauchy('data', alpha=alpha, beta=beta, value=g, observed=True)
###
return locals()
def lighthouse(data):
# Uniform priors
x = pymc.Uniform('x', lower=0, upper=10)
y = pymc.Uniform('y', lower=0, upper=10)
# Likelihood
L = pymc.Cauchy('L', alpha=x, beta=y, value=data, observed=True)
return pymc.Model([x, y, L])
def make_normal_baseline_hmm(y_data, X_data, baseline_end, initial_params):
""" Construct a PyMC2 scalar normal-emmisions HMM with a
stochastic reporting period start time parameter and baseline, reporting
parameters for all other stochastics/estimated terms in the model.
The reporting period start time parameter is given a discrete uniform
distribution starting from the first observation after the baseline to the
end of the series.
Parameters
==========
y_data: pandas.DataFrame
Usage/response observations.
X_data: list of pandas.DataFrame
List of design matrices for each state. Each must
span the entire length of observations (i.e. `y_data`).
baseline_end: pandas.tslib.Timestamp
End of baseline period (inclusive), beginning of reporting period.
initial_params: NormalHMMInitialParams
An object containing the following fields/members:
Returns
=======
A pymc.Model object used for sampling.
"""
N_states = len(X_data)
N_obs = X_data[0].shape[0]
alpha_trans = initial_params.alpha_trans
# TODO: If we wanted a distribution over the time
# when a renovation becomes effective...
baseline_idx = X_data[0].index.get_loc(baseline_end)
reporting_start = pymc.DiscreteUniform("reporting_start",
baseline_idx + 1,
N_obs,
value=baseline_idx + 1)
trans_mat_baseline = TransProbMatrix("trans_mat_baseline",
alpha_trans,
value=initial_params.trans_mat)
trans_mat_reporting = TransProbMatrix("trans_mat_reporting",
alpha_trans,
value=initial_params.trans_mat)
@pymc.deterministic(trace=True, plot=False)
def N_baseline(rs_=reporting_start):
return rs_ - 1
states_baseline_0 = initial_params.states[slice(0, baseline_idx)]
states_baseline = HMMStateSeq("states_baseline",
trans_mat_baseline,
N_baseline,
p0=initial_params.p0,
value=states_baseline_0)
@pymc.deterministic(trace=True, plot=False)
def N_reporting(rs_=reporting_start):
return N_obs - rs_
states_reporting_0 = initial_params.states[slice(baseline_idx, N_obs)]
# TODO, FIXME: p0 should depend on states_baseline and trans_mat_baseline,
# no?
states_reporting = HMMStateSeq("states_reporting",
trans_mat_reporting,
N_reporting,
p0=initial_params.p0,
value=states_reporting_0)
@pymc.deterministic(trace=True, plot=False)
def states(sb_=states_baseline, sr_=states_reporting):
return np.concatenate([sb_, sr_])
Ws = initial_params.Ws
betas = [[], []]
for s in range(N_states):
size_s = len(initial_params.betas[s])
baseline_beta_s = pymc.Cauchy('base-beta-{}'.format(s),
initial_params.betas[s],
Ws[s],
value=initial_params.betas[s],
size=size_s if size_s > 1 else None)
betas[0] += [baseline_beta_s]
reporting_beta_s = pymc.Cauchy('rep-beta-{}'.format(s),
initial_params.betas[s],
Ws[s],
value=initial_params.betas[s],
size=size_s if size_s > 1 else None)
betas[1] += [reporting_beta_s]
del s, baseline_beta_s, reporting_beta_s, size_s
Vs = initial_params.Vs
mu = HMMLinearCombination('mu', X_data, betas, states)
@pymc.deterministic(trace=False, plot=False)
def V(states_=states, V_=Vs):
return V_[states_]
if y_data is not None:
y_data = np.ma.masked_invalid(y_data).astype(np.object)
y_data.set_fill_value(None)
y_rv = pymc.Normal('y',
mu,
1. / V,
value=y_data,
observed=True if y_data is not None else False)
del initial_params
return pymc.Model(locals())
#----------------------------------------------------------------------
# Perform MCMC:
# set up our Stochastic variables, mu and gamma
mu = pymc.Uniform('mu', -5, 5)
log_gamma = pymc.Uniform('log_gamma', -10, 10, value=0)
@pymc.deterministic
def gamma(log_gamma=log_gamma):
return np.exp(log_gamma)
# set up our observed variable x
x = pymc.Cauchy('x', mu, gamma, observed=True, value=xi)
# set up our model dictionary
model = dict(mu=mu, log_gamma=log_gamma, gamma=gamma, x=x)
# perform the MCMC
S = pymc.MCMC(model)
S.sample(iter=50000, burn=5000)
# extract the traces we're interested in
trace_mu = S.trace('mu')[:]
trace_gamma = S.trace('gamma')[:]
# compute histogram of results to plot below
L_MCMC, mu_bins, gamma_bins = np.histogram2d(trace_mu,
trace_gamma,
# Import relevant modules
import pymc
import numpy as np
def hit(n, a, b):
h = np.tan(np.random.uniform(low=np.pi / 2., high=3 * np.pi / 2.,
size=n)) * b + a
return h
# Some data
n = 300
a = 1.
b = 1.5
# Priors on unknown parameters:a
alpha = pymc.Uniform('pa', lower=0.0, upper=2.0)
#alpha = pymc.Normal('pa', mu=1.0, tau=1/.3**2)
beta = pymc.Uniform('pb', lower=0.0, upper=2.0)
#beta = pymc.Normal('pb', mu=1.0, tau=1/.3**2)
h = hit(n, a, b)
# Binomial likelihood for data
hh = pymc.Cauchy('hits', alpha=alpha, beta=beta, value=h, observed=True)