def fit(self, X, y, y_error=1, x_error=None, *,
sample_kwargs={'draws': 1000, 'target_accept': 0.9,
'return_inferencedata': False}):
kwds = {}
if self.kwds is not None:
kwds.update(self.kwds)
kwds['fit_intercept'] = False
model = self._choose_regressor()
self.clf_ = model(**kwds)
self.fit_intercept = False
if x_error is not None:
x_error = np.atleast_2d(x_error)
with pm.Model():
# slope and intercept of eta-ksi relation
slope = pm.Flat('slope', shape=(X.shape[0], ))
inter = pm.Flat('inter')
# intrinsic scatter of eta-ksi relation
int_std = pm.HalfFlat('int_std')
# standard deviation of Gaussian that ksi are drawn from (assumed mean zero)
tau = pm.HalfFlat('tau', shape=(X.shape[0],))
# intrinsic ksi
mu = pm.Normal('mu', mu=0, sigma=tau, shape=(X.shape[0],))
# Some wizzarding with the dimensions all around.
ksi = pm.Normal('ksi', mu=mu, tau=tau, shape=X.T.shape)
# intrinsic eta-ksi linear relation + intrinsic scatter
eta = pm.Normal('eta', mu=(tt.dot(slope.T, ksi.T) + inter),
sigma=int_std, shape=y.shape)
# observed xi, yi
x = pm.Normal('xi', mu=ksi.T, sigma=x_error, observed=X, shape=X.shape) # noqa: F841
y = pm.Normal('yi', mu=eta, sigma=y_error, observed=y, shape=y.shape)
self.trace = pm.sample(**sample_kwargs)
# TODO: make it optional to choose a way to define best
HND, edges = np.histogramdd(np.hstack((self.trace['slope'],
self.trace['inter'][:, None])), bins=50)
w = np.where(HND == HND.max())
# choose the maximum posterior slope and intercept
slope_best = [edges[i][w[i][0]] for i in range(len(edges) - 1)]
intercept_best = edges[-1][w[-1][0]]
self.clf_.coef_ = np.array([intercept_best, *slope_best])
return self
def fit_adj_pass_model(successes, attempts):
## inputs are two lists in the form:
## successes = [successful long passes, total successful passes]
## attempts = [attempted long passes, total attempted passes]
## returns:
## sl, a numpy array of shape (6000,N) containing 6000 posterior samples of success probabilites (N is the number of players in the
## original data frame who have registered non-zero expected succcesses)
## sb, an empty list
## kk, boolean indicating which players have actually registered non-zero expected successes
## 'adj_pass', character string indicating the model type.
import numpy as np
import pymc3 as pm
import pymc3.distributions.transforms as tr
import theano.tensor as tt
LonCmp = successes[0]
TotCmp = successes[1]
LonAtt = attempts[0]
TotAtt = attempts[1]
kk = (LonCmp > 0) & np.isfinite(LonAtt)
LonCmp = LonCmp[kk]
LonAtt = LonAtt[kk]
TotCmp = TotCmp[kk]
TotAtt = TotAtt[kk]
ShCmp = TotCmp - LonCmp
ShAtt = TotAtt - LonAtt
average_long_tendency = np.mean(LonAtt / TotAtt)
N = np.sum(kk)
def logp_ab(value):
''' prior density'''
return tt.log(tt.pow(tt.sum(value), -5 / 2))
with pm.Model() as model:
# Uninformative prior for alpha and beta
ab_short = pm.HalfFlat('ab_short',
shape=2,
testval=np.asarray([1., 1.]))
ab_long = pm.HalfFlat('ab_long',
shape=2,
testval=np.asarray([1., 1.]))
pm.Potential('p(a_s, b_s)', logp_ab(ab_short))
pm.Potential('p(a_l, b_l)', logp_ab(ab_long))
lambda_short = pm.Beta('lambda_s', alpha=ab_short[0], beta=ab_short[1], shape=N)
lambda_long = pm.Beta('lambda_l', alpha=ab_long[0], beta=ab_long[1], shape=N)
y_short = pm.Binomial('y_s', p=lambda_short, observed=ShCmp, n=ShAtt)
y_long = pm.Binomial('y_l', p=lambda_short * lambda_long, observed=LonCmp, n=LonAtt)
approx = pm.fit(n=30000)
s_sh = approx.sample(6000)['lambda_s']
s_lo = approx.sample(6000)['lambda_l']
sl = average_long_tendency * s_lo + (1 - average_long_tendency) * s_sh
return [sl, [], kk, 'adj_pass']
def fit(self, matches, target):
lineups = set(matches['t1_lineup'].unique()).union(
matches['t2_lineup'].unique())
self.lineup_f2id = dict(enumerate(
lineups, 0)) # start from 0 for zero-based indexing
self.lineup_id2f = {v: k for k, v in self.lineup_f2id.items()}
t1 = matches['t1_lineup'].map(self.lineup_id2f)
t2 = matches['t2_lineup'].map(self.lineup_id2f)
# threshold_date = str(datetime.datetime.strptime(matches['date'].max(), '%Y-%m-%d %H:%M') -\
# datetime.timedelta(days=self.time_span))
# t1_older = matches[matches['date'] <= threshold_date]['t1_lineup'].map(self.lineup_id2f)
# t2_older = matches[matches['date'] <= threshold_date]['t2_lineup'].map(self.lineup_id2f)
# t1_newer = matches[matches['date'] > threshold_date]['t1_lineup'].map(self.lineup_id2f)
# t2_newer = matches[matches['date'] > threshold_date]['t2_lineup'].map(self.lineup_id2f)
t_num = len(lineups) # number of teams
# obs_older = target[matches['date'] <= threshold_date]
# obs_newer = target[matches['date'] > threshold_date]
# modeling older observations
with pm.Model() as model:
sigma = pm.HalfFlat('sigma', shape=t_num)
alpha = pm.Normal('alpha', mu=0, sigma=sigma, shape=t_num)
theta = pm.Deterministic('theta', alpha[t1] - alpha[t2])
y = pm.Bernoulli('y', logit_p=theta, observed=target)
self.trace = pm.sample(self.fit_iters, tune=self.tune)
'''# modeling newer observations
def make_model(spec: ModelSpec, dat, basis, unfold, aPosterior):
with pm.Model() as model:
# Prior for alpha
if isinstance(spec.alphaPrior, float):
alpha = spec.alphaPrior
elif isinstance(spec.alphaPrior, AlphaLognormal):
alphaLN = aPosterior.lognormal(scale=spec.alphaPrior.scale)
alpha = pm.Lognormal('alpha', mu=alphaLN.mu, sd=alphaLN.sig)
elif spec.alphaPrior is None:
alpha = pm.HalfFlat('alpha')
else:
raise Exception("Unknown prior for alpha")
# Prior for phi
nPhi = len(basis)
om = unfold.omegas[0].mat
chol = np.linalg.cholesky(np.linalg.inv(om))
low = np.repeat(0, nPhi)
if spec.phiPrior == "positive":
phiDistr = pm.Bound(pm.MvNormal, lower=low)
elif spec.phiPrior == "any":
phiDistr = pm.MvNormal
phi = phiDistr('phi',
mu=np.zeros(nPhi),
chol=chol / np.sqrt(alpha),
shape=nPhi)
# Experimental data
f = pm.Normal(
'f',
mu=pm.math.dot(unfold.K, phi),
sd=dat['err'].values,
shape=len(dat),
observed=dat['cnt'].values,
)
return model
def fit_counts_model(counts, mins_played):
## estimates a hierarchical poisson model for count data
## takes as input:
## counts, a numpy array of shape (num_players,) containing the total numbers of actions completed (across all games)
## mins_played, a numpy array of shape (num_players,) containing the total number of minutes each player was observed for
## returns:
## sl, a numpy array of shape (6000,N) containing 6000 posterior samples of actions per 90 (N is the number of players in the
## original data frame who have actually played minutes)
## sb, a numpy array of shape (6000,2) containing 6000 posterior samples of the population-level gamma shape parameter &
## the population-level mean
## kk, boolean indicating which players have actually played minutes
import numpy as np
import pymc3 as pm
kk = (mins_played > 0) & np.isfinite(counts)
mins_played = mins_played[kk]
counts = counts[kk]
N = counts.shape[0]
with pm.Model() as model:
beta = pm.HalfNormal('beta', sigma=100)
mu = pm.HalfFlat('mu')
lambdas = pm.Gamma('lambdas', alpha=mu * beta, beta=beta, shape=N)
lambda_tilde = lambdas * mins_played
y = pm.Poisson('y', lambda_tilde, observed=counts)
approx = pm.fit(n=30000)
sl = approx.sample(6000)['lambdas'] * 90
sb = np.c_[approx.sample(6000)['beta'], approx.sample(6000)['mu']]
return [sl, sb, kk, 'count']
def fit(self,
X,
y,
y_error,
x_error,
sample_kwargs={
'draws': 1000,
'target_accept': 0.9
}):
X = np.atleast_2d(X)
x_error = np.atleast_2d(x_error)
with pm.Model():
# slope and intercept of eta-ksi relation
slope = pm.Flat('slope', shape=(X.shape[0], ))
inter = pm.Flat('inter')
# intrinsic scatter of eta-ksi relation
int_std = pm.HalfFlat('int_std')
# standard deviation of Gaussian that ksi are drawn from (assumed mean zero)
tau = pm.HalfFlat('tau', shape=(X.shape[0], ))
# intrinsic ksi
mu = pm.Normal('mu', mu=0, sd=tau, shape=(X.shape[0], ))
# Some wizzarding with the dimensions all around.
ksi = pm.Normal('ksi', mu=mu, tau=tau, shape=X.T.shape)
# intrinsic eta-ksi linear relation + intrinsic scatter
eta = pm.Normal('eta',
mu=(tt.dot(slope.T, ksi.T) + inter),
sd=int_std,
shape=y.shape)
# observed xi, yi
x = pm.Normal('xi',
mu=ksi.T,
sd=x_error,
observed=X,
shape=X.shape)
y = pm.Normal('yi', mu=eta, sd=y_error, observed=y, shape=y.shape)
self.trace = pm.sample(**sample_kwargs)
return self
def main():
if len(sys.argv) < 2 or len(sys.argv) > 3:
print(
'usage: python3 inference_dir.py [chain no] [optional output no]')
sys.exit()
elif len(sys.argv) == 2:
c = int(sys.argv[1])
d = int(sys.argv[1])
if len(sys.argv) == 3:
c = int(sys.argv[1])
d = int(sys.argv[2])
np.random.seed(c)
np.random.shuffle(lang_ind)
np.random.shuffle(sound_ind)
lang_minibatch = pm.Minibatch(lang_ind, 500)
sound_minibatch = pm.Minibatch(sound_ind, 500)
model_ln = pm.Model()
with model_ln:
beta = pm.HalfFlat('beta')
"theta = language-level prior over components"
theta = tt.stack([
pm.Dirichlet('theta_{}'.format(l), a=tt.ones(K) * beta, shape=K)
for l in range(L)
])
psi = [
pm.MvNormal('psi_{}'.format(k), mu=[0] * S, cov=Sigma, shape=S)
for k in range(K)
]
"phi = component-level collection of distributions over sound change"
phi = tt.stack([
tt.concatenate([
pm.Deterministic(
'phi_{}_{}'.format(k, x),
tt.nnet.softmax(psi[k][s_breaks[x][0]:s_breaks[x][1]])[0])
for x in range(X)
]) for k in range(K)
])
target = pm.DensityDist('target',
logprob(theta=theta, phi=phi),
observed=dict(lang_array=lang_minibatch,
sound_array=sound_minibatch),
total_size=N)
inference_ln = pm.ADVI()
inference_ln.fit(50000,
obj_optimizer=pm.adam(learning_rate=.01,
beta1=uniform(.7, .9)),
callbacks=[pm.callbacks.CheckParametersConvergence()])
trace_ln = inference_ln.approx.sample()
posterior = {
k: trace_ln[k]
for k in trace_ln.varnames if not k.endswith('__')
}
posterior['ELBO'] = inference_ln.hist
f = open('posterior_ln_shuffle_{}.pkl'.format(d), 'wb')
pkl.dump(posterior, f)
f.close()
def constructBasicModel(pdfDict):
"""
Construct model without axions! (Null hypothesis)
"""
with pm.Model() as model:
# We using HalfFlat cuz we dgaf -- probably we should switch to a more informative prior
Tritium = pm.HalfFlat("Tritium")
Bkg = pm.HalfFlat("Bkg")
Fe55 = pm.HalfFlat("Fe55")
Zn65 = pm.HalfFlat("Zn65")
Ge68 = pm.HalfFlat("Ge68")
# Generate array of deterministic variables (per bin)
det = Tritium * pdfDict['Tritium'] + Bkg * pdfDict[
'Bkg'] + Fe55 * pdfDict['Fe55'] + Zn65 * pdfDict[
'Zn65'] + Ge68 * pdfDict['Ge68']
L = pm.Poisson("L", mu=det, observed=pdfDict['Data'])
return model
def _gen_d_vars_pm(tmñ=(), fmt_nmbrs='{}'):
egr = {}
for p, líms in líms_paráms.items():
nmbr = fmt_nmbrs.format(p)
if aprioris is None:
if líms[0] is None:
if líms[1] is None:
dist_pm = pm.Flat(nmbr, shape=tmñ)
else:
if líms[1] == 0:
dist_pm = -pm.HalfFlat(nmbr, shape=tmñ)
else:
dist_pm = líms[1] - pm.HalfFlat(nmbr,
shape=tmñ)
else:
if líms[1] is None:
if líms[0] == 0:
dist_pm = pm.HalfFlat(nmbr, shape=tmñ)
else:
dist_pm = líms[0] + pm.HalfFlat(nmbr,
shape=tmñ)
else:
dist_pm = pm.Uniform(nmbr,
lower=líms[0],
upper=líms[1],
shape=tmñ)
else:
dist, prms = aprioris[p]
if (líms[0] is not None
or líms[1] is not None) and dist != pm.Uniform:
acotada = pm.Bound(dist, lower=líms[0], upper=líms[1])
dist_pm = acotada(nmbr, shape=tmñ, **prms)
else:
if dist == pm.Uniform:
prms['lower'] = max(prms['lower'], líms[0])
prms['upper'] = min(prms['upper'], líms[1])
dist_pm = dist(nmbr, shape=tmñ, **prms)
egr[p] = dist_pm
return egr
def constructModel(pdfDict, energyBins):
"""
Construct pymc3 model
"""
with pm.Model() as model:
# We using HalfFlat cuz we dgaf -- probably we should switch to a more informative prior
Axion = pm.HalfFlat("Axion")
Tritium = pm.HalfFlat("Tritium")
Bkg = pm.HalfFlat("Bkg")
Fe55 = pm.HalfFlat("Fe55")
Zn65 = pm.HalfFlat("Zn65")
Ge68 = pm.HalfFlat("Ge68")
# Create the detector efficiency deterministic
# NOTE: Problem with
# Mu = pm.Normal('Mu', mu = 0.36, sd = 0.5)
# Sig = pm.Normal('Sig', mu = 1.26, sd = 0.5)
# eff = 0.5*(1+tt.erf((pdfDict['Energy'] - Mu)/(tt.sqrt(2)*Sig)))
# Reparameterize efficiency as logistic function
Mu = pm.Normal('Mu', mu=0.77, sd=0.1)
Sig = pm.Normal('Sig', mu=0.56, sd=0.1)
eff = 1. / (1. + tt.exp(-(pdfDict['Energy'] - Mu) / Sig))
# Generate array of deterministic variables (per bin)
det = (Tritium * pdfDict['Tritium'] + Bkg * pdfDict['Bkg'] +
Axion * pdfDict['Axion'] + Fe55 * pdfDict['Fe55'] +
Zn65 * pdfDict['Zn65'] + Ge68 * pdfDict['Ge68']) * eff
# det = Tritium*pdfDict['Tritium'] + Bkg*pdfDict['Bkg'] + Axion*pdfDict['Axion'] + Fe55*pdfDict['Fe55'] + Zn65*pdfDict['Zn65'] + Ge68*pdfDict['Ge68']
L = pm.Poisson("L", mu=det, observed=pdfDict['Data'])
return model
def test_model_not_drawable_prior(self):
data = np.random.poisson(lam=10, size=200)
model = pm.Model()
with model:
mu = pm.HalfFlat("sigma")
pm.Poisson("foo", mu=mu, observed=data)
trace = pm.sample(tune=1000)
with model:
with pytest.raises(ValueError) as excinfo:
pm.sample_prior_predictive(50)
assert "Cannot sample" in str(excinfo.value)
samples = pm.sample_posterior_predictive(trace, 50)
assert samples["foo"].shape == (50, 200)
def main():
if len(sys.argv) < 2 or len(sys.argv) > 3:
print(
'usage: python3 inference_dir.py [chain no] [optional output no]')
sys.exit()
elif len(sys.argv) == 2:
c = int(sys.argv[1])
d = int(sys.argv[1])
if len(sys.argv) == 3:
c = int(sys.argv[1])
d = int(sys.argv[2])
np.random.seed(c)
lang_minibatch = pm.Minibatch(lang_ind, 500)
sound_minibatch = pm.Minibatch(sound_ind, 500)
model_dir = pm.Model()
with model_dir:
beta = pm.HalfFlat('beta')
"theta = language-level prior over components"
theta = tt.stack([
pm.Dirichlet('theta_{}'.format(l), a=tt.ones(K) * beta, shape=K)
for l in range(L)
])
phi = tt.stack([
tt.concatenate([
pm.Dirichlet('phi_{}_{}'.format(k, x),
a=tt.ones(R[x]) * alpha,
shape=R[x]) for x in range(X)
]) for k in range(K)
])
target = pm.DensityDist('target',
logprob(theta=theta, phi=phi),
observed=dict(lang_array=lang_minibatch,
sound_array=sound_minibatch),
total_size=N)
inference_dir = pm.ADVI()
inference_dir.fit(
50000,
obj_optimizer=pm.adam(learning_rate=.01, beta1=uniform(.7, .9)),
callbacks=[pm.callbacks.CheckParametersConvergence()])
trace_dir = inference_dir.approx.sample()
posterior = {
k: trace_dir[k]
for k in trace_dir.varnames if not k.endswith('__')
}
posterior['ELBO'] = inference_dir.hist
f = open('posterior_dir_{}.pkl'.format(d), 'wb')
pkl.dump(posterior, f)
f.close()
def _get_posterior_samples(self, obs, n_samples, seed):
def tegpd_logp(x, xi, sigma):
#returns the sum of log-liklihoods
if xi != 0:
return tt.sum(-tt.log(sigma) -
(1.0 / xi + 1) * tt.log(1 + xi / sigma * x))
else:
return tt.sum(-tt.log(sigma) - x / sigma)
obs = np.array(obs)
x_max = np.max(obs)
#Bayesian specification and inference
gp_model = pm.Model()
with gp_model:
#xi, sigma = get_priors(prior_name)
xi = pm.Normal('xi', mu=0, sigma=1)
sigma = pm.HalfFlat('sigma')
#sigma is remapped to values that prevent the loglikelihood to be -Inf; this happens if sigma is such that
# the theoretical upper bound of the data distribution is lower than their observed values.
X = pm.DensityDist("tegpd",
tegpd_logp,
observed={
"xi": xi,
"sigma":
(-xi * x_max).clip(0, np.Inf) + sigma,
"x": obs
})
trace = pm.sample(n_samples, random_seed=seed)
#get sampled posteriors
xi_samples = trace.get_values("xi")
sigma_samples = trace.get_values("sigma") + (-xi_samples * x_max).clip(
0, np.Inf)
mat = np.concatenate([
np.array(sigma_samples).reshape(-1, 1),
np.array(xi_samples).reshape(-1, 1)
],
axis=1)
self.posterior_sigma = np.ascontiguousarray(mat[:, 0],
dtype=np.float64)
self.posterior_xi = np.ascontiguousarray(mat[:, 1], dtype=np.float64)
self.n_posterior = len(self.posterior_sigma)
def mcmcBinomial(data):
def hyper_prior(value):
''' prior density'''
return tt.log(tt.pow(tt.sum(value), -5 / 2))
with pm.Model() as model:
# Uninformative prior for alpha and beta
#true_rates = pm.Beta('true_rates', a, b, size=5)
ab = pm.HalfFlat('alpha_beta', shape=2, testval=np.asarray([1., 1.]))
pm.Potential('p(alpha, beta)', hyper_prior(ab))
#Allows you to do algrebra with RVs
X = pm.Deterministic('X', tt.log(ab[0] / ab[1]))
Z = pm.Deterministic('Z', tt.log(tt.sum(ab)))
theta = pm.Beta('theta', alpha=ab[0], beta=ab[1])
#p = pm.Binomial('y', p=theta, observed=y, n=n)
p = pm.Bernoulli('y', theta, observed=data)
trace = pm.sample(5000, tune=2000, target_accept=0.95)
return (trace)
def fit_successes_model(successes, attempts):
## estimates a hierarchical binomial model for success rate data
## takes as input:
## successes, a numpy array of shape (num_players,) containing the total numbers of successful actions (across all games)
## attempts, a numpy array of shape (num_players,) containing the total numbers of attempted actions (across all games)
## returns:
## sl, a numpy array of shape (6000,N) containing 6000 posterior samples of success probabilites (N is the number of players in the
## original data frame who have actually attempted a pass)
## sb, a numpy array of shape (6000,2) containing 6000 posterior samples of the population-level beta parameters
## kk, boolean indicating which players have actually attempted a pass
import numpy as np
import pymc3 as pm
import pymc3.distributions.transforms as tr
import theano.tensor as tt
kk = (attempts > 0) & np.isfinite(successes)
attempts = attempts[kk]
successes = successes[kk]
N = attempts.shape[0]
def logp_ab(value):
''' prior density'''
return tt.log(tt.pow(tt.sum(value), -5 / 2))
with pm.Model() as model:
# Uninformative prior for alpha and beta
ab = pm.HalfFlat('ab',
shape=2,
testval=np.asarray([1., 1.]))
pm.Potential('p(a, b)', logp_ab(ab))
lambdas = pm.Beta('lambdas', alpha=ab[0], beta=ab[1], shape=N)
p = pm.Binomial('y', p=lambdas, observed=successes, n=attempts)
approx = pm.fit(n=30000)
sl = approx.sample(6000)['lambdas'] * 100
sb = approx.sample(6000)['ab']
return [sl, sb, kk, 'success']
BASE_NAME = '{}_{}_{}C_{}_{}'.format(DATE, RUN, TEMP, CARBON, OPERATOR)
# ################################
# Nothing below here should change
# ################################
if os.path.isdir('output') == False:
os.mkdir('output')
# Load and trim the data to start at 0D = 0.1
data = pd.read_csv('{}_growth.csv'.format(BASE_NAME))
data = data[(data['OD_600'] >= 0.1) & (data['OD_600'] <= 0.8)]
with pm.Model() as model:
a0 = pm.HalfNormal('a0', sd=1)
lam = pm.HalfFlat('lambda')
gamma = mwc.bayes.Jeffreys('gamma', lower=1E-9, upper=100)
# Compute the expected value.
time = data['elapsed_time_min'].values
mu = np.log(a0) + time * lam
# Define the likelihood and sample.
like = pm.Cauchy('like', mu, gamma, observed=np.log(data['OD_600'].values))
trace = pm.sample(tune=5000, draws=5000)
trace_df = mwc.stats.trace_to_dataframe(trace, model)
stats = mwc.stats.compute_statistics(trace_df)
# %% Compute the best fit and credible region
modes = {}
hpds = {}
def _to_pymc3_distribution(name, par):
"""
Create a pymc3 continuous distribution from a Bounds object.
Parameters
----------
name : str
Name of parameter
par : refnx.analysis.Parameter
The parameter to wrap
Returns
-------
d : pymc3.Distribution
The pymc3 distribution
"""
import pymc3 as pm
import theano.tensor as T
from theano.compile.ops import as_op
dist = par.bounds
# interval and both lb, ub are finite
if (isinstance(dist, Interval) and
np.isfinite([dist.lb, dist.ub]).all()):
return pm.Uniform(name, dist.lb, dist.ub)
# no bounds
elif (isinstance(dist, Interval) and
np.isneginf(dist.lb) and
np.isinf(dist.lb)):
return pm.Flat(name)
# half open uniform
elif isinstance(dist, Interval) and not np.isfinite(dist.lb):
return dist.ub - pm.HalfFlat(name)
# half open uniform
elif isinstance(dist, Interval) and not np.isfinite(dist.ub):
return dist.lb + pm.HalfFlat(name)
# it's a PDF
if isinstance(dist, PDF):
dist_gen = getattr(dist.rv, 'dist', None)
if isinstance(dist.rv, stats.rv_continuous):
dist_gen = dist.rv
if isinstance(dist_gen, type(stats.uniform)):
if hasattr(dist.rv, 'args'):
p = pm.Uniform(name, dist.rv.args[0],
dist.rv.args[1] + dist.rv.args[0])
else:
p = pm.Uniform(name, 0, 1)
return p
# norm from scipy.stats
if isinstance(dist_gen, type(stats.norm)):
if hasattr(dist.rv, 'args'):
p = pm.Normal(name, mu=dist.rv.args[0], sd=dist.rv.args[1])
else:
p = pm.Normal(name, mu=0, sd=1)
return p
# not open, uniform, or normal, so fall back to DensityDist.
d = as_op(itypes=[T.dscalar], otypes=[T.dscalar])(dist.logp)
r = as_op(itypes=[T.dscalar], otypes=[T.dscalar])(dist.rvs)
p = pm.DensityDist(name, d, random=r)
return p
def fit(self,
X,
y,
y_error=1,
x_error=None,
*,
sample_kwargs={
'draws': 1000,
'target_accept': 0.9
}):
kwds = {}
if self.kwds is not None:
kwds.update(self.kwds)
kwds['fit_intercept'] = False
model = self._choose_regressor()
self.clf_ = model(**kwds)
self.fit_intercept = False
if x_error is not None:
x_error = np.atleast_2d(x_error)
with pm.Model():
# slope and intercept of eta-ksi relation
slope = pm.Flat('slope', shape=(X.shape[0], ))
inter = pm.Flat('inter')
# intrinsic scatter of eta-ksi relation
int_std = pm.HalfFlat('int_std')
# standard deviation of Gaussian that ksi are drawn from (assumed mean zero)
tau = pm.HalfFlat('tau', shape=(X.shape[0], ))
# intrinsic ksi
mu = pm.Normal('mu', mu=0, sd=tau, shape=(X.shape[0], ))
# Some wizzarding with the dimensions all around.
ksi = pm.Normal('ksi', mu=mu, tau=tau, shape=X.T.shape)
# intrinsic eta-ksi linear relation + intrinsic scatter
eta = pm.Normal('eta',
mu=(tt.dot(slope.T, ksi.T) + inter),
sd=int_std,
shape=y.shape)
# observed xi, yi
x = pm.Normal('xi',
mu=ksi.T,
sd=x_error,
observed=X,
shape=X.shape)
y = pm.Normal('yi', mu=eta, sd=y_error, observed=y, shape=y.shape)
self.trace = pm.sample(**sample_kwargs)
# TODO big: make it optional to choose a way to define best
# TODO quick: use np.histogramdd
H2D, bins1, bins2 = np.histogram2d(self.trace['slope'][:, 0],
self.trace['inter'],
bins=50)
w = np.where(H2D == H2D.max())
# choose the maximum posterior slope and intercept
slope_best = bins1[w[0][0]]
intercept_best = bins2[w[1][0]]
self.clf_.coef_ = np.array([intercept_best, slope_best])
return self
def linear_bayesian_flat_prior(x, y, number_samples = 3000):
'''Generates a Bayesian linear regression with half-flat priors gaussian
likelihood
Returns a dict with the model that can be used to compare, the trace
and main plots'''
# Set container
result = dict.fromkeys(["model",
"trace",
"posterior_pred",
"plot_param",
"plot_data",
"plot_uncertainty"], None)
try :
with pm.Model() as model:
# Define priors
# sigma = pm.HalfFlat('sigma')
# intercept = pm.distributions.continuous.HalfFlat('Intercept')
# beta_1 = pm.distributions.continuous.HalfFlat('x')
sigma = pm.HalfFlat('sigma')
intercept = pm.HalfFlat('Intercept')
beta_1 = pm.HalfFlat('x')
# Define likelihood
likelihood = pm.Normal('y', mu = intercept + beta_1 * x,
sigma=sigma, observed=y)
# Inference!
trace = pm.sample(number_samples , cores=2) # draw 3000 posterior samples using NUTS sampling
result["trace"] = trace
posterior_pred = pm.sample_posterior_predictive(trace)
result["posterior_pred"] = posterior_pred
result["model"] = model
plot_param = plt.figure(figsize=(7, 7))
pm.traceplot(trace)
plt.tight_layout()
result["plot_param"] = plot_param
plot_data = plt.figure(figsize=(7, 7))
plt.plot(x, y, 'x', label = 'data')
pm.plot_posterior_predictive_glm(trace, samples=number_samples,
label='posterior predictive regression lines',
eval = np.linspace(0, np.max(x), 50))
plt.title('Posterior predictive regression lines')
plt.legend(loc=0)
plt.xlabel('x')
plt.ylabel('y');
result["plot_data"] = plot_data
return(result)
except RuntimeError:
return(np.NaN)
shape=len(N_samples))
#y = pm.Bernoulli('y', p=θ[group_idx], observed=data)
y = pm.Binomial('y', p=theta, observed=G_samples, n=N_samples)
trace = pm.sample(1000)
#https://docs.pymc.io/notebooks/GLM-hierarchical-binominal-model.html
def logp_ab(value):
''' prior density'''
return tt.log(tt.pow(tt.sum(value), -5 / 2))
with pm.Model() as model:
# Uninformative prior for alpha and beta
ab = pm.HalfFlat('ab', shape=2, testval=np.asarray([1., 1.]))
pm.Potential('p(a, b)', logp_ab(ab))
alpha = pm.Deterministic('alpha', ab[0])
beta = pm.Deterministic('beta', ab[1])
theta = pm.Beta('θ', alpha=alpha, beta=beta, shape=len(N_samples))
y = pm.Binomial('y', p=theta, observed=G_samples, n=N_samples)
trace = pm.sample(1000)
az.plot_trace(trace)
plt.savefig('hbayes_binom_covid_trace.pdf', dpi=300)
print(az.summary(trace))
axes = az.plot_forest(trace,
var_names='θ',
hdi_prob=0.95,
def main(input_dir, output_dir, dataset, model_type, n_samples, n_tune, target_accept, n_cores, seed, init, profile):
'''Fit log-parabola model to DATASET.
Parameters
----------
input_dir : [type]
input directory containing subdirs for each instrument with dl3 data
output_dir : [type]
where to save the results. traces and two plots
dataset : string
telescope name
model_type : string
whether to use the profile likelihood ('wstat' or 'profile') or not ('full')
n_samples : int
number of samples to draw
n_tune : int
number of tuning steps
target_accept : float
target accept fraction for the pymc sampler
n_cores : int
number of cpu cores to use
seed : int
random seed
init : string
pymc init string
profile : bool
whether to output debugging/profiling information to the console
Raises
------
NotImplementedError
This does not yet work on the joint dataset. but thats good enough for me.
'''
np.random.seed(seed)
if dataset == 'joint':
#TODO need to calculate mu_b for each observation independently.
raise NotImplementedError('This is not implemented for the joint dataset yet.')
# observations, lo, hi = load_joint_spectrum_observation(input_dir)
else:
p = os.path.join(input_dir, dataset)
observations, lo, hi = load_spectrum_observations(p)
prepare_output(output_dir)
# TODO: this has to happen for every observation independently
exposure_ratio = observations[0].alpha[0]
# print(exposure_ratio)
on_data, off_data = get_observed_counts(observations)
integrator = init_integrators(observations)
print('On Data')
display_data(on_data)
print('Off Data')
display_data(off_data)
print('--' * 30)
print(f'Fitting data for {dataset} in {len(observations)} observations. ')
print(f'Using {len(on_data)} bins with { on_data.sum()} counts in on region and {off_data.sum()} counts in off region.')
print(f'Fit range is: {(lo, hi) * u.TeV}.')
model = pm.Model(theano_config={'compute_test_value': 'ignore'})
with model:
# amplitude = pm.TruncatedNormal('amplitude', mu=4, sd=1, lower=0.01, testval=4)
# alpha = pm.TruncatedNormal('alpha', mu=2.5, sd=1, lower=0.00, testval=2.5)
# beta = pm.TruncatedNormal('beta', mu=0.5, sd=0.5, lower=0.00000, testval=0.5)
amplitude = pm.HalfFlat('amplitude', testval=4)
alpha = pm.HalfFlat('alpha', testval=2.5)
beta = pm.HalfFlat('beta', testval=0.5)
mu_s = forward_fold_log_parabola_symbolic(integrator, amplitude, alpha, beta, observations)
# mu_s = forward_fold_log_parabola_analytic(amplitude, alpha, beta, observations)
if model_type == 'wstat':
print('Building profiled likelihood model')
mu_b = pm.Deterministic('mu_b', calc_mu_b(mu_s, on_data, off_data, exposure_ratio))
else:
print('Building full likelihood model')
mu_b = pm.HalfFlat('mu_b', shape=len(off_data))
pm.Poisson('background', mu=mu_b, observed=off_data, shape=len(off_data))
pm.Poisson('signal', mu=mu_s + exposure_ratio * mu_b, observed=on_data, shape=len(on_data))
print('--' * 30)
print('Model debug information:')
for RV in model.basic_RVs:
print(RV.name, RV.logp(model.test_point))
if profile:
model.profile(model.logpt).summary()
print(model.check_test_point())
print('--' * 30)
print('Plotting landscape:')
fig, _ = plot_landscape(model, off_data)
fig.savefig(os.path.join(output_dir, 'landscape.pdf'))
print('--' * 30)
print('Printing graphs:')
theano.printing.pydotprint(mu_s, outfile=os.path.join(output_dir, 'graph_mu_s.pdf'), format='pdf', var_with_name_simple=True)
theano.printing.pydotprint(mu_s + exposure_ratio * mu_b, outfile=os.path.join(output_dir, 'graph_n_on.pdf'), format='pdf', var_with_name_simple=True)
print('--' * 30)
print('Sampling likelihood:')
with model:
trace = pm.sample(n_samples, cores=n_cores, tune=n_tune, init=init, seed=[seed] * n_cores)
print('--' * 30)
print(f'Fit results for {dataset}')
print(trace['amplitude'].mean(), trace['alpha'].mean(), trace['beta'].mean())
print(np.median(trace['amplitude']), np.median(trace['alpha']), np.median(trace['beta']))
print('--' * 30)
# print('Plotting traces')
# plt.figure()
# varnames = ['amplitude', 'alpha', 'beta'] if model_type != 'full' else ['amplitude', 'alpha', 'beta', 'mu_b']
# pm.traceplot(trace, varnames=varnames)
# plt.savefig(os.path.join(output_dir, 'traces.pdf'))
p = os.path.join(output_dir, 'num_samples.txt')
with open(p, "w") as text_file:
text_file.write(f'\\num{{{n_samples}}}')
p = os.path.join(output_dir, 'num_chains.txt')
with open(p, "w") as text_file:
text_file.write(f'\\num{{{n_cores}}}')
p = os.path.join(output_dir, 'num_tune.txt')
with open(p, "w") as text_file:
text_file.write(f'\\num{{{n_tune}}}')
plt.figure()
pm.energyplot(trace)
plt.savefig(os.path.join(output_dir, 'energy.pdf'))
# plt.figure()
# pm.autocorrplot(trace, burn=n_tune)
# plt.savefig(os.path.join(output_dir, 'autocorr.pdf'))
plt.figure()
pm.forestplot(trace, varnames=['amplitude', 'alpha', 'beta'])
plt.savefig(os.path.join(output_dir, 'forest.pdf'))
trace_output = os.path.join(output_dir, 'traces')
print(f'Saving traces to {trace_output}')
with model:
pm.save_trace(trace, trace_output, overwrite=True)
def test_half_flat(self):
with pm.Model():
f = pm.HalfFlat('f')
with pytest.raises(ValueError):
f.random(1)
def dummy_model_unfold():
model = pm.Model(theano_config={"compute_test_value": "ignore"})
with model:
pm.HalfFlat("mu_b", shape=2)
pm.Lognormal("expected_counts", shape=2)
return model
def main(input_dir, config_file, output_dir, dataset, model_type, tau,
n_samples, n_tune, target_accept, n_cores, seed, init):
prepare_output(output_dir)
config = load_config(config_file, dataset)
fit_range = config['fit_range']
path = os.path.join(input_dir, dataset)
observations = load_data(path, config)
e_true_bins = config['e_true_bins']
e_reco_bins = config['e_reco_bins']
# exposure_ratio = observations[0].alpha
# from IPython import embed; embed()
on_data, off_data, excess, exposure_ratio = get_observed_counts(
observations, fit_range=fit_range, bins=e_reco_bins)
print(f'Exposure ratio {exposure_ratio}')
# from IPython import embed; embed()
# print(f'On Data {on_data.shape}\n')
# display_data(on_data)
# print(f'\n\n Off Data {off_data.shape}\n')
# display_data(off_data)
print(f'Excess {excess.shape} \n')
idx = np.searchsorted(e_reco_bins.to_value(u.TeV),
fit_range.to_value(u.TeV))
lo, up = idx[0], idx[1] + 1
indices = np.argwhere(excess > 5)
display_data(excess, mark_indices=indices, low_index=lo, high_index=up)
print('--' * 30)
print(f'Unfolding data for: {dataset.upper()}. ')
# print(f'IRF with {len( config['e_true_bins'] ) - 1, len( config['e_reco_bins'] ) - 1}')
print(
f'Using {len(on_data)} bins with { on_data.sum()} counts in on region and {off_data.sum()} counts in off region.'
)
area_scaling = 1
print(observations[0].aeff.data.data.to_value(u.km**2).astype(np.float32) *
area_scaling)
model = pm.Model(theano_config={'compute_test_value': 'ignore'})
with model:
# mu_b = pm.TruncatedNormal('mu_b', shape=len(off_data), sd=5, mu=off_data, lower=0.01)
# expected_counts = pm.Lognormal('expected_counts', shape=len(config['e_true_bins']) - 1, testval=10, sd=1)
expected_counts = pm.TruncatedNormal('expected_counts',
shape=len(e_true_bins) - 1,
testval=0.5,
mu=2,
sd=50,
lower=0.0001)
# expected_counts = pm.HalfFlat('expected_counts', shape=len(e_true_bins) - 1, testval=10)
# c = expected_counts / area_scaling
mu_s = forward_fold(expected_counts,
observations,
fit_range=fit_range,
area_scaling=area_scaling)
if model_type == 'wstat':
print('Building profiled likelihood model')
mu_b = pm.Deterministic(
'mu_b', calc_mu_b(mu_s, on_data, off_data, exposure_ratio))
else:
print('Building full likelihood model')
mu_b = pm.HalfFlat('mu_b', shape=len(off_data))
# mu_b = pm.Lognormal('mu_b', shape=len(off_data), sd=5)
pm.Poisson('background', mu=mu_b + 1E-5, observed=off_data)
pm.Poisson('signal',
mu=mu_s + exposure_ratio * mu_b + 1E-5,
observed=on_data)
print('--' * 30)
print('Model debug information:')
for RV in model.basic_RVs:
print(RV.name, RV.logp(model.test_point))
print('--' * 30)
print('Sampling likelihood:')
with model:
trace = pm.sample(n_samples,
cores=n_cores,
tune=n_tune,
init=init,
seed=[seed] * n_cores)
trace_output = os.path.join(output_dir, 'traces')
print(f'Saving traces to {trace_output}')
with model:
pm.save_trace(trace, trace_output, overwrite=True)
print('--' * 30)
print('Plotting result')
# print(area_scaling)
fig, [ax1, ax2] = plt.subplots(2,
1,
figsize=(10, 7),
sharex=True,
gridspec_kw={'height_ratios': [3, 1]})
plot_unfolding_result(trace,
bins=e_true_bins,
area_scaling=area_scaling,
fit_range=fit_range,
ax=ax1)
plot_excees(excess, bins=config['e_reco_bins'], ax=ax2)
plt.savefig(os.path.join(output_dir, 'result.pdf'))
print('--' * 30)
print('Plotting Diagnostics')
print(pm.summary(trace).round(2))
# plt.figure()
# pm.traceplot(trace)
# plt.savefig(os.path.join(output_dir, 'traces.pdf'))
plt.figure()
pm.energyplot(trace)
plt.savefig(os.path.join(output_dir, 'energy.pdf'))
# try:
# plt.figure()
# pm.autocorrplot(trace, burn=n_tune)
# plt.savefig(os.path.join(output_dir, 'autocorr.pdf'))
# except:
# print('Could not plot auttocorrelation')
plt.figure()
pm.forestplot(trace)
plt.savefig(os.path.join(output_dir, 'forest.pdf'))
p = os.path.join(output_dir, 'num_samples.txt')
with open(p, "w") as text_file:
text_file.write(f'\\num{{{n_samples}}}')
p = os.path.join(output_dir, 'num_chains.txt')
with open(p, "w") as text_file:
text_file.write(f'\\num{{{n_cores}}}')
p = os.path.join(output_dir, 'num_tune.txt')
with open(p, "w") as text_file:
text_file.write(f'\\num{{{n_tune}}}')