def test_sample(self):
with self.SMC_test:
mtrace = pm.sample(draws=self.samples, step=pm.SMC())
x = mtrace['X']
mu1d = np.abs(x).mean(axis=0)
np.testing.assert_allclose(self.muref, mu1d, rtol=0., atol=0.03)
def main():
n = 4
mu1 = np.ones(n) * (1. / 2)
with pm.Model() as ATMIP_test:
X = pm.Uniform('X',
shape=n,
lower=-2. * np.ones_like(mu1),
upper=2. * np.ones_like(mu1),
testval=-1. * np.ones_like(mu1))
kd4 = pm.Lognormal('kd4', mu=np.log(0.3), sd=1)
# k_d4 = pm.Lognormal('k_d4', mu=np.log(6E-3), sd=9)
# kSOCSon = pm.Lognormal('kSOCSon', mu=np.log(1E-6), sd = 2)
# kpa = pm.Lognormal('kpa', mu=np.log(1E-6), sd = 2)
# R1 = pm.Uniform('R1', lower=900, upper=5000)
# R2 = pm.Uniform('R2', lower=900, upper=5000)
# gamma = pm.Uniform('gamma', lower=2, upper=30)
llk = pm.Potential('llk', two_gaussians(X, kd4))
with ATMIP_test:
trace = pm.sample(100, chains=50, step=pm.SMC())
plt.figure()
pm.traceplot(trace)
plt.savefig("mc_testing.pdf")
s = pm.stats.summary(trace)
s.to_csv('mcmc_parameter_summary.csv')
def test_start(self):
with pm.Model() as model:
a = pm.Poisson("a", 5)
b = pm.HalfNormal("b", 10)
y = pm.Normal("y", a, b, observed=[1, 2, 3, 4])
start = {
"a": np.random.poisson(5, size=500),
"b_log__": np.abs(np.random.normal(0, 10, size=500)),
}
trace = pm.sample(500, start=start, step=pm.SMC())
def test_sample_n_core(self, cores, stage):
step_kwargs = {'homepath': self.test_folder, 'stage': stage}
with self.ATMIP_test:
mtrace = pm.sample(draws=self.samples,
chains=self.chains,
cores=cores,
step=pm.SMC(),
step_kwargs=step_kwargs)
x = mtrace.get_values('X')
mu1d = np.abs(x).mean(axis=0)
np.testing.assert_allclose(self.muref, mu1d, rtol=0., atol=0.03)
def test_ml(self):
data = np.repeat([1, 0], [50, 50])
marginals = []
a_prior_0, b_prior_0 = 1., 1.
a_prior_1, b_prior_1 = 20., 20.
for alpha, beta in ((a_prior_0, b_prior_0), (a_prior_1, b_prior_1)):
with pm.Model() as model:
a = pm.Beta('a', alpha, beta)
y = pm.Bernoulli('y', a, observed=data)
trace = pm.sample(2000, step=pm.SMC())
marginals.append(model.marginal_likelihood)
# compare to the analytical result
assert abs((marginals[1] / marginals[0]) - 4.0) <= 1
def test_discrete_continuous(self):
with pm.Model() as model:
a = pm.Poisson('a', 5)
b = pm.HalfNormal('b', 10)
y = pm.Normal('y', a, b, observed=[1, 2, 3, 4])
trace = pm.sample(step=pm.SMC())
az.plot_trace(trace_BF)
plt.savefig('B11197_05_11.png', dpi=300)
# In[17]:
pM1 = trace_BF['model_index'].mean()
pM0 = 1 - pM1
BF = (pM0 / pM1) * (p[1] / p[0])
BF
# In[18]:
with pm.Model() as model_BF_0:
theta = pm.Beta('theta', 4, 8)
y = pm.Bernoulli('y', theta, observed=y_d)
trace_BF_0 = pm.sample(2500, step=pm.SMC())
with pm.Model() as model_BF_1:
theta = pm.Beta('theta', 8, 4)
y = pm.Bernoulli('y', theta, observed=y_d)
trace_BF_1 = pm.sample(2500, step=pm.SMC())
# In[19]:
model_BF_0.marginal_likelihood / model_BF_1.marginal_likelihood
# ## Bayes factors and information criteria
# In[20]:
traces = []
az.plot_trace(trace_bf)
# %%
pm1 = trace_bf['model_index'].mean()
pm0 = 1 - pm1
bf = (pm0 / pm1) * (p[1] / p[0])
# %%
bf
# %%
with pm.Model() as model_bf_0:
theta = pm.Beta('theta', 4, 8)
y = pm.Bernoulli('y', theta, observed=y_d)
trace_bf_0 = pm.sample(2500, step=pm.SMC())
with pm.Model() as model_bf_1:
theta = pm.Beta('theta', 8, 4)
y = pm.Bernoulli('y', theta, observed=y_d)
trace_bf_1 = pm.sample(2500, step=pm.SMC())
model_bf_0.marginal_likelihood / model_bf_1.marginal_likelihood
# %%
traces = []
waics = []
for coins, heads in [(30, 9), (300, 90)]:
y_d = np.repeat([0, 1], [coins - heads, heads])
for priors in [(4, 8), (8, 4)]:
with pm.Model() as model:
def beam_model(f):
return gaussian_beam(f, beam_gauss_width)
nsamp = 6000
# Set whether to use the beam_model
if fitinfo_dict[gal][name]['use_beam']:
fit_beam_model = beam_model
else:
fit_beam_model = None
out, summ, trace, fit_model = \
fit_pspec_model(freqs, ps1D,
ps1D_stddev,
beam_model=fit_beam_model,
step=pm.SMC(),
nsamp=nsamp,
fixB=fitinfo_dict[gal][name]['fixB'])
row_names.append("{0}_{1}_{2}".format(gal.lower(), name, res_type))
fit_results['logA'].append(np.array(summ['mean'])[0])
fit_results['ind'].append(np.array(summ['mean'])[1])
# fit_results['logB'].append(np.array(summ['mean'])[2])
fit_results['logA_std'].append(np.array(summ['sd'])[0])
fit_results['ind_std'].append(np.array(summ['sd'])[1])
# fit_results['logB_std'].append(np.array(summ['sd'])[2])
plt.figure(figsize=(8.4, 2.9))
'confidence',
]
target_name = 'awareness'
experiment = 'e1'
# for some of the variables, we need to rescale them to a more preferable range like 0-1
name_for_scale = ['awareness']
# ['ah', 'av', 'bj', 'cm', 'db', 'ddb', 'fcm', 'kf', 'kk', 'ml', 'qa','sk', 'yv']
# get one of the participants' data
transition_matrix, sub = [], []
transition_count = []
for participant, df_sub in df.groupby('participant'):
awareness = df_sub['awareness'].values - 1
with pm.Model() as model:
a = pm.Beta('a', 0.5, 0.5)
yl = pm.Bernoulli('yl', a, observed=awareness)
trace = pm.sample(1000, step=pm.SMC(), random_seed=42)
# for 1-back
temp = pd.crosstab(pd.Series(df_sub['awareness'].values[1:], name='N'),
pd.Series(df_sub['awareness'].values[:-1],
name='N-1'),
normalize=1)
transition_matrix.append(temp.get_values().flatten())
temp = pd.crosstab(
pd.Series(df_sub['awareness'].values[1:], name='N'),
pd.Series(df_sub['awareness'].values[:-1], name='N-1'),
)
transition_count.append(temp.get_values().flatten())
sub.append(participant)
df1_transition = pd.DataFrame(transition_matrix,
columns=[
'unaware-unaware', 'aware-unaware',
def fit_pspec_model(
freqs,
ps1D,
ps1D_stddev,
beam_model=None,
ntune=2000,
nsamp=6000,
step=pm.SMC(),
cores=1,
chains=100,
fixB=False,
noise_term=False,
progressbar=True,
return_model=False,
):
def powerlaw_model(f, logA, ind, logB=-20):
return 10**logA * f**-ind + 10**logB
if beam_model is not None:
if noise_term:
def powerlaw_fit_model(f, logA, ind, logB=-20, logC=-20):
return powerlaw_model(f, logA, ind,
logB) * beam_model(f) + 10**logC
else:
def powerlaw_fit_model(f, logA, ind, logB=-20):
return powerlaw_model(f, logA, ind, logB) * beam_model(f)
else:
if noise_term:
def powerlaw_fit_model(f, logA, ind, logB=-20, logC=-20):
return powerlaw_model(f, logA, ind, logB) + 10**logC
else:
powerlaw_fit_model = powerlaw_model
# Try a pymc model to fit
with pm.Model() as model:
logA = pm.Uniform('logA', -20., 20.)
ind = pm.Uniform('index', 0.0, 10.)
if not fixB:
logB = pm.Uniform('logB', -20., 20.)
else:
logB = -20.
# Weak Gaussian priors
# logA = pm.Normal('logA', 0., 10.)
# ind = pm.Normal('index', 0.0, 3.)
# if not fixB:
# logB = pm.Normal('logB', 0., 10.)
# else:
# logB = -20.
if noise_term:
logC = pm.Uniform('logC', -20., 20.)
# logC = pm.Normal('logC', 0., 10.)
ps_vals = pm.Normal('obs',
powerlaw_fit_model(freqs,
logA,
ind,
logB=logB,
logC=logC),
sd=ps1D_stddev,
observed=ps1D)
else:
ps_vals = pm.Normal('obs',
powerlaw_fit_model(freqs, logA, ind,
logB=logB),
sd=ps1D_stddev,
observed=ps1D)
# step = pm.Slice()
# step = pm.NUTS()
# step = pm.SMC()
trace = pm.sample(nsamp,
tune=ntune,
step=step,
progressbar=progressbar,
cores=cores,
chains=chains)
summ = pm.summary(trace)
out = [np.array(summ['mean']), np.array(summ['sd'])]
if return_model:
return out, summ, trace, powerlaw_fit_model, model
else:
return out, summ, trace, powerlaw_fit_model
def fit_broken_pspec_model(freqs,
ps1D,
ps1D_stddev,
beam_model=None,
ntune=2000,
nsamp=6000,
step=pm.SMC(),
cores=1,
chains=100,
fixB=False,
noise_term=False,
progressbar=True,
return_model=False,
trace_name=None):
# https://docs.astropy.org/en/stable/api/astropy.modeling.powerlaws.SmoothlyBrokenPowerLaw1D.html
def broken_powerlaw_model(f,
logA,
ind1,
ind2,
break_f,
logB=-20,
delta=0.1):
A = 10**logA
B = 10**logB
return A * (f / break_f)**-ind1 * (0.5 *
(1 + (f / break_f)**(1 / delta)))**(
(ind1 - ind2) * delta) + B
if beam_model is not None:
if noise_term:
def powerlaw_fit_model(f,
logA,
ind1,
ind2,
break_f,
logB=-20,
logC=-20):
return broken_powerlaw_model(f, logA, ind1, ind2, break_f,
logB) * beam_model(f) + 10**logC
else:
def powerlaw_fit_model(f, logA, ind1, ind2, break_f, logB=-20):
return broken_powerlaw_model(f, logA, ind1, ind2, break_f,
logB) * beam_model(f)
else:
if noise_term:
def powerlaw_fit_model(f,
logA,
ind1,
ind2,
break_f,
logB=-20,
logC=-20):
return broken_powerlaw_model(f, logA, ind1, ind2, break_f,
logB) + 10**logC
else:
powerlaw_fit_model = broken_powerlaw_model
# Try a pymc model to fit
with pm.Model() as model:
logA = pm.Uniform('logA', -20., 20.)
ind1 = pm.Uniform('index1', 0.0, 10.)
# logA = pm.Normal('logA', 0., 10.)
# ind1 = pm.Normal('index1', 0.0, 3.)
# if not fixB:
# logB = pm.Normal('logB', 0., 10.)
# else:
# logB = -20.
# Second index is a perturbation on the first.
ind2 = ind1 + pm.Normal('index2', 0.0, 10.)
break_f = pm.Uniform('break_f', freqs.min(), freqs.max())
if not fixB:
logB = pm.Uniform('logB', -20., 20.)
else:
logB = -20.
if noise_term:
logC = pm.Uniform('logC', -20., 20.)
# logC = pm.Normal('logC', 0., 10.)
ps_vals = pm.Normal('obs',
powerlaw_fit_model(freqs,
logA,
ind1,
ind2,
break_f,
logB=logB,
logC=logC),
sd=ps1D_stddev,
observed=ps1D,
shape=freqs.shape)
else:
ps_vals = pm.Normal('obs',
powerlaw_fit_model(freqs,
logA,
ind1,
ind2,
break_f,
logB=logB),
sd=ps1D_stddev,
observed=ps1D,
shape=freqs.shape)
# step = pm.Slice()
# step = pm.NUTS()
# step = pm.SMC()
if trace_name is not None:
trace = pm.load_trace(trace_name)
else:
trace = pm.sample(nsamp,
tune=ntune,
step=step,
progressbar=progressbar,
cores=cores,
chains=chains)
summ = pm.summary(trace)
out = [np.array(summ['mean']), np.array(summ['sd'])]
if return_model:
return out, summ, trace, powerlaw_fit_model, model
else:
return out, summ, trace, powerlaw_fit_model
with mixedEffect:
tracede = pm.sample(5000, njobs=50, tune=1000, step=pm.DEMetropolis())
pm.traceplot(tracede, lines={
'w': w0,
'z': z0
})
#%% SMC
n_chains = 500
samples = 1000
tune_interval = 25
with mixedEffect:
mtrace = pm.sample(samples,
chains=n_chains,
step=pm.SMC(tune_interval=tune_interval))
#%%
pm.traceplot(mtrace, lines={
'w': w0,
'z': z0
})
#%% plot advi and NUTS (copy from pymc3 example)
burnin = 1000
from scipy import stats
import seaborn as sns
gbij = approx.bij
means = gbij.rmap(approx.mean.eval())
cov = approx.cov.eval()
sds = gbij.rmap(np.diag(cov)**.5)
