def _build_model(self, data):
data = _data_df2dict(data)
with pm.Model() as model:
# Priors
# NOTE: we need another variable if we deal with losses, which goes
# to the value function
β = pm.Bound(pm.Normal, lower=0)('beta', mu=1, sd=1000)
γ = pm.Bound(pm.Normal, lower=0)('gamma', mu=0, sd=1000)
τ = pm.Bound(pm.Normal, lower=0)('tau', mu=0, sd=1000)
# TODO: pay attention to the choice function & it's params
α = pm.Exponential('alpha', lam=1)
ϵ = 0.01
value_diff = (self._value_function(γ, data['B']) -
self._value_function(γ, data['A']))
time_diff = (self._time_weighing_function(τ, data['DB']) -
self._time_weighing_function(τ, data['DA']))
diff = value_diff - β * time_diff
# Choice function: psychometric
P_chooseB = pm.Deterministic('P_chooseB',
choice_func_psychometric2(α, ϵ, diff))
# Likelihood of observations
r_likelihood = pm.Bernoulli('r_likelihood',
p=P_chooseB,
observed=data['R'])
return model
def build_model(model_name, data_set, property_types):
# Build the likelihood operator.
surrogate_model = StollWerthSurrogate(data_set.molecular_weight)
log_likelihood = StollWerthOp(data_set, property_types, surrogate_model)
# Define the potentially 'fixed' model constants.
bond_length = data_set.bond_length.to(unit.nanometer).magnitude
quadrupole = 0.0
# Build the model
with pymc3.Model() as model:
epsilon = pymc3.Bound(pymc3.Exponential, 0.0)("epsilon",
lam=1.0 / 400.0)
sigma = pymc3.Bound(pymc3.Exponential, 0.0)("sigma", lam=1.0 / 5.0)
if model_name == "AUA" or model_name == "AUA+Q":
bond_length = pymc3.Bound(pymc3.Exponential, 0.0)("bond_length",
lam=1.0 / 3.0)
if model_name == "AUA+Q":
quadrupole = pymc3.Bound(pymc3.Exponential, 0.0)("quadrupole",
lam=1.0)
theta = tt.as_tensor_variable(
[epsilon, sigma, bond_length, quadrupole])
pymc3.DensityDist(
"likelihood",
lambda v: log_likelihood(v),
observed={"v": theta},
)
return model
def submodel2(x, y, yerr, parent):
with pm.Model(name="granulation", model=parent) as submodel:
# The parameters of SHOTerm kernel for non-periodicity granulation
mean2 = pm.Normal("mean2", mu=0.0, sd=10.0)
#logz = pm.Uniform("logz", lower=np.log(2 * np.pi / 4), upper=np.log(2*np.pi/vgp.min_period))
#sigma = pm.HalfCauchy("sigma", 3.0)
#logw0 = pm.Normal("logw0", mu=logz, sd=2.0)
logw0 = pm.Bound(pm.Normal,
lower=np.log(2 * np.pi / 2.5),
upper=np.log(2 * np.pi / self.min_period))(
"logw0", mu=np.log(2 * np.pi / 0.8), sd=1)
logSw4 = pm.Normal("logSw4",
mu=np.log(np.var(y) * (2 * np.pi / 2)**4),
sd=5)
logs22 = pm.Normal("logs22", mu=np.log(np.mean(yerr)), sd=2.0)
logQ = pm.Bound(pm.Normal,
lower=np.log(1 / 2),
upper=np.log(2))("logQ",
mu=np.log(1 / np.sqrt(2)),
sd=1)
kernel2 = xo.gp.terms.SHOTerm(log_Sw4=logSw4,
log_w0=logw0,
log_Q=logQ)
gp2 = xo.gp.GP(kernel2, x, yerr**2 + tt.exp(logs22))
loglike2 = gp2.log_likelihood(y - mean2)
return logw0, logQ, gp2, loglike2
def set_prior(self, param, abund=False, name_param=None):
# Read distribution configuration
dist_name = self.priorDict[param][0]
dist_loc, dist_scale = self.priorDict[param][1], self.priorDict[param][2]
dist_norm, dist_reLoc = self.priorDict[param][3], self.priorDict[param][4]
# Load the corresponding probability distribution
probDist = getattr(pymc3, dist_name)
if abund:
priorFunc = probDist(name_param, dist_loc, dist_scale) * dist_norm + dist_reLoc
elif probDist.__name__ in ['HalfCauchy']: # These distributions only have one parameter
priorFunc = probDist(param, dist_loc, shape=self.total_regions) * dist_norm + dist_reLoc
elif probDist.__name__ == 'Uniform':
# priorFunc = probDist(param, lower=dist_loc, upper=dist_scale) * dist_norm + dist_reLoc
if param == 'logOH':
priorFunc = pymc3.Bound(pymc3.Normal, lower=7.1, upper=9.1)('logOH', mu=8.0, sigma=1.0, testval=8.1)
if param == 'logU':
priorFunc = pymc3.Bound(pymc3.Normal, lower=-4.0, upper=-1.5)('logU', mu=-2.75, sigma=1.5, testval=-2.75)
if param == 'logNO':
priorFunc = pymc3.Bound(pymc3.Normal, lower=-2.0, upper=0.0)('logNO', mu=-1.0, sigma=0.5, testval=-1.0)
else:
priorFunc = probDist(param, dist_norm, dist_scale, shape=self.total_regions) * dist_norm + dist_reLoc
self.paramDict[param] = priorFunc
return
def v2_model(observations,
nulls,
null_sd,
null_b,
null_dispersed_prob,
iter_count=2000,
tune_iters=2000):
with pm.Model() as model:
# Probability of being a DE gene
de_prob = pm.Beta('de_prob', alpha=1., beta=5.)
# Probability of being downregulated
down_prob = pm.Beta('down_prob', alpha=1., beta=1.)
dispersed_prob = null_dispersed_prob
mu_pos = pm.Lognormal('mu_pos', mu=-3, sd=1.)
mu_neg = pm.Lognormal('mu_neg', mu=-3, sd=1.)
sd_pos = pm.Gamma('sd_pos', alpha=0.01, beta=1.)
sd_neg = pm.Gamma('sd_neg', alpha=0.01, beta=1.)
nu_pos = pm.Gamma('nu_pos', alpha=5., beta=1.)
nu_neg = pm.Gamma('nu_neg', alpha=5., beta=1.)
spike_component = pm.Normal.dist(mu=0., sd=null_sd)
slab_component = pm.Laplace.dist(mu=0., b=null_b)
# Sample from Gaussian-Laplace mixture for null (spike-and-slab mixture)
pm.Mixture('null',
comp_dists=[spike_component, slab_component],
w=tt.as_tensor([1. - dispersed_prob, dispersed_prob]),
observed=nulls)
pos_component = pm.Bound(pm.StudentT, lower=0.).dist(mu=mu_pos,
sd=sd_pos,
nu=nu_pos)
neg_component = pm.Bound(pm.StudentT, upper=0.).dist(mu=-mu_neg,
sd=sd_neg,
nu=nu_neg)
pm.Mixture('obs',
w=tt.as_tensor([(1. - de_prob) * (1. - dispersed_prob),
(1. - de_prob) * dispersed_prob,
de_prob * (1. - down_prob),
de_prob * down_prob]),
comp_dists=[
spike_component, slab_component, pos_component,
neg_component
],
observed=observations)
pm.Deterministic('log_prob', model.logpt)
for RV in model.basic_RVs:
print(RV.name, RV.logp(model.test_point))
trace = pm.sample(iter_count, tune=tune_iters, chains=4)
ppc = pm.sample_ppc(trace, samples=iter_count, model=model)
return ({'trace': trace, 'ppc': ppc})
def case_count_model_us_states(df):
# Normalize inputs in a way that is sensible:
# People per test: normalize to South Korea
# assuming S.K. testing is "saturated"
ppt_sk = np.log10(51500000. / 250000)
df['people_per_test_normalized'] = (
np.log10(df['people_per_test_7_days_ago']) - ppt_sk)
n = len(df)
# For each country, let:
# c_obs = number of observed cases
c_obs = df['num_pos_7_days_ago'].values
# c_star = number of true cases
# d_obs = number of observed deaths
d_obs = df[['death', 'num_pos_7_days_ago']].min(axis=1).values
# people per test
people_per_test = df['people_per_test_normalized'].values
covid_case_count_model = pm.Model()
with covid_case_count_model:
# Priors:
mu_0 = pm.Beta('mu_0', alpha=1, beta=100, testval=0.01)
# sig_0 = pm.Uniform('sig_0', lower=0.0, upper=mu_0 * (1 - mu_0))
alpha = pm.Bound(pm.Normal, lower=0.0)(
'alpha', mu=8, sigma=3, shape=1)
beta = pm.Bound(pm.Normal, upper=0.0)(
'beta', mu=-1, sigma=1, shape=1)
# beta = pm.Normal('beta', mu=0, sigma=1, shape=3)
sigma = pm.HalfNormal('sigma', sigma=0.5, testval=0.1)
# sigma_1 = pm.HalfNormal('sigma_1', sigma=2, testval=0.1)
# Model probability of case under-reporting as logistic regression:
mu_model_logit = alpha + beta * people_per_test
tau_logit = pm.Normal('tau_logit',
mu=mu_model_logit,
sigma=sigma,
shape=n)
tau = np.exp(tau_logit) / (np.exp(tau_logit) + 1)
c_star = c_obs / tau
# Binomial likelihood:
d = pm.Binomial('d',
n=c_star,
p=mu_0,
observed=d_obs)
return covid_case_count_model
def get_model(self, vfield0, sigma_vfield0, rlim=1 * u.kpc):
# Number of prior mixture components:
with pm.Model() as model:
# True distance:
BoundedR = pm.Bound(UniformSpaceDensity,
lower=0,
upper=rlim.to_value(u.pc))
r = BoundedR("r", rlim.to_value(u.pc), shape=(self.N, 1))
# Milky Way velocity distribution
K = vfield0.shape[0]
w = pm.Dirichlet('w', a=np.ones(K))
# Set up means and variances:
meanvs = []
sigvs = []
for k in range(K):
vtmp = pm.Normal(f'vmean{k}', vfield0[k], 10., shape=3) # HACK
BoundedNormal = pm.Bound(pm.Normal, lower=1.5, upper=5.3)
lnstmp = BoundedNormal(f'lns{k}', np.log(sigma_vfield0[k]),
0.2)
stmp = pm.Deterministic(f'vsig{k}', tt.exp(lnstmp))
meanvs.append(vtmp)
sigvs.append(stmp)
pvdists = []
for k in range(K):
pvtmp = pm.MvNormal.dist(meanvs[k],
tau=np.eye(3) * 1 / sigvs[k]**2,
shape=3)
pvdists.append(pvtmp)
vxyz = pm.Mixture('vxyz',
w=w,
comp_dists=pvdists,
shape=(self.N, 3))
# Velocity in tangent plane coordinates
vtan = tt.batched_dot(self.Ms, vxyz)
model_pm = vtan[:, :2] / r * pc_mas_yr_per_km_s
model_rv = vtan[:, 2:3]
model_y = tt.concatenate((1000 / r, model_pm, model_rv), axis=1)
pm.Deterministic('model_y', model_y)
# val = pm.MvNormal('like', mu=model_y, tau=Cinv, observed=y)
dy = self.ys - model_y
pm.Potential(
'chisq',
-0.5 * tt.batched_dot(dy, tt.batched_dot(self.Cinvs, dy)))
return model
def hierarchical_model(**kwargs):
'''
Hierarchical model for roi
'''
data = load_dataset(group=kwargs['group'],
roi=kwargs['roi'],
task=kwargs['task'],
condition=kwargs['condition'],
path=kwargs['path'])
subject_ids = data.subject.unique()
subject_idx = np.array([idx - 1 for idx in data.subject.values])
subject_idx = handle_irregular_idx(subject_idx)
n_subjects = len(subject_ids)
with pm.Model() as hierarchical_model:
# Hyperpriors for group nodes
mu_a = pm.Normal('mu_alpha', mu=0., sd=1)
mu_b = pm.Normal('mu_beta', mu=0., sd=1)
#sigma_a = pm.HalfCauchy('sigma_alpha', 1)
#sigma_b = pm.HalfCauchy('sigma_b', 1)
sigma_a = pm.Uniform('sigma_alpha', 0, 100)
sigma_b = pm.Uniform('sigma_beta', 0, 100)
# Parameters for each subject
BoundedNormalAlpha = pm.Bound(pm.Normal, lower=0, upper=5)
BoundedNormalBeta = pm.Bound(pm.Normal, lower=0, upper=1)
a = BoundedNormalAlpha('alpha', mu=mu_a, sd=sigma_a, shape=n_subjects)
b = BoundedNormalBeta('beta', mu=mu_b, sd=sigma_b, shape=n_subjects)
# Model error
#eps = pm.HalfCauchy('eps', 1)
eps = pm.Uniform('eps', 0, 100)
# Model prediction of voxel activation
x_est = data.thresh_x.values * a[
subject_idx] - data.n_activity.values * b[
subject_idx] + data.noise.values
# Data likelihood
y = pm.Normal('y', mu=x_est, sd=eps, observed=data.raw_x.values)
return hierarchical_model
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 singleband_gp(self, lower=5, upper=50, seed=42):
# x, y, yerr = make_data_nice(x, y, yerr)
np.random.seed(seed)
with pm.Model() as model:
# The mean flux of the time series
mean = pm.Normal("mean", mu=0.0, sd=10.0)
# A jitter term describing excess white noise
logs2 = pm.Normal("logs2",
mu=2 * np.log(np.mean(self.yerr)),
sd=2.0)
# A term to describe the non-periodic variability
logSw4 = pm.Normal("logSw4", mu=np.log(np.var(self.y)), sd=5.0)
logw0 = pm.Normal("logw0", mu=np.log(2 * np.pi / 10), sd=5.0)
# The parameters of the RotationTerm kernel
logamp = pm.Normal("logamp", mu=np.log(np.var(self.y)), sd=5.0)
BoundedNormal = pm.Bound(pm.Normal,
lower=np.log(lower),
upper=np.log(upper))
logperiod = BoundedNormal("logperiod",
mu=np.log(self.init_period),
sd=5.0)
logQ0 = pm.Normal("logQ0", mu=1.0, sd=10.0)
logdeltaQ = pm.Normal("logdeltaQ", mu=2.0, sd=10.0)
mix = xo.distributions.UnitUniform("mix")
# Track the period as a deterministic
period = pm.Deterministic("period", tt.exp(logperiod))
# Set up the Gaussian Process model
kernel = xo.gp.terms.SHOTerm(log_Sw4=logSw4,
log_w0=logw0,
Q=1 / np.sqrt(2))
kernel += xo.gp.terms.RotationTerm(log_amp=logamp,
period=period,
log_Q0=logQ0,
log_deltaQ=logdeltaQ,
mix=mix)
gp = xo.gp.GP(kernel,
self.x,
self.yerr**2 + tt.exp(logs2),
mean=mean)
# Compute the Gaussian Process likelihood and add it into the
# the PyMC3 model as a "potential"
gp.marginal("gp", observed=self.y)
# Compute the mean model prediction for plotting purposes
pm.Deterministic("pred", gp.predict())
# Optimize to find the maximum a posteriori parameters
map_soln = xo.optimize(start=model.test_point)
self.model = model
self.map_soln = model
return map_soln, model
def get_bayesian_model(model_type,
Y,
shots,
m_gates,
mu_AB,
cov_AB,
alpha_ref,
alpha_lower=0.5,
alpha_upper=0.999,
alpha_testval=0.9,
p_lower=0.9,
p_upper=0.999,
p_testval=0.95,
RvsI=None,
IvsR=None,
sigma_theta=0.004):
# Bayesian model
# from https://iopscience.iop.org/arti=RvsI, cle/10.1088/1367-2630/17/1/013042/pdf
# see https://docs.pymc.io/api/model.html
RB_model = pm.Model()
with RB_model:
total_shots = np.full(Y.shape, shots)
#Priors for unknown model parameters
alpha = pm.Uniform("alpha",
lower=alpha_lower,
upper=alpha_upper,
testval=alpha_ref)
BoundedMvNormal = pm.Bound(pm.MvNormal, lower=0.0)
AB = BoundedMvNormal("AB",
mu=mu_AB,
testval=mu_AB,
cov=np.diag(cov_AB),
shape=(2))
if model_type == "hierarchical":
GSP = AB[0] * alpha**m_gates + AB[1]
theta = pm.Beta("GSP", mu=GSP, sigma=sigma_theta, shape=Y.shape[1])
# Likelihood (sampling distribution) of observations
p = pm.Binomial("Counts_h", p=theta, observed=Y, n=total_shots)
elif model_type == "tilde":
p_tilde = pm.Uniform("p_tilde",
lower=p_lower,
upper=p_upper,
testval=p_testval)
GSP = AB[0] * (RvsI * alpha**m_gates + IvsR *
(alpha * p_tilde)**m_gates) + AB[1]
# Likelihood (sampling distribution) of observations
p = pm.Binomial("Counts_t", p=GSP, observed=Y, n=total_shots)
else: # defaul model "pooled"
GSP = AB[0] * alpha**m_gates + AB[1]
# Likelihood (sampling distribution) of observations
p = pm.Binomial("Counts_p", p=GSP, observed=Y, n=total_shots)
return RB_model
def get_bayesian_model_hierarchical(
model_type,
Y): # modified for accelerated BM with EPCest as extra parameter
# Bayesian model
# from https://iopscience.iop.org/article/10.1088/1367-2630/17/1/013042/pdf
# see https://docs.pymc.io/api/model.html
RBH_model = pm.Model()
with RBH_model:
#Priors for unknown model parameters
alpha = pm.Uniform("alpha",
lower=alpha_lower,
upper=alpha_upper,
testval=alpha_ref)
BoundedMvNormal = pm.Bound(pm.MvNormal, lower=0.0)
AB = BoundedMvNormal("AB",
mu=mu_AB,
testval=mu_AB,
cov=np.diag(cov_AB),
shape=(2))
# Expected value of outcome
GSP = AB[0] * alpha**m_gates + AB[1]
total_shots = np.full(Y.shape, shots)
theta = pm.Beta("GSP", mu=GSP, sigma=sigma_theta, shape=Y.shape[1])
# Likelihood (sampling distribution) of observations
p = pm.Binomial("Counts", p=theta, observed=Y, n=total_shots)
return RBH_model
def _gen_d_vars_pm(tmñ=(), fmt_nmbrs='{}'):
egr = {}
norm = {}
for p, líms in líms_paráms.items():
nmbr = fmt_nmbrs.format(p)
if aprioris is None:
if líms[0] is líms[1] is None:
final = pm.Normal(name=nmbr, mu=0, sd=100 ** 2, shape=tmñ)
else:
dist_norm = pm.Normal(name='transf' + nmbr, mu=0, sd=1, shape=tmñ)
if líms[0] is None:
final = pm.Deterministic(nmbr, líms[1] - pm.math.exp(dist_norm))
elif líms[1] is None:
final = pm.Deterministic(nmbr, líms[0] + pm.math.exp(dist_norm))
else:
final = pm.Deterministic(
nmbr, (pm.math.tanh(dist_norm) / 2 + 0.5) * (líms[1] - líms[0]) + líms[0]
)
norm[p] = dist_norm
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])
final = acotada(nmbr, shape=tmñ, **prms)
else:
if dist == pm.Uniform:
prms['lower'] = max(prms['lower'], líms[0])
prms['upper'] = min(prms['upper'], líms[1])
final = dist(nmbr, shape=tmñ, **prms)
egr[p] = final
for p, v in egr.items():
if p not in norm:
norm[p] = v
return {'final': egr, 'norm': norm}
def sample_explore(n=20, ntrials=25, steepness_alpha=1., steepness_beta=1., x_midpoint_prec=4., yscale_alpha=1., yscale_beta=.5):
trials = np.arange(ntrials)
steepness_dist = pm.Gamma.dist(steepness_alpha, steepness_beta)
BoundNormal = pm.Bound(pm.Normal, lower=0, upper=ntrials)
x_midpoint_dist = BoundNormal.dist(mu=ntrials/2., sd=ntrials/x_midpoint_prec)
yscale_dist = pm.Gamma.dist(yscale_alpha, yscale_beta)
steepness = steepness_dist.random(size=n)
x_midpoint = x_midpoint_dist.random(size=n)
yscale = yscale_dist.random(size=n)
position = trials[:,None] - x_midpoint[None,:]
growth = np.exp(-steepness * position)
denom = 1 + growth * yscale
explore_param = 1 - (1. / denom)
x = np.linspace(0,30)
steepness_pdf = np.exp(steepness_dist.logp(x).eval())
x_midpoint_pdf = np.exp(x_midpoint_dist.logp(x).eval())
yscale_pdf = np.exp(yscale_dist.logp(x).eval())
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8,5))
ax1.plot(x, steepness_pdf)
ax1.plot(x, x_midpoint_pdf)
ax1.plot(x, yscale_pdf)
ax2.plot(explore_param)
def granulation_model(self):
peak = self.period_prior()
x = self.lc.lcf.time
y = self.lc.lcf.flux
yerr = self.lc.lcf.flux_err
with pm.Model() as model:
# The mean flux of the time series
mean = pm.Normal("mean", mu=0.0, sd=10.0)
# A jitter term describing excess white noise
logs2 = pm.Normal("logs2", mu=2*np.log(np.min(sigmaclip(yerr)[0])), sd=1.0)
logw0 = pm.Bound(pm.Normal, lower=-0.5, upper=np.log(2 * np.pi / self.min_period))("logw0", mu=0.0, sd=5)
logSw4 = pm.Normal("logSw4", mu=np.log(np.var(y)), sd=5)
kernel = xo.gp.terms.SHOTerm(log_Sw4=logSw4, log_w0=logw0, Q=1 / np.sqrt(2))
#GP model
gp = xo.gp.GP(kernel, x, yerr**2 + tt.exp(logs2))
# Compute the Gaussian Process likelihood and add it into the
# the PyMC3 model as a "potential"
pm.Potential("loglike", gp.log_likelihood(y - mean))
# Compute the mean model prediction for plotting purposes
pm.Deterministic("pred", gp.predict())
# Optimize to find the maximum a posteriori parameters
map_soln = xo.optimize(start=model.test_point)
return model, map_soln
def submodel1(x,y,yerr,parent):
with pm.Model(name="rotation_", model=parent) as submodel:
# The mean flux of the time series
mean1 = pm.Normal("mean1", mu=0.0, sd=10.0)
# A jitter term describing excess white noise
logs21 = pm.Normal("logs21", mu=np.log(np.mean(yerr)), sd=2.0)
# The parameters of the RotationTerm kernel
logamp = pm.Normal("logamp", mu=np.log(np.var(y)), sd=5.0)
#logperiod = pm.Uniform("logperiod", lower=np.log(vgp.min_period), upper=np.log(vgp.max_period))
logperiod = pm.Bound(pm.Normal, lower=np.log(self.min_period),
upper=np.log(self.max_period))("logperiod", mu=np.log(peak["period"]), sd=1.0)
logQ0 = pm.Uniform("logQ0", lower=-15, upper=5)
logdeltaQ = pm.Uniform("logdeltaQ", lower=-15, upper=5)
mix = pm.Uniform("mix", lower=0, upper=1.0)
# Track the period as a deterministic
period = pm.Deterministic("period", tt.exp(logperiod))
kernel1 = xo.gp.terms.RotationTerm(
log_amp=logamp,
period=period,
log_Q0=logQ0,
log_deltaQ=logdeltaQ,
mix=mix)
gp1 = xo.gp.GP(kernel1, x, yerr**2 + tt.exp(logs21))
# Compute the Gaussian Process likelihood and add it into the
# the PyMC3 model as a "potential"
loglike1 = gp1.log_likelihood(y - mean1)
#pred1 = pm.Deterministic("pred1", gp1.predict())
return logperiod, logQ0, gp1, loglike1
def test_bounded(self):
# A bit crude...
BoundedNormal = pm.Bound(pm.Normal, upper=0)
def ref_rand(size, tau):
return -st.halfnorm.rvs(size=size, loc=0, scale=tau ** -0.5)
pymc3_random(BoundedNormal, {'tau': Rplus}, ref_rand=ref_rand)
def bayes_model(training_samples) -> pm.model.Model:
"""
Solve for posterior distributions using pymc3
"""
with pm.Model() as model:
# Priors for the mu parameter of the
# Poisson distribution P.
# Note: mu = mean(P)
mu_goal_for = pm.Uniform(
'mu_goal_for', 0, 5*60
)
mu_goal_against = pm.Uniform(
'mu_goal_against', 0, 5*60
)
mu_no_goal = pm.Uniform(
'mu_no_goal', 0, 5*60
)
# Observations to train the model on
obs_goal_for = pm.Poisson(
'obs_goal_for',
mu=mu_goal_for,
observed=training_samples[0],
)
obs_goal_against = pm.Poisson(
'obs_goal_against',
mu=mu_goal_against,
observed=training_samples[1],
)
obs_no_goal = pm.Poisson(
'obs_no_goal',
mu=mu_no_goal,
observed=training_samples[2],
)
# Outcome probabilities
p_goal_for = pm.Bound(pm.Poisson, upper=5*60)('p_goal_for', mu=mu_goal_for)
p_goal_against = pm.Bound(pm.Poisson, upper=5*60)('p_goal_against', mu=mu_goal_against)
p_no_goal = pm.Bound(pm.Poisson, upper=5*60)('p_no_goal', mu=mu_no_goal)
# Fit model
step = pm.Metropolis()
trace = pm.sample(18000, step=step)
return model, trace
def test_bounded_dist(self):
with pm.Model() as model:
BoundedNormal = pm.Bound(pm.Normal, lower=0.0)
x = BoundedNormal("x", mu=aet.zeros((3, 1)), sd=1 * aet.ones((3, 1)), shape=(3, 1))
with model:
prior_trace = pm.sample_prior_predictive(5)
assert prior_trace["x"].shape == (5, 3, 1)
def _gen_d_vars_pm_jer():
dists_base = _gen_d_vars_pm(tmñ=(len(set(nv_jerarquía[0])), ),
fmt_nmbrs='mu_{}_nv_' +
str(len(nv_jerarquía) - 1))
egr = {}
for p, líms in líms_paráms.items():
mu = dists_base[p]
sg = pm.HalfNormal(name='sg_{}'.format(p), sd=10,
shape=(1, )) # type: pm.model.TransformedRV
if líms[0] is líms[1] is None:
for í, nv in enumerate(nv_jerarquía[:-1]):
últ_niv = í == (len(nv_jerarquía) - 2)
tmñ_nv = nv.shape
nmbr_mu = p if últ_niv else 'mu_{}_nv_{}'.format(
p,
len(nv_jerarquía) - 2 - í)
nmbr_sg = 'sg_{}_nv_{}'.format(
p,
len(nv_jerarquía) - 2 - í)
mu = pm.Normal(name=nmbr_mu,
mu=mu[nv],
sd=sg[nv],
shape=tmñ_nv)
if not últ_niv:
sg = pm.HalfNormal(name=nmbr_sg.format(p, í),
sd=obs_y.values.ptp(),
shape=tmñ_nv)
else:
for í, nv in enumerate(nv_jerarquía[:-1]):
tmñ_nv = nv.shape
últ_niv = í == (len(nv_jerarquía) - 2)
nmbr_mu = p if últ_niv else 'mu_{}_nv_{}'.format(
p,
len(nv_jerarquía) - 2 - í)
nmbr_sg = 'sg_{}_nv_{}'.format(
p,
len(nv_jerarquía) - 2 - í)
acotada = pm.Bound(pm.Normal,
lower=líms[0],
upper=líms[1])
mu = acotada(nmbr_mu,
mu=mu[nv],
sd=sg[nv],
shape=tmñ_nv)
if not últ_niv:
sg = pm.HalfNormal(name=nmbr_sg.format(p, í),
sd=obs_y.values.ptp(),
shape=tmñ_nv)
egr[p] = mu
return egr
def harmonic_fit_mcmc(time, X, frq, mask=None, axis=0, basetime=None, **kwargs):
"""
Harmonic fitting using Bayesian inference
"""
tday = 86400.
# Convert the time to days
dtime = SecondsSince(time, basetime=basetime )
dtime /= tday
# Convert the frequencies to radians / day
omega = [ff*tday for ff in frq]
# Number of parameters
n_params = 2*len(omega) + 1
nomega = len(omega)
print('Number of Parametrs: %d\n'%n_params, omega)
with pm.Model() as my_model:
###
# Create priors for each of our variables
BoundNormal = pm.Bound(pm.Normal, lower=0.0)
# Mean
beta_mean = pm.Normal('beta_mean', mu=0, sd=1)
beta_re = pm.Normal('beta_re', mu=1., sd = 5., shape=nomega)
beta_im = pm.Normal('beta_im', mu=1., sd = 5., shape=nomega)
#beta_s=[beta_mean]
# Harmonics
#for n in range(0,2*len(omega),2):
# beta_s.append(pm.Normal('beta_%d_re'%(n//2), mu=1., sd = 5.))
# beta_s.append(pm.Normal('beta_%d_im'%(n//2), mu=1., sd = 5.))
# The mean function
mu_x = sine_model(beta_mean, beta_re, beta_im, omega, dtime)
###
# Generate the likelihood function using the deterministic variable as the mean
sigma = pm.HalfNormal('sigma',5.)
X_obs = pm.Normal('X_obs', mu=mu_x, sd=sigma, observed=X)
mp = pm.find_MAP()
print(mp)
# Inference step...
step = None
start = None
trace = pm.sample(500, tune=1000, start = start, step=step, cores=2,
)#nuts_kwargs=dict(target_accept=0.95, max_treedepth=16, k=0.5))
# Return the trace and the parameter stats
return trace, my_model, omega, dtime
def harmonic_fit_mcmc_arn(time, X, frq, arn=1, mask=None, axis=0, basetime=None, **kwargs):
"""
Harmonic fitting using Bayesian inference
Model the errors using an auto-regressive model
"""
tday = 86400.
# Convert the time to days
dtime = SecondsSince(time, basetime=basetime )
nt = dtime.shape[0]
dtime /= tday
# Convert the frequencies to radians / day
omega = [ff*tday for ff in frq]
#omega = frq
# Number of parameters
n_params = 2*len(omega) + 1
print('Number of Parametrs: %d\n'%n_params, omega)
with pm.Model() as my_model:
###
# Create priors for each of our variables
BoundNormal = pm.Bound(pm.Normal, lower=0.0)
# Mean
beta_mean = pm.Normal('beta_mean', mu=0, sd=1)
beta_s=[beta_mean]
# Harmonics
for n in range(0,2*len(omega),2):
beta_s.append(pm.Normal('beta_%d_re'%(n//2), mu=1., sd = 5.))
beta_s.append(pm.Normal('beta_%d_im'%(n//2), mu=1., sd = 5.))
###
# Generate the likelihood function using the deterministic variable as the mean
mu_x = sine_model_notrend(beta_s, omega, dtime)
# Use an autoregressive model for the error term
beta = pm.Normal('beta', mu=0, sigma=1., shape=arn)
#sigma = pm.InverseGamma('sigma',1,1)
sigma = pm.HalfNormal('sigma',1)
X_obs = pm.AR('X_obs', beta, sigma=sigma, observed=X - mu_x)
# Inference step...
step = None
start = None
trace = pm.sample(500, tune=1000, start = start, step=step, cores=2,
return_inferencedata=False)#nuts_kwargs=dict(target_accept=0.95, max_treedepth=16, k=0.5))
# Return the trace and the parameter stats
return trace, my_model, omega, dtime
def _powerlaw_prior(self, key):
"""
Map the bilby PowerLaw prior to a PyMC3 style function
"""
# check prior is a PowerLaw
pymc3, STEP_METHODS, floatX = self._import_external_sampler()
theano, tt, as_op = self._import_theano()
if isinstance(self.priors[key], PowerLaw):
# check power law is set
if not hasattr(self.priors[key], 'alpha'):
raise AttributeError("No 'alpha' attribute set for PowerLaw prior")
if self.priors[key].alpha < -1.:
# use Pareto distribution
palpha = -(1. + self.priors[key].alpha)
return pymc3.Bound(
pymc3.Pareto, upper=self.priors[key].minimum)(
key, alpha=palpha, m=self.priors[key].maximum)
else:
class Pymc3PowerLaw(pymc3.Continuous):
def __init__(self, lower, upper, alpha, testval=1):
falpha = alpha
self.lower = lower = tt.as_tensor_variable(floatX(lower))
self.upper = upper = tt.as_tensor_variable(floatX(upper))
self.alpha = alpha = tt.as_tensor_variable(floatX(alpha))
if falpha == -1:
self.norm = 1. / (tt.log(self.upper / self.lower))
else:
beta = (1. + self.alpha)
self.norm = 1. / (beta * (tt.pow(self.upper, beta) -
tt.pow(self.lower, beta)))
transform = pymc3.distributions.transforms.interval(
lower, upper)
super(Pymc3PowerLaw, self).__init__(
transform=transform, testval=testval)
def logp(self, value):
upper = self.upper
lower = self.lower
alpha = self.alpha
return pymc3.distributions.dist_math.bound(
alpha * tt.log(value) + tt.log(self.norm),
lower <= value, value <= upper)
return Pymc3PowerLaw(key, lower=self.priors[key].minimum,
upper=self.priors[key].maximum,
alpha=self.priors[key].alpha)
else:
raise ValueError("Prior for '{}' is not a Power Law".format(key))
def __init__(self, light_curve, rotation_period, n_spots, contrast,
latitude_cutoff=10, partition_lon=True):
pm.gp.mean.Mean.__init__(self)
if contrast is None:
contrast = pm.TruncatedNormal("contrast", lower=0.01, upper=0.99,
testval=0.4, mu=0.5, sigma=0.5)
self.f0 = pm.TruncatedNormal("f0", mu=1, sigma=1,
testval=light_curve.flux.max(),
lower=-1, upper=2)
self.eq_period = pm.TruncatedNormal("P_eq",
lower=0.8 * rotation_period,
upper=1.2 * rotation_period,
mu=rotation_period,
sigma=0.2 * rotation_period,
testval=rotation_period)
BoundedHalfNormal = pm.Bound(pm.HalfNormal, lower=1e-6, upper=0.99)
self.shear = BoundedHalfNormal("shear", sigma=0.2, testval=0.01)
self.comp_inclination = pm.Uniform("comp_inc",
lower=np.radians(0),
upper=np.radians(90),
testval=np.radians(1))
if partition_lon:
lon_lims = 2 * np.pi * np.arange(n_spots + 1) / n_spots
lower = lon_lims[:-1]
upper = lon_lims[1:]
else:
lower = 0
upper = 2 * np.pi
self.lon = pm.Uniform("lon",
lower=lower,
upper=upper,
shape=(1, n_spots))
self.lat = pm.TruncatedNormal("lat",
lower=np.radians(latitude_cutoff),
upper=np.radians(180 - latitude_cutoff),
mu=np.pi / 2,
sigma=np.pi / 2,
shape=(1, n_spots))
self.rspot = BoundedHalfNormal("R_spot",
sigma=0.2,
shape=(1, n_spots),
testval=0.3)
self.contrast = contrast
self.spot_period = self.eq_period / (1 - self.shear *
pm.math.sin(self.lat - np.pi / 2) ** 2)
self.sin_lat = pm.math.sin(self.lat)
self.cos_lat = pm.math.cos(self.lat)
self.sin_c_inc = pm.math.sin(self.comp_inclination)
self.cos_c_inc = pm.math.cos(self.comp_inclination)
def graded_response_model(dataset, n_categories):
"""Defines the mcmc model for the graded response model.
Args:
dataset: [n_items, n_participants] 2d array of measured responses
n_categories: number of polytomous values (i.e. Number of Likert Levels)
Returns:
model: PyMC3 model to run
"""
n_items, n_people = dataset.shape
n_levels = n_categories - 1
# Need small deviation in offset to
# fit into pymc framework
mu_value = linspace(-0.1, 0.1, n_levels)
# Run through 0, K - 1
observed = dataset - dataset.min()
graded_mcmc_model = pm.Model()
with graded_mcmc_model:
# Ability Parameters
ability = pm.Normal("Ability", mu=0, sigma=1, shape=n_people)
# Discrimination multilevel prior
rayleigh_scale = pm.Lognormal("Rayleigh_Scale",
mu=0,
sigma=1 / 4,
shape=1)
discrimination = pm.Bound(Rayleigh, lower=0.25)(name='Discrimination',
beta=rayleigh_scale,
offset=0.25,
shape=n_items)
# Threshold multilevel prior
sigma_difficulty = pm.HalfNormal('Difficulty_SD', sigma=1, shape=1)
for ndx in range(n_items):
thresholds = pm.Normal(
f"Thresholds{ndx}",
mu=mu_value,
sigma=sigma_difficulty,
shape=n_levels,
transform=pm.distributions.transforms.ordered)
# Compute the log likelihood
kernel = discrimination[ndx] * ability
probabilities = pm.OrderedLogistic(f'Log_Likelihood{ndx}',
cutpoints=thresholds,
eta=kernel,
observed=observed[ndx])
return graded_mcmc_model
def _build_model(self, data):
data = _data_df2dict(data)
with pm.Model() as model:
# Priors
k = pm.Bound(pm.Normal, lower=-0.005)('k', mu=0.001, sd=0.5)
s = pm.Bound(pm.Normal, lower=0)('s', mu=1, sd=2)
α = pm.Exponential('alpha', lam=1)
ϵ = 0.01
# Value functions
VA = pm.Deterministic('VA', data['A'] * self._df(k, s, data['DA']))
VB = pm.Deterministic('VB', data['B'] * self._df(k, s, data['DB']))
# Choice function: psychometric
P_chooseB = pm.Deterministic(
'P_chooseB', choice_func_psychometric(α, ϵ, VA, VB))
# Likelihood of observations
r_likelihood = pm.Bernoulli('r_likelihood',
p=P_chooseB,
observed=data['R'])
return model
def SIR_training(self, sequence, totalpopulation):
self.popu = totalpopulation
self.data = sequence[:]
acc_infect = sequence[:, 0] / totalpopulation
basic_model = pm.Model()
n = len(acc_infect)
I = acc_infect[0]
R = 0
S = 1 - I
with basic_model:
BoundedNormal = pm.Bound(pm.Normal, lower=0.0, upper=1.0)
BoundedNormal2 = pm.Bound(pm.Normal, lower=1.0, upper=10.0)
theta = []
r0 = BoundedNormal2('R_0', mu=self.r0, sigma=0.72)
gamma = BoundedNormal('gamma', mu=self.gamma, sigma=0.02)
beta = pm.Deterministic('beta', r0 * gamma)
ka = pm.Gamma('ka', 2, 0.0001)
Lambda1 = pm.Gamma('Lambda1', 2, 0.0001)
qu = pm.Uniform('qu', lower=0.1, upper=1.0)
theta.append(
pm.Deterministic('theta_' + str(0), pm.math.stack([S, I, R])))
for i in range(1, n):
states = theta[i - 1]
solve_theta = pm.Deterministic(
'solve_theta_' + str(i),
ka * pm.math.stack([
states[0] - qu * beta * states[0] * states[1],
states[1] + qu * beta * states[0] * states[1] -
gamma * states[1], states[2] + gamma * states[1]
]))
theta.append(
pm.Dirichlet('theta_' + str(i), a=solve_theta, shape=(3)))
real_infect = pm.Beta('real_infect_' + str(i),
Lambda1 * theta[i][1],
Lambda1 * (1 - theta[i][1]),
observed=acc_infect[i])
step = pm.Metropolis()
Trace = pm.sample(2000, cores=16, chains=1, init='auto', step=step)
self.trace = Trace
def pymc_train(X_train, Y_train, X_test, Y_test, penalty='L2'):
fs = np.sign(np.asarray([pearsonr(x, Y_train)[0] for x in X_train.T]))
with pm.Model() as logistic_model:
if penalty is 'L2':
b = pm.Bound(pm.Normal, lower=0)('b',
sd=1.,
shape=X_train.shape[0])
else:
b = pm.Bound(pm.Laplace, lower=0)('b',
b=1.,
shape=X_train.shape[0])
u = pm.Normal('u', 0, sd=10)
bs = pm.Deterministic('bs', tt.mul(fs, b))
p = pm.math.invlogit(u + tt.dot(X_train, bs))
likelihood = pm.Bernoulli('likelihood', p, observed=Y_train)
return pm.sample(10000)
def mock(self,
muB,
sigmaB,
muC,
sigmaC,
noise,
n_galaxies,
phi_limit=np.pi / 2.0):
"""
Generate a mock dataset
"""
# Define number of galaxies in the mock dataset and the uncertainty in the observation of q
self.n_galaxies = n_galaxies
self.sigmaq = noise
# Galaxy orientation is isotropic in space. mu=cos(theta)
self.mu = np.random.rand(self.n_galaxies)
self.phi = phi_limit * np.random.rand(self.n_galaxies)
# Generate truncated normal distributions using PYMC3
tmpB = pm.Bound(pm.Normal, lower=0.0, upper=1.0)
tmpC = pm.Bound(pm.Normal, lower=0.0, upper=1.0)
# Sample from these distributions
B = tmpB.dist(mu=muB, sd=sigmaB).random(size=self.n_galaxies)
C = tmpC.dist(mu=muC, sd=sigmaC).random(size=self.n_galaxies)
BC = np.vstack([B, C])
BC = np.sort(BC, axis=0)
self.C, self.B = BC[0, :], BC[1, :]
# Compute axial ratios
q = self.axial_ratio(self.B, self.C, self.mu, self.phi)
# Generate fake observations by adding Gaussian noise
self.qobs = q + self.sigmaq * np.random.randn(self.n_galaxies)
def analyze_robust1(data):
with pm.Model() as model:
# priors might be adapted here to be less flat
mu = pm.Normal('mu',
mu=0.,
sd=100.,
shape=2,
testval=np.median(data.T, axis=1))
bound_sigma = pm.Bound(pm.Normal, lower=0.)
sigma = bound_sigma('sigma',
mu=0.,
sd=100.,
shape=2,
testval=mad(data, axis=0))
rho = pm.Uniform('r', lower=-1., upper=1., testval=0)
cov = pm.Deterministic('cov', covariance(sigma, rho))
bound_nu = pm.Bound(pm.Gamma, lower=1.)
nu = bound_nu('nu', alpha=2, beta=10)
mult_t = pm.MvStudentT('mult_t',
nu=nu,
mu=mu,
Sigma=cov,
observed=data)
return model