def _noise_variance(hyper_params, verbose=0):
dist_std_noise = hyper_params.dist_std_noise
if dist_std_noise == 'tr_normal':
h1 = pm.HalfNormal('h1', tau=1.0)
h2 = pm.HalfNormal('h2', tau=1.0)
if 10 <= verbose:
print('Truncated normal for prior scales')
elif dist_std_noise == 'log_normal':
h1 = pm.Lognormal('h1', tau=1.0)
h2 = pm.Lognormal('h2', tau=1.0)
if 10 <= verbose:
print('Log normal for prior scales')
elif dist_std_noise == 'uniform':
h1 = pm.Uniform('h1', upper=1.0)
h2 = pm.Uniform('h2', upper=1.0)
if 10 <= verbose:
print('Uniform for prior scales')
else:
raise ValueError("Invalid value of dist_std_noise: %s" %
dist_std_noise)
return h1, h2
def __init__(self, signal, err, init_period=None, predict_at=None, psd_at=None):
super().__init__(signal, err, init_period)
with pm.Model() as model:
# The mean flux of the time series
mean = pm.Normal("mean", mu=self.mean, sd=self.sigma)
# A jitter term describing excess white noise
log_jitter = pm.Normal("log_jitter", mu=np.log(self.jitter), sd=2.0)
# The parameters of the BrownianTerm kernel
sigma = pm.Lognormal("sigma", mu=np.log(self.sigma), sd=2.0)
period = pm.Lognormal(
"period", mu=np.log(self.init_period), sd=self.sigma_period
)
log_tau = pm.Uniform("log_tau", lower=0.0, upper=np.log(10))
tau = pm.math.exp(log_tau) * period
mix = pm.Uniform("mix", lower=0.0, upper=0.5)
Q = 0.01
sigma_1 = sigma * pm.math.sqrt(mix)
f = pm.math.sqrt(1 - 4 * Q ** 2)
w0 = 2 * Q / (tau * (1 - f))
S0 = (1 - mix) * sigma ** 2 / (0.5 * w0 * Q * (1 + 1 / f))
# Set up the Gaussian Process model
kernel1 = celerite2.theano.terms.SHOTerm(sigma=sigma_1, tau=tau, rho=period)
kernel2 = celerite2.theano.terms.SHOTerm(S0=S0, w0=w0, Q=Q)
kernel = kernel1 + kernel2
gp = celerite2.theano.GaussianProcess(kernel, mean=mean)
gp.compute(self.t, diag=self.err ** 2 + pm.math.exp(log_jitter), quiet=True)
gp.marginal("obs", observed=self.y)
if predict_at is not None:
pm.Deterministic("pred", gp.predict(self.y, predict_at))
if psd_at is not None:
pm.Deterministic("psd", kernel.get_psd(2 * np.pi * psd_at))
self.model = model
def __init__(self, signal, err, init_period=None, predict_at=None, psd_at=None):
super().__init__(signal, err, init_period)
with pm.Model() as model:
# The mean flux of the time series
mean = pm.Normal("mean", mu=self.mean, sd=self.sigma)
# A jitter term describing excess white noise
log_jitter = pm.Normal("log_jitter", mu=np.log(self.jitter), sd=2.0)
# The parameters of the RotationTerm kernel
sigma = pm.Lognormal("sigma", mu=np.log(self.sigma), sd=2.0)
period = pm.Lognormal(
"period", mu=np.log(self.init_period), sd=self.sigma_period
)
Q0 = pm.Lognormal("Q0", mu=1.0, sd=5.0)
dQ = pm.Lognormal("dQ", mu=2.0, sd=5.0)
f = pm.Uniform("f", lower=0.0, upper=1.0)
# Set up the Gaussian Process model
kernel = celerite2.theano.terms.RotationTerm(
sigma=sigma,
period=period,
Q0=Q0,
dQ=dQ,
f=f,
)
gp = celerite2.theano.GaussianProcess(kernel, mean=mean)
gp.compute(self.t, diag=self.err ** 2 + pm.math.exp(log_jitter), quiet=True)
gp.marginal("obs", observed=self.y)
if predict_at is not None:
pm.Deterministic("pred", gp.predict(self.y, predict_at))
if psd_at is not None:
pm.Deterministic("psd", kernel.get_psd(2 * np.pi * psd_at))
self.model = model
def construct_model(config, tree, sequence_dict):
topology = TreeTopology(tree)
sequence_dict_encoded = pylo.transform.encode_sequences(sequence_dict)
pattern_dict, pattern_counts = pylo.transform.group_sequences(
sequence_dict_encoded)
pattern_counts = tt.as_tensor_variable(pattern_counts)
child_patterns = tt.as_tensor_variable(
topology.build_sequence_table(pattern_dict))
def get_lognormal_params(var):
return {
'mu': config['prior_params'][var]['m'],
'sd': config['prior_params'][var]['s']
}
with pm.Model() as model:
pop_size = pm.Lognormal('pop_size', **get_lognormal_params('pop_size'))
pop_func = ConstantPopulationFunction(topology, pop_size)
tree_heights = CoalescentTree('tree', topology, pop_func)
kappa = pm.Lognormal('kappa', **get_lognormal_params('kappa'))
pi = pm.Dirichlet('pi', a=np.ones(4))
substitution_model = HKYSubstitutionModel(kappa, pi)
branch_lengths = topology.get_child_branch_lengths(tree_heights)
sequences = LeafSequences('sequences', topology, substitution_model,
branch_lengths, child_patterns,
pattern_counts)
return model
def test_scalar_ode_1_param(self):
"""Test running model for a scalar ODE with 1 parameter"""
def system(y, t, p):
return np.exp(-t) - p[0] * y[0]
times = np.array([
0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5,
7.0, 7.5
])
yobs = np.array([
0.31, 0.57, 0.51, 0.55, 0.47, 0.42, 0.38, 0.3, 0.26, 0.22, 0.22,
0.14, 0.14, 0.09, 0.1
])[:, np.newaxis]
ode_model = DifferentialEquation(func=system,
t0=0,
times=times,
n_states=1,
n_theta=1)
with pm.Model() as model:
alpha = pm.HalfCauchy("alpha", 1)
y0 = pm.Lognormal("y0", 0, 1)
sigma = pm.HalfCauchy("sigma", 1)
forward = ode_model(theta=[alpha], y0=[y0])
y = pm.Lognormal("y",
mu=pm.math.log(forward),
sd=sigma,
observed=yobs)
trace = pm.sample(100, tune=0, chains=1)
assert trace["alpha"].size > 0
assert trace["y0"].size > 0
assert trace["sigma"].size > 0
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 build(self):
"""The PyMC model that incorporates Bayesian Statistics in order to store what the likelihood of the model is for a given point."""
M = pm.Model()
with M:
kfwd, endo, activeEndo, kRec, kDeg, sortF = commonTraf(
trafficking=self.traf)
rxnrates = pm.Lognormal(
"rxn", sigma=0.5, shape=6) # 6 reverse rxn rates for IL2/IL15
nullRates = T.ones(
4, dtype=np.float64) # k27rev, k31rev, k33rev, k35rev
Rexpr_2Ra = pm.Lognormal("Rexpr_2Ra", sigma=0.5,
shape=1) # Expression: IL2Ra
Rexpr_2Rb = pm.Lognormal("Rexpr_2Rb", sigma=0.5,
shape=1) # Expression: IL2Rb
Rexpr_15Ra = pm.Lognormal("Rexpr_15Ra", sigma=0.5,
shape=1) # Expression: IL15Ra
Rexpr_gc = pm.Lognormal("Rexpr_gc", sigma=0.5,
shape=1) # Expression: gamma chain
unkVec = T.concatenate(
(kfwd, rxnrates, nullRates, endo, activeEndo, sortF, kRec,
kDeg, Rexpr_2Ra, Rexpr_2Rb, Rexpr_gc, Rexpr_15Ra,
nullRates * 0.0))
Y_15 = self.dst15.calc(
unkVec
) # fitting the data based on dst15.calc for the given parameters
sd_15 = T.minimum(
T.std(Y_15), 0.03
) # Add bounds for the stderr to help force the fitting solution
pm.Deterministic("Y_15", T.sum(T.square(Y_15)))
pm.Normal("fitD_15", sigma=sd_15,
observed=Y_15) # experimental-derived stderr is used
if self.traf:
Y_int = self.IL2Rb.calc(
unkVec) # fitting the data based on IL2Rb surface data
sd_int = T.minimum(
T.std(Y_int), 0.02
) # Add bounds for the stderr to help force the fitting solution
pm.Deterministic("Y_int", T.sum(T.square(Y_int)))
pm.Normal("fitD_int", sigma=sd_int, observed=Y_int)
Y_gc = self.gc.calc(
unkVec) # fitting the data using IL2Ra- cells
sd_gc = T.minimum(
T.std(Y_gc), 0.02
) # Add bounds for the stderr to help force the fitting solution
pm.Deterministic("Y_gc", T.sum(T.square(Y_gc)))
pm.Normal("fitD_gc", sigma=sd_gc, observed=Y_gc)
# Save likelihood
pm.Deterministic("logp", M.logpt)
return M
def build_model(X1, X2, timeV, conv0=0.1, confl=None, apop=None, dna=None):
""" Builds then returns the PyMC model. """
assert X1.shape == X2.shape
M = pm.Model()
with M:
conversions = conversionPriors(conv0)
d, apopfrac = deathPriors(1)
# parameters for drug 1, 2; assumed to be the same for both phenotypes
hill = pm.Lognormal("hill", shape=2)
IC50 = pm.Lognormal("IC50", shape=2)
EmaxGrowth = pm.Beta("EmaxGrowth", 1.0, 1.0, shape=2)
EmaxDeath = pm.Lognormal("EmaxDeath", -2.0, 0.5, shape=2)
# E_con values; first death then growth
GrowthCon = pm.Lognormal("GrowthCon", np.log10(0.03), 0.1)
# Calculate the death rate
death_rates = blissInteract(X1, X2, hill, IC50, EmaxDeath, justAdd=True) # pylint: disable=unsubscriptable-object
# Calculate the growth rate
growth_rates = GrowthCon * (1 - blissInteract(X1, X2, hill, IC50, EmaxGrowth)) # pylint: disable=unsubscriptable-object
pm.Deterministic("EmaxGrowthEffect", GrowthCon * EmaxGrowth)
# Test the dimension of growth_rates
growth_rates = T.opt.Assert("growth_rates did not match X1 size")(growth_rates, T.eq(growth_rates.size, X1.size))
lnum, eap, deadapop, deadnec = theanoCore(timeV, growth_rates, death_rates, apopfrac, d)
# Test the size of lnum
lnum = T.opt.Assert("lnum did not match X1*timeV size")(lnum, T.eq(lnum.size, X1.size * timeV.size))
confl_exp, apop_exp, dna_exp = convSignal(lnum, eap, deadapop, deadnec, conversions)
# Compare to experimental observation
if confl is not None:
confl_obs = T.flatten(confl_exp - confl)
pm.Normal("confl_fit", sd=T.std(confl_obs), observed=confl_obs)
conflmean = T.mean(confl, axis=1)
confl_exp_mean = T.mean(confl_exp, axis=1)
pm.Deterministic("conflResid", (confl_exp_mean - conflmean) / conflmean[0])
if apop is not None:
apop_obs = T.flatten(apop_exp - apop)
pm.Normal("apop_fit", sd=T.std(apop_obs), observed=apop_obs)
if dna is not None:
dna_obs = T.flatten(dna_exp - dna)
pm.Normal("dna_fit", sd=T.std(dna_obs), observed=dna_obs)
return M
def commonTraf(trafficking=True):
""" Set the common trafficking parameter priors. """
kfwd = pm.Lognormal("kfwd", mu=np.log(0.001), sigma=0.5, shape=1)
if trafficking:
endo = pm.Lognormal("endo", mu=np.log(0.1), sigma=0.1, shape=1)
activeEndo = pm.Lognormal("activeEndo", sigma=0.1, shape=1)
kRec = pm.Lognormal("kRec", mu=np.log(0.1), sigma=0.1, shape=1)
kDeg = pm.Lognormal("kDeg", mu=np.log(0.01), sigma=0.2, shape=1)
sortF = pm.Beta("sortF", alpha=12, beta=80, shape=1)
else:
# Assigning trafficking to zero to fit without trafficking
endo = activeEndo = kRec = kDeg = T.zeros(1, dtype=np.float64)
sortF = T.ones(1, dtype=np.float64) * 0.5
return kfwd, endo, activeEndo, kRec, kDeg, sortF
def fit(self, X, B, T):
n, k = X.shape
with pymc3.Model() as m:
beta_sd = pymc3.Exponential(
'beta_sd', 1.0) # Weak prior for the regression coefficients
beta = pymc3.Normal('beta', mu=0, sd=beta_sd,
shape=(k, )) # Regression coefficients
c = sigmoid(dot(X, beta)) # Conversion rates for each example
k = pymc3.Lognormal('k', mu=0, sd=1.0) # Weak prior around k=1
lambd = pymc3.Exponential('lambd', 0.1) # Weak prior
# PDF of Weibull: k * lambda * (x * lambda)^(k-1) * exp(-(t * lambda)^k)
LL_observed = log(c) + log(k) + log(
lambd) + (k - 1) * (log(T) + log(lambd)) - (T * lambd)**k
# CDF of Weibull: 1 - exp(-(t * lambda)^k)
LL_censored = log((1 - c) + c * exp(-(T * lambd)**k))
# We need to implement the likelihood using pymc3.Potential (custom likelihood)
# https://github.com/pymc-devs/pymc3/issues/826
logp = B * LL_observed + (1 - B) * LL_censored
logpvar = pymc3.Potential('logpvar', logp.sum())
self.trace = pymc3.sample(n_simulations=500,
tune=500,
discard_tuned_samples=True,
njobs=1)
print('done')
print('done 2')
def track_1var_2par_ode_ess(self):
def freefall(y, t, p):
return 2.0 * p[1] - p[0] * y[0]
# Times for observation
times = np.arange(0, 10, 0.5)
y = np.array([
-2.01, 9.49, 15.58, 16.57, 27.58, 32.26, 35.13, 38.07, 37.36,
38.83, 44.86, 43.58, 44.59, 42.75, 46.9, 49.32, 44.06, 49.86,
46.48, 48.18
]).reshape(-1, 1)
ode_model = pm.ode.DifferentialEquation(func=freefall,
times=times,
n_states=1,
n_theta=2,
t0=0)
with pm.Model() as model:
# Specify prior distributions for some of our model parameters
sigma = pm.HalfCauchy("sigma", 1)
gamma = pm.Lognormal("gamma", 0, 1)
# If we know one of the parameter values, we can simply pass the value.
ode_solution = ode_model(y0=[0], theta=[gamma, 9.8])
# The ode_solution has a shape of (n_times, n_states)
Y = pm.Normal("Y", mu=ode_solution, sd=sigma, observed=y)
t0 = time.time()
trace = pm.sample(500, tune=1000, chains=2, cores=2, random_seed=0)
tot = time.time() - t0
ess = pm.ess(trace)
return np.mean([ess.sigma, ess.gamma]) / tot
def create_model(change_points, params_model):
with cov19.Cov19Model(**params_model) as model:
lambda_t_log = cov19.lambda_t_with_sigmoids(
pr_median_lambda_0=0.4,
pr_sigma_lambda_0=0.5,
change_points_list=change_points,
)
mu = pm.Lognormal(name="mu", mu=np.log(1 / 8), sigma=0.2)
pr_median_delay = 10
prior_I = cov19.make_prior_I(lambda_t_log,
mu,
pr_median_delay=pr_median_delay)
new_I_t = cov19.SIR(lambda_t_log, mu, pr_I_begin=prior_I)
new_cases_inferred_raw = cov19.delay_cases(
new_I_t,
pr_median_delay=pr_median_delay,
pr_median_scale_delay=0.3)
new_cases_inferred = cov19.week_modulation(new_cases_inferred_raw)
cov19.student_t_likelihood(new_cases_inferred)
return model
def create_model(change_points, params_model):
with cov19.Cov19Model(**params_model) as model:
lambda_t_log = cov19.model.lambda_t_with_sigmoids(
pr_median_lambda_0=0.4,
pr_sigma_lambda_0=0.5,
change_points_list=change_points,
name_lambda_t="lambda_t",
)
mu = pm.Lognormal(name="mu", mu=np.log(1 / 8), sigma=0.2)
pr_median_delay = 10
prior_I = cov19.model.uncorrelated_prior_I(
lambda_t_log=lambda_t_log, mu=mu, pr_median_delay=pr_median_delay)
new_I_t = cov19.model.SIR(lambda_t_log=lambda_t_log,
mu=mu,
pr_I_begin=prior_I)
new_cases = cov19.model.delay_cases(
cases=new_I_t,
pr_mean_of_median=pr_median_delay,
name_cases="delayed_cases",
)
new_cases = cov19.model.week_modulation(new_cases,
name_cases="new_cases")
cov19.model.student_t_likelihood(new_cases)
return model
def test_sample_find_MAP_does_not_modify_start():
# see https://github.com/pymc-devs/pymc3/pull/4458
with pm.Model():
pm.Lognormal("untransformed")
# make sure find_Map does not modify the start dict
start = {"untransformed": 2}
pm.find_MAP(start=start)
assert start == {"untransformed": 2}
# make sure sample does not modify the start dict
start = {"untransformed": 0.2}
pm.sample(draws=10,
step=pm.Metropolis(),
tune=5,
start=start,
chains=3)
assert start == {"untransformed": 0.2}
# make sure sample does not modify the start when passes as list of dict
start = [{"untransformed": 2}, {"untransformed": 0.2}]
pm.sample(draws=10,
step=pm.Metropolis(),
tune=5,
start=start,
chains=2)
assert start == [{"untransformed": 2}, {"untransformed": 0.2}]
def build_model(conv0, doses, timeV, expTable):
""" Builds then returns the pyMC model. """
growth_model = pm.Model()
with growth_model:
conversions = conversionPriors(conv0)
d, apopfrac = deathPriors(len(doses))
# Specify vectors of prior distributions
# Growth rate
div = pm.Uniform("div", lower=0.0, upper=0.035, shape=len(doses))
# Rate of entering apoptosis or skipping straight to death
deathRate = pm.Lognormal("deathRate", np.log(0.001), 0.5, shape=len(doses))
lnum, eap, deadapop, deadnec = theanoCore(timeV, div, deathRate, apopfrac, d)
# Convert model calculations to experimental measurement units
confl_exp, apop_exp, dna_exp = convSignal(lnum, eap, deadapop, deadnec, conversions)
# Observed error values for confl
confl_obs = T.reshape(confl_exp, (-1,)) - expTable["confl"]
pm.Normal("dataFit", sd=T.std(confl_obs), observed=confl_obs)
# Observed error values for apop
apop_obs = T.reshape(apop_exp, (-1,)) - expTable["apop"]
pm.Normal("dataFita", sd=T.std(apop_obs), observed=apop_obs)
# Observed error values for dna
dna_obs = T.reshape(dna_exp, (-1,)) - expTable["dna"]
pm.Normal("dataFitd", sd=T.std(dna_obs), observed=dna_obs)
return growth_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 _sample_pymc3(cls, dist, size):
"""Sample from PyMC3."""
import pymc3
pymc3_rv_map = {
'BetaDistribution': lambda dist:
pymc3.Beta('X', alpha=float(dist.alpha), beta=float(dist.beta)),
'CauchyDistribution': lambda dist:
pymc3.Cauchy('X', alpha=float(dist.x0), beta=float(dist.gamma)),
'ChiSquaredDistribution': lambda dist:
pymc3.ChiSquared('X', nu=float(dist.k)),
'ExponentialDistribution': lambda dist:
pymc3.Exponential('X', lam=float(dist.rate)),
'GammaDistribution': lambda dist:
pymc3.Gamma('X', alpha=float(dist.k), beta=1/float(dist.theta)),
'LogNormalDistribution': lambda dist:
pymc3.Lognormal('X', mu=float(dist.mean), sigma=float(dist.std)),
'NormalDistribution': lambda dist:
pymc3.Normal('X', float(dist.mean), float(dist.std)),
'GaussianInverseDistribution': lambda dist:
pymc3.Wald('X', mu=float(dist.mean), lam=float(dist.shape)),
'ParetoDistribution': lambda dist:
pymc3.Pareto('X', alpha=float(dist.alpha), m=float(dist.xm)),
'UniformDistribution': lambda dist:
pymc3.Uniform('X', lower=float(dist.left), upper=float(dist.right))
}
dist_list = pymc3_rv_map.keys()
if dist.__class__.__name__ not in dist_list:
return None
with pymc3.Model():
pymc3_rv_map[dist.__class__.__name__](dist)
return pymc3.sample(size, chains=1, progressbar=False)[:]['X']
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 create_model(change_points, params_model):
with cov19.model.Cov19Model(**params_model) as model:
# Create the an array of the time dependent infection rate lambda
lambda_t_log = cov19.model.lambda_t_with_sigmoids(
pr_median_lambda_0=0.4,
pr_sigma_lambda_0=0.5,
change_points_list=
change_points, # The change point priors we constructed earlier
name_lambda_t=
"lambda_t", # Name for the variable in the trace (see later)
)
# set prior distribution for the recovery rate
mu = pm.Lognormal(name="mu", mu=np.log(1 / 8), sigma=0.01)
# This builds a decorrelated prior for I_begin for faster inference.
# It is not necessary to use it, one can simply remove it and use the default argument
# for pr_I_begin in cov19.SIR
prior_I = cov19.model.uncorrelated_prior_I(
lambda_t_log=lambda_t_log,
mu=mu,
pr_median_delay=10,
name_I_begin="I_begin",
name_I_begin_ratio_log="I_begin_ratio_log",
pr_sigma_I_begin=2,
n_data_points_used=5,
)
# Use lambda_t_log and mu to run the SIR model
new_cases = cov19.model.SIR(
lambda_t_log=lambda_t_log,
mu=mu,
name_new_I_t="new_I_t",
name_I_t="I_t",
name_I_begin="I_begin",
pr_I_begin=prior_I,
)
# Delay the cases by a lognormal reporting delay
new_cases = cov19.model.delay_cases(
cases=new_cases,
name_cases="delayed_cases",
name_delay="delay",
name_width="delay-width",
pr_mean_of_median=10,
pr_sigma_of_median=0.2,
pr_median_of_width=0.5,
)
# Modulate the inferred cases by a abs(sin(x)) function, to account for weekend effects
# Also adds the "new_cases" variable to the trace that has all model features.
new_cases = cov19.model.week_modulation(
cases=new_cases,
name_cases="new_cases",
)
# Define the likelihood, uses the new_cases_obs set as model parameter
cov19.model.student_t_likelihood(new_cases)
return model
def test_vector_ode_1_param(self):
"""Test running model for a vector ODE with 1 parameter"""
def system(y, t, p):
ds = -p[0] * y[0] * y[1]
di = p[0] * y[0] * y[1] - y[1]
return [ds, di]
times = np.array(
[0.0, 0.8, 1.6, 2.4, 3.2, 4.0, 4.8, 5.6, 6.4, 7.2, 8.0])
yobs = np.array([
[1.02, 0.02],
[0.86, 0.12],
[0.43, 0.37],
[0.14, 0.42],
[0.05, 0.43],
[0.03, 0.14],
[0.02, 0.08],
[0.02, 0.04],
[0.02, 0.01],
[0.02, 0.01],
[0.02, 0.01],
])
ode_model = DifferentialEquation(func=system,
t0=0,
times=times,
n_states=2,
n_odeparams=1)
with pm.Model() as model:
R = pm.Lognormal("R", 1, 5)
sigma = pm.HalfCauchy("sigma", 1, shape=2)
forward = ode_model(odeparams=[R], y0=[0.99,
0.01]).reshape(yobs.shape)
y = pm.Lognormal("y",
mu=pm.math.log(forward),
sd=sigma,
observed=yobs)
trace = pm.sample(100, tune=0, chains=1)
assert trace["R"].size > 0
assert trace["sigma"].size > 0
def deathPriors(numApop):
""" Setup priors for cell death parameters. """
# Rate of moving from apoptosis to death, assumed invariant wrt. treatment
d = pm.Lognormal("d", np.log(0.01), 0.5)
# Fraction of dying cells that go through apoptosis
apopfrac = pm.Beta("apopfrac", 1.0, 1.0, shape=numApop)
return d, apopfrac
def nurse_model_p1(df):
xo = df['pos'].values.copy()
yo = df['Ns_size'].values.copy()
ind, _ = pmu.multilabel_encoder(df, ['i_ind'])
nind = len(np.unique(ind))
trt, _ = pmu.multilabel_encoder(df, ['i_treatday'])
ntrt = len(np.unique(trt))
trt_in_ind = pmu.embeded_index(df, 'i_ind', 'i_treatday')
with pm.Model() as ns_p1_mod:
# single
Vmax_n_mu = pm.Normal('Vmax_n_mu', mu=np.log(80), sd=0.15)
Vmax_n_l = pm.Deterministic('Vmax_n_l', Vmax_n_mu * tt.ones(nind))
Vmax_n = pm.Deterministic('Vmax_n', tt.exp(Vmax_n_l))
r_n_mu = pm.Normal('r_n_mu', mu=np.log(3),
sd=0.25) # location of grand mean
r_n_sd = pm.HalfNormal('r_n_sd', sd=0.1)
r_n_vn = pm.Normal('r_n_vn', mu=0, sd=1, shape=nind)
r_n_l = pm.Deterministic('r_n_l', r_n_mu + r_n_sd * r_n_vn)
r_n = pm.Deterministic('r_n', tt.exp(r_n_l))
t_n_mu = pm.Normal('t_n_mu', mu=3, sd=3)
t_n_sd = pm.HalfNormal('t_n_sd', sd=3)
t_n_vn = pm.Normal('t_n_vn', mu=0, sd=1, shape=nind)
t_n = pm.Deterministic('t_n', t_n_mu + t_n_sd * t_n_vn)
r_d_mu = pm.Normal('r_d_mu', mu=np.log(0.85),
sd=0.20) # location of grand mean
r_d_sd = pm.HalfNormal('r_d_sd', sd=0.25)
r_d_vn = pm.Normal('r_d_vn', mu=0, sd=1, shape=nind)
r_d_l = pm.Deterministic('r_d_l', r_d_mu + r_d_sd * r_d_vn)
r_d = pm.Deterministic('r_d', tt.exp(r_d_l))
t_d_mu = pm.Normal('t_d_mu', mu=np.log(1), sd=0.25)
t_d_sd = pm.HalfNormal('t_d_sd', sd=0.25)
t_d_vn = pm.Normal('t_d_vn', mu=0, sd=1, shape=nind)
t_d = pm.Deterministic('t_d', -2.50 + tt.exp(t_d_mu + t_d_sd * t_d_vn))
Vmin_n_mu = pm.Normal('Vmin_n_mu', mu=np.log(10), sd=0.25)
Vmin_n = pm.Deterministic('Vmin_n', tt.exp(Vmin_n_mu) * tt.ones(nind))
nu_n = pm.Deterministic('nu_n', tt.ones(nind))
nu_d = pm.Deterministic('nu_d', tt.ones(nind))
f=bu.rise_and_fall_r( xo, Vmax_n[ind], t_n[ind], r_n[ind], nu_n[ind], \
t_d[ind], r_d[ind], nu_d[ind], Vmin_n[ind])
sdo_o = pm.Lognormal('sdo_o', mu=np.log(5.), sd=0.25)
yobs = pm.Normal('yobs', f, sd=sdo_o, observed=yo)
return ns_p1_mod
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(self):
with pm.Model() as model:
w = pm.Lognormal('lengthscale', 0, 4)
h2 = pm.Lognormal('variance', 0, 4)
# sigma = pm.Lognormal('sigma', 0, 4)
p = pm.Lognormal('p', 5, 4)
f_cov = h2 * pm.gp.cov.Periodic(1, period=p, ls=w)
gp = pm.gp.Latent(cov_func=f_cov)
f = gp.prior('f', X=self.X_train)
s2 = pm.Lognormal('Gaussian_noise', -4, 4)
y_ = pm.StudentT('y', mu=f, nu=s2, observed=self.Y_train)
#start = pm.find_MAP()
step = pm.Metropolis()
db = pm.backends.Text('trace')
trace = pm.sample(2000, step, chains=1, njobs=1)# start=start)
pm.traceplot(trace, varnames=['lengthscale', 'variance', 'Gaussian_noise'])
plt.show()
return trace
def build(self):
"""The PyMC model that incorporates Bayesian Statistics in order to store what the likelihood of the model is for a given point."""
M = pm.Model()
with M:
kfwd, endo, activeEndo, kRec, kDeg, sortF = commonTraf()
nullRates = T.ones(
6, dtype=np.float64) # associated with IL2 and IL15
Tone = T.ones(1, dtype=np.float64)
k27rev = pm.Lognormal("k27rev", mu=np.log(0.1), sigma=1,
shape=1) # associated with IL7
k33rev = pm.Lognormal("k33rev", mu=np.log(0.1), sigma=1,
shape=1) # associated with IL4
# constant according to measured number per cell. gc, blank, IL7R, blank, IL4R
Rexpr = (np.array([0.0, 0.0, 328.0, 0.0, 2591.0, 0.0, 254.0, 0.0])
* endo) / (1.0 + ((kRec * (1.0 - sortF)) /
(kDeg * sortF)))
# indexing same as in model.hpp
unkVec = T.concatenate(
(kfwd, nullRates, k27rev, Tone, k33rev, Tone, endo, activeEndo,
sortF, kRec, kDeg, Rexpr))
self.act.calc(
unkVec, M
) # fitting the data based on act.calc for the given parameters
if self.pretreat is True:
Y_cross = self.cross.calc(
unkVec) # fitting the data based on cross.calc
pm.Deterministic("Y_cross", T.sum(T.square(Y_cross)))
sd_cross = T.minimum(T.std(Y_cross), 0.1)
pm.Normal(
"fitD_cross", sigma=sd_cross,
observed=Y_cross) # the stderr is definitely less than 0.2
# Save likelihood
pm.Deterministic("logp", M.logpt)
return M
def build_model(self):
""" Builds then returns the pyMC model. """
M = pm.Model()
with M:
# The three values here are div and deathrate
# Assume just one IC50 for simplicity
lIC50 = pm.Normal("IC50s", 2.0)
Emin_growth = pm.Uniform("Emin_growth",
lower=0.0,
upper=self.Emax_growth)
Emax_death = pm.Lognormal("Emax_death", -2.0, 2.0)
# Import drug concentrations into theano vector
drugCs = T._shared(self.drugCs)
# Drug term since we're using constant IC50 and hill slope
drugTerm = 1.0 / (1.0 +
T.pow(10.0,
(lIC50 - drugCs) * pm.Lognormal("hill")))
# Do actual conversion to parameters for each drug condition
growthV = self.Emax_growth + (Emin_growth -
self.Emax_growth) * drugTerm
# Calculate the growth rate
# _Assuming deathrate in the absence of drug is zero
GR = growthV - Emax_death * drugTerm
# Calculate the number of live cells
lnum = T.exp(GR * self.time)
# Normalize live cell data to control, as is similar to measurements
# Residual between model prediction and measurement
residual = self.lObs - (lnum / lnum[0])
pm.Normal("dataFitlnum", sd=T.std(residual), observed=residual)
return M
def multidimensional_twopl_model(dataset, n_factors):
"""Defines the mcmc model for multidimensional 2PL logistic estimation.
Args:
dataset: [n_items, n_participants] 2d array of measured responses
n_factors: (int) number of factors to extract
Returns:
model: PyMC3 model to run
"""
if n_factors < 2:
raise AssertionError(f"Multidimensional 2PL model requires "
f"two or more factors specified!")
n_items, n_people = dataset.shape
observed = dataset.astype('int')
diagonal_indices, lower_indices = get_discrimination_indices(n_items, n_factors)
lower_length = lower_indices[0].shape[0]
twopl_pymc_model = pm.Model()
with twopl_pymc_model:
# Ability Parameters (Standardized Normal)
ability = pm.Normal("Ability", mu=0, sigma=1, shape=(n_factors, n_people))
# Difficuly multilevel prior
sigma_difficulty = pm.HalfNormal('Difficulty_SD', sigma=1, shape=1)
difficulty = pm.Normal("Difficulty", mu=0,
sigma=sigma_difficulty, shape=n_items)
# The main diagonal must be non-negative
discrimination = tt.zeros((n_items, n_factors), dtype=theano.config.floatX)
diagonal_discrimination = pm.Lognormal('Diagonal Discrimination', mu=0,
sigma=0.25, shape=n_factors)
lower_discrimination = pm.Normal('Lower Discrimination', sigma=1,
shape=lower_length)
discrimination = tt.set_subtensor(discrimination[diagonal_indices],
diagonal_discrimination)
discrimination = tt.set_subtensor(discrimination[lower_indices],
lower_discrimination)
# Compute the probabilities
kernel = pm.math.dot(discrimination, ability)
kernel += difficulty[:, None]
probabilities = pm.Deterministic("PL_Kernel", pm.math.invlogit(kernel))
# Compute the log likelihood
log_likelihood = pm.Bernoulli("Log_Likelihood", p=probabilities, observed=observed)
return twopl_pymc_model
def make_model(scale=1e-3, dims=slice(None), prior=10):
if is_multico is False:
A = data['A'][index,dims]
Ainv = data['Ainv'][dims,index]
b = data['b'][index]
s_Ainv = theano.shared(Ainv)
s_A = theano.shared(A)
s_b = theano.shared(b)
samp_mapping, dev_start = project(t_samp, A, Ainv, b)
with pm.Model() as model:
decomp = pm.Dirichlet('decomp', ct_prior*prior, shape=ct_prior.shape,
testval=ct_start)#, transform=StickBreaking5(ct_prior.shape[0]))
ct_expr = list()
if samp_scale is True:
scale = pm.Lognormal('scale', testval=10)
for i, cell_type in enumerate(cell_types):
if cell_type == 'background':
dev_samp = pm.Normal('comb '+cell_type, mu=background['mean'][index],
sigma=background['std'][index]/scale, shape=(1, n_features),
testval=t_samp)
ct_expr.append(dev_samp)
continue
if is_multico is True:
A = chars[cell_type]['A'][index,dims]
Ainv = chars[cell_type]['Ainv'][dims,index]
b = chars[cell_type]['b'][index]
s_Ainv = theano.shared(Ainv)
s_A = theano.shared(A)
s_b = theano.shared(b)
samp_mapping, dev_start = project(t_samp, A, Ainv, b)
n = A.shape[1]
samp = pm.Normal(cell_type, sigma=scale, shape=(1, n))
else:
samp = pm.MvNormal(cell_type, chars[cell_type]['mean'][dims],
cov=chars[cell_type]['sigma'][dims, dims]*scale,
shape=(1, A.shape[1]),
testval=chars[cell_type]['mean'][dims])
if sample_deviation is True:
deviation = pm.Normal('deviation '+cell_type, mu=var[cell_type]['mean'][index],
sigma=var[cell_type]['std'][index]*scale,
shape=(1, n_features), testval=dev_start)
else:
deviation = theano.shared(dev_start)
dev_samp = pm.Deterministic('comb '+cell_type,
combine_and_embed(samp, deviation, s_A, s_Ainv, s_b))
ct_expr.append(dev_samp)
ct_expr = tt.concatenate(ct_expr, axis=0)
transcriptome = pm.Deterministic('trans', mix(ct_expr, decomp))
pot = pm.Potential('obs', dist.logp(transcriptome))
#obs = pm.Multinomial('obs', seq_depth, transcriptome, observed=sample, dtype='int64')
return model
def model_gp(self):
"""
TODO - Need to describe what is happening here.
Complete docs when model is settled on. Probably quiet a
long docs needed to explain.
"""
warnings.warn('This model is developmental - use carefully')
dnu = 10**self.asy_result['summary'].loc['mean'].dnu
self.pm_model = pm.Model()
dnu_fac = 0.03 # Prior on mode frequency has width 3% of Dnu.
height_fac = 0.4 # Lognorrmal prior on height has std=0.4.
back_fac = 0.5 # Lognorrmal prior on back has std=0.5.
with self.pm_model:
l0 = pm.Normal('l0',
self.start['l0'],
dnu * dnu_fac,
shape=len(self.start['l0']))
l2 = pm.Normal('l2',
self.start['l2'],
dnu * dnu_fac,
shape=len(self.start['l2']))
# Place a GP over the l=0 mode widths ...
m0 = pm.Normal('gradient0', 0, 10)
c0 = pm.Normal('intercept0', 0, 10)
sigma0 = pm.Lognormal('sigma0', np.log(1.0), 1.0)
ls = pm.Lognormal('ls', np.log(0.3), 1.0)
mean_func0 = pm.gp.mean.Linear(coeffs=m0, intercept=c0)
cov_func0 = sigma0 * pm.gp.cov.ExpQuad(1, ls=ls)
self.gp0 = pm.gp.Latent(cov_func=cov_func0, mean_func=mean_func0)
ln_width0 = self.gp0.prior('ln_width0', X=self.n)
width0 = pm.Deterministic('width0', pm.math.exp(ln_width0))
# and on the l=2 mode widths
m2 = pm.Normal('gradient2', 0, 10)
c2 = pm.Normal('intercept2', 0, 10)
sigma2 = pm.Lognormal('sigma2', np.log(1.0), 1.0)
mean_func2 = pm.gp.mean.Linear(coeffs=m2, intercept=c2)
cov_func2 = sigma2 * pm.gp.cov.ExpQuad(1, ls=ls)
self.gp2 = pm.gp.Latent(cov_func=cov_func2, mean_func=mean_func2)
ln_width2 = self.gp2.prior('ln_width2', X=self.n)
width2 = pm.Deterministic('width2', pm.math.exp(ln_width2))
#Carry on
height0 = pm.Lognormal('height0',
np.log(self.start['height0']),
height_fac,
shape=len(self.start['l0']))
height2 = pm.Lognormal('height2',
np.log(self.start['height2']),
height_fac,
shape=len(self.start['l2']))
back = pm.Lognormal('back',
np.log(1.0),
back_fac,
shape=len(self.start['l2']))
limit = self.model(l0, l2, width0, width2, height0, height2, back)
yobs = pm.Gamma('yobs',
alpha=1,
beta=1.0 / limit,
observed=self.ladder_p)
def conversionPriors(conv0):
""" Sets the various fluorescence conversion priors. """
# Set up conversion rates
confl_conv = pm.Lognormal("confl_conv", np.log(conv0), 0.1)
apop_conv = pm.Lognormal("apop_conv", np.log(conv0) - 2.06, 0.1)
dna_conv = pm.Lognormal("dna_conv", np.log(conv0) - 1.85, 0.1)
# Priors on conv factors
pm.Lognormal("confl_apop", -2.06, 0.0647, observed=apop_conv / confl_conv)
pm.Lognormal("confl_dna", -1.85, 0.125, observed=dna_conv / confl_conv)
pm.Lognormal("apop_dna", 0.222, 0.141, observed=dna_conv / apop_conv)
# Offset values for apop and dna
apop_offset = pm.Lognormal("apop_offset", np.log(0.1), 0.1)
dna_offset = pm.Lognormal("dna_offset", np.log(0.1), 0.1)
return ((confl_conv, apop_conv, dna_conv), (apop_offset, dna_offset))
