def sample_bandits(self, n=1):
bb_score = np.zeros(n)
choices = np.zeros(n)
P0_samples = [np.random.rand()]
P1_samples = [np.random.rand()]
P2_samples = [np.random.rand()]
for k in range(n):
# sample from the bandits's priors, and select the largest sample
choice = np.argmax([np.random.choice(P0_samples), np.random.choice(P1_samples), np.random.choice(P2_samples)])
print();
print();
print(k, choice);
# sample the chosen bandit
result = self.bandits.pull(choice)
# update priors and score
self.wins[choice] += result
self.trials[choice] += 1
bb_score[k] = result
self.N += 1
choices[k] = choice
if choice == 0:
P0 = pm.Uniform('P0', 0, 1)
X0 = pm.Binomial('X0', value = self.wins[0], n = self.trials[0], p = P0, observed = True)
mcmc0 = pm.MCMC([P0, X0])
mcmc0.sample(15000, 5000)
P0_samples = mcmc0.trace('P0')[:]
elif choice == 1:
P1 = pm.Uniform('P1', 0, 1)
X1 = pm.Binomial('X1', value = self.wins[1], n = self.trials[1], p = P1, observed = True)
mcmc1 = pm.MCMC([P1, X1])
mcmc1.sample(15000, 5000)
P1_samples = mcmc1.trace('P1')[:]
else:
P2 = pm.Uniform('P2', 0, 1)
X2 = pm.Binomial('X2', value = self.wins[2], n = self.trials[2], p = P2, observed = True)
mcmc2 = pm.MCMC([P2, X2])
mcmc2.sample(15000, 5000)
P2_samples = mcmc2.trace('P2')[:]
self.bb_score = np.r_[self.bb_score, bb_score]
self.choices = np.r_[self.choices, choices]
return
def binomial_model():
n_samples = 100
xs = intX(np.random.binomial(n=1, p=0.2, size=n_samples))
with pm.Model() as model:
p = pm.Beta("p", alpha=1, beta=1)
pm.Binomial("xs", n=1, p=p, observed=xs)
return model
def test_model_02(x):
# https://github.com/pymc-devs/pymc
# Import relevant modules
import pymc
import numpy as np
# Some data
n = 5 * np.ones(4, dtype=int)
#x = np.array([-.86, -.3, -.05, .73])
# Priors on unknown parameters
alpha = pymc.Normal('alpha', mu=0, tau=.01)
beta = pymc.Normal('beta', mu=0, tau=.01)
# Arbitrary deterministic function of parameters
@pymc.deterministic
def theta(a=alpha, b=beta):
"""theta = logit^{-1}(a+b)"""
return pymc.invlogit(a + b * x)
# Binomial likelihood for data
d = pymc.Binomial('d',
n=n,
p=theta,
value=np.array([0., 1., 3., 5.]),
observed=True)
return locals()
def posterior_upvote_ratio(upvotes, downvotes, samples = 20000):
p = pm.Uniform("p", 0, 1, value = 0.5)
n = upvotes + downvotes
obs_upvotes = pm.Binomial("obs", n, p, value = upvotes, observed = True)
model = pm.Model([p, obs_upvotes])
mcmc = pm.MCMC(model)
mcmc.sample(samples)
return mcmc.trace("p")[:]
def test_layers(self):
with pm.Model(rng_seeder=232093) as model:
a = pm.Uniform("a", lower=0, upper=1, size=10)
b = pm.Binomial("b", n=1, p=a, size=10)
b_sampler = compile_pymc([], b, mode="FAST_RUN")
avg = np.stack([b_sampler() for i in range(10000)]).mean(0)
npt.assert_array_almost_equal(avg, 0.5 * np.ones((10,)), decimal=2)
def test_single_observation(self):
with pm.Model():
p = pm.Uniform("p", 0, 1)
pm.Binomial("w", p=p, n=2, observed=1)
inference_data = pm.sample(500, chains=2, return_inferencedata=True)
assert inference_data
assert inference_data.log_likelihood["w"].shape == (2, 500, 1)
def indep_samples(x1,n1,x2,n2):
class experimental_data(object):
def __init__(self,x1,n1,x2,n2):
self.data1 = np.hstack( (np.ones((x1,)) , np.zeros((n1-x1,))) )
self.data2 = np.hstack( (np.ones((x2,)) , np.zeros((n2-x2,))) )
### for testing purposes
#example = True
data = experimental_data(x1,n1,x2,n2)
#if example:
# example_data1 = np.hstack( (np.ones((15,)) , np.zeros((20,))) )
# example_data2 = np.hstack( (np.ones((16,)) , np.zeros((23,))) )
# sim_data_size = 14
# data1 = example_data1
# data2 = example_data2
p1_val = np.mean(data.data1)
p2_val = np.mean(data.data2)
ind_val = p1_val+p2_val-p1_val*p2_val
print "P1 = " + str(p1_val)
print "P2 = " + str(p2_val)
print "Independence = " + str(ind_val)
p1 = pymc.Beta('p1',alpha=0.5,beta=0.5)
p2 = pymc.Beta('p2',alpha=0.5,beta=0.5)
x1 = pymc.Binomial('x',n=len(data.data1),p=p1,value=np.sum(data.data1),observed=True)
x2 = pymc.Binomial('x',n=len(data.data2),p=p2,value=np.sum(data.data2),observed=True)
@pymc.deterministic
def ind_assump(p1=p1,p2=p2):
return p1+p2-p1*p2
return locals()
#@pymc.deterministic
#def sim():
# sim_data = pymc.Binomial('sim',n=sim_data_size, p=ind_assump)
# return sim_data
def get_Models():
#Full Model (Beta & Binomial)
nN, nA, nB = 3, 5, 1
aD = [0, 3, 1]
Beta = pm.Beta('Beta', alpha=nA, beta=nB)
# @UndefinedVariable
BinomD = [
pm.Binomial('BinomD_' + str(i),
n=nN,
p=Beta,
observed=True,
value=aD[i]) for i in range(len(aD))
]
# @UndefinedVariable @UnusedVariable
BinomQ = pm.Binomial('BinomQ', n=nN, p=Beta)
# @UndefinedVariable
#Collapsed Model (Binomial)
nA2 = nA + sum(aD)
nB2 = nB + nN * len(aD) - sum(aD)
BetaBinQ = pm.Betabin('BetaBinQ', n=nN, alpha=nA2, beta=nB2)
# @UndefinedVariable
return np.concatenate([[Beta, BinomQ, BetaBinQ], BinomD])
def posterior_upvote_ratio(upvotes, downvotes, samples=20000):
""" This function accepts the number of upvotes and downvotes a particular
comment received, and the number of posterior samples to return to the
user. Assumes a uniform prior.
"""
N = upvotes + downvotes
upvote_ratio = pm.Uniform("upvote_ratio", 0, 1)
observations = pm.Binomial("obs",
N,
upvote_ratio,
value=upvotes,
observed=True)
# do the fitting; first do a MAP as it is cheap and useful.
map_ = pm.MAP([upvote_ratio, observations]).fit()
mcmc = pm.MCMC([upvote_ratio, observations])
mcmc.sample(samples, samples / 4)
return mcmc.trace("upvote_ratio")[:]
def main():
N = 100
p = pm.Uniform("freq_cheating", 0, 1)
true_answers = pm.Bernoulli("truths", p, size=N)
first_coin_flips = pm.Bernoulli("first_flips", 0.5, size=N)
second_coin_flips = pm.Bernoulli("second_flips", 0.5, size=N)
@pm.deterministic
def observed_proportion(t_a=true_answers,
fc=first_coin_flips,
sc=second_coin_flips):
result = t_a & fc | ~fc & sc
return float(sum(result)) / len(result)
X = 35
observations = pm.Binomial("obs",
N,
observed_proportion,
value=X,
observed=True)
model = pm.Model([
p, true_answers, first_coin_flips, second_coin_flips,
observed_proportion, observations
])
# To be explained in Chapter 3!
mcmc = pm.MCMC(model)
mcmc.sample(40000, 15000)
figsize(12.5, 3)
p_trace = mcmc.trace("freq_cheating")[:]
plt.hist(p_trace,
histtype="stepfilled",
normed=True,
alpha=0.85,
bins=30,
label="posterior distribution",
color="#348ABD")
plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.3)
plt.xlim(0, 1)
plt.legend()
plt.show()
def test_transformed(self):
n = 18
at_bats = 45 * np.ones(n, dtype=int)
hits = np.random.randint(1, 40, size=n, dtype=int)
draws = 50
with pm.Model() as model:
phi = pm.Beta("phi", alpha=1.0, beta=1.0)
kappa_log = pm.Exponential("logkappa", lam=5.0)
kappa = pm.Deterministic("kappa", at.exp(kappa_log))
thetas = pm.Beta("thetas", alpha=phi * kappa, beta=(1.0 - phi) * kappa, size=n)
y = pm.Binomial("y", n=at_bats, p=thetas, observed=hits)
gen = pm.sample_prior_predictive(draws)
assert gen.prior["phi"].shape == (1, draws)
assert gen.prior_predictive["y"].shape == (1, draws, n)
assert "thetas" in gen.prior.data_vars
def mymodel():
# Some data
n = 5 * np.ones(4, dtype=int)
x = np.array([-.86, -.3, -.05, .73])
# Priors on unknown parameters
alpha = pymc.Normal('alpha', mu=0, tau=.01)
beta = pymc.Normal('beta', mu=0, tau=.01)
# Arbitrary deterministic function of parameters
@pymc.deterministic
def theta(a=alpha, b=beta):
"""theta = logit^{-1}(a+b)"""
return pymc.invlogit(a + b * x)
# Binomial likelihood for data
d = pymc.Binomial('d',
n=n,
p=theta,
value=np.array([0., 1., 3., 5.]),
observed=True)
def test_duplicate_vars():
with pytest.raises(ValueError) as err:
with pm.Model():
pm.Normal("a")
pm.Normal("a")
err.match("already exists")
with pytest.raises(ValueError) as err:
with pm.Model():
pm.Normal("a")
pm.Normal("a", transform=transforms.log)
err.match("already exists")
with pytest.raises(ValueError) as err:
with pm.Model():
a = pm.Normal("a")
pm.Potential("a", a**2)
err.match("already exists")
with pytest.raises(ValueError) as err:
with pm.Model():
pm.Binomial("a", 10, 0.5)
pm.Normal("a", transform=transforms.log)
err.match("already exists")
# Initialize constants
N = 100 # 100 of students
p = pm.Uniform("freq_cheating", 0, 1) # The freq I want
#-----------------------------------
# Modeling
true_answer = pm.Bernoulli("truths", p, size=N)
first_coin_flips = pm.Bernoulli("firtst_flips", 0.5, size=N)
second_coin_flips = pm.Bernoulli("second_flips", 0.5, size=N)
@pm.deterministic
def p_skewed(p=p):
return 0.5 * p + 0.25
yes_responses = pm.Binomial("number_cheaters",
100,
p_skewed,
value=35,
observed=True)
print("{0} : {1}".format(yes_responses, yes_responses.value))
model = pm.Model([yes_responses, p_skewed, p])
# to be explain in Chapter 3
mcmc = pm.MCMC(model)
mcmc.sample(25000, 2500)
#-----------------------------------
# plot the answer
figsize(12.5, 3)
p_trace = mcmc.trace("freq_cheating")[:]
plt.hist(p_trace,
histtype="stepfilled",
normed=True,
alpha=0.85,
def make_model(cls):
with pm.Model() as model:
p = pm.Beta("p", [0.5, 0.5, 1.0], [0.5, 0.5, 1.0], size=3)
pm.Binomial("y", p=p, n=[4, 12, 9], observed=[1, 2, 9])
return model
# Import relevant modules
import pymc
import numpy as np
# Some data
n = 5 * np.ones(4, dtype=int)
x = np.array([-.86, -.3, -.05, .73])
# Priors on unknown parameters
alpha = pymc.Normal('alpha', mu=0, tau=.01)
beta = pymc.Normal('beta', mu=0, tau=.01)
# Arbitrary deterministic function of parameters
@pymc.deterministic
def theta(a=alpha, b=beta):
"""theta = logit^{-1}(a+b)"""
return pymc.invlogit(a + b * x)
# Binomial likelihood for data
d = pymc.Binomial('d', n=n, p=theta, value=np.array([0.,1.,3.,5.]),\
observed=True)
# Simple dose-response model
n = [5]*4
dose = [-.86,-.3,-.05,.73]
x = [0,1,3,5]
alpha = pm.Normal('alpha', mu=0.0, tau=0.01)
beta = pm.Normal('beta', mu=0.0, tau=0.01)
@pm.deterministic
def theta(a=alpha, b=beta, d=dose):
"""theta = inv_logit(a+b)"""
return pm.invlogit(a+b*d)
"""deaths ~ binomial(n, p)"""
deaths = pm.Binomial('deaths', n=n, p=theta, value=x, observed=True)
my_model = [alpha, beta, theta, deaths]
# Instantiate and run sampler
S = pm.MCMC(my_model)
S.sample(10000, burn=5000)
# Calculate and plot Geweke scores
scores = pm.geweke(S, intervals=20)
pm.Matplot.geweke_plot(scores)
# Geweke plot for a single parameter
trace = S.trace('alpha')[:]
alpha_scores = pm.geweke(trace, intervals=20)
pm.Matplot.geweke_plot(alpha_scores, 'alpha')
def make_model(N,k,X,backend,manifold):
"""
A standard spatial logistic regression.
- N: Number sampled at each location
- k: Number positive at each location
- X: x,y,z coords of each location
- Backend: The linear algebra backend. So far, this has to be 'cholmod'.
- manifold: The manifold to work on. So far, this has to be 'spherical'.
"""
# Make the Delaunay triangulation.
neighbors, triangles, trimap, b = manifold.triangulate_sphere(X)
# Uncomment to visualize the triangulation.
# manifold.plot_triangulation(X,neighbors)
# Generate the C, Ctilde and G matrix in SciPy 'lil' format.
triangle_areas = [manifold.triangle_area(X, t) for t in triangles]
Ctilde = manifold.Ctilde(X, triangles, triangle_areas)
C = manifold.C(X, triangles, triangle_areas)
G = manifold.G(X, triangles, triangle_areas)
# Convert to SciPy 'csc' format for efficient use by the CHOLMOD backend.
C = backend.into_matrix_type(C)
Ctilde = backend.into_matrix_type(Ctilde)
G = backend.into_matrix_type(G)
# Kappa is the scale parameter. It's a free variable.
kappa = pm.Exponential('kappa',1,value=3)
# Fix the value of alpha.
alpha = 2.
# amp is the overall amplitude. It's a free variable that will probably be highly confounded with kappa.
amp = pm.Exponential('amp', .0001, value=100)
# A constant mean.
m = pm.Uninformative('m',value=0)
@pm.deterministic(trace=False)
def M(m=m,n=len(X)):
"""The mean vector"""
return np.ones(n)*m
@pm.deterministic(trace=False)
def Q(kappa=kappa, alpha=alpha, amp=amp, Ctilde=Ctilde, G=G, backend=backend):
"The precision matrix."
out = operators.mod_frac_laplacian_precision(Ctilde, G, kappa, alpha, backend)/np.asscalar(amp)**2
return out
# Do all the precomputation you can based on the sparsity pattern alone.
# Note that if alpha is made free, this needs to be free also, as the sparsity
# pattern will be changeable.
pattern_products = backend.pattern_to_products(Q.value)
@pm.deterministic(trace=False)
def precision_products(Q=Q, p=pattern_products):
"All the analysis of the precision matrix that the backend needs to do MVN computations."
try:
return backend.precision_to_products(Q, **p)
except backend.NonPositiveDefiniteError:
return None
# The random field.
empirical_S = pm.logit((k+1)/(N+2.))
S=pymc_objects.SparseMVN('S',M, precision_products, backend, value=empirical_S)
@pm.deterministic(trace=False)
def p(S=S):
"""The success probability."""
return pm.invlogit(S)
# The data.
data = pm.Binomial('data', n=N, p=p, value=k, observed=True)
# A Fortran representation of the likelihood, to allow for fast Metropolis steps without querying data.logp.
likelihood_variables = np.vstack((np.resize(N,k.shape),k)).T
likelihood_string = """
lkp = dexp({X})/(1.0D0+dexp({X}))
lkp = lv(i,2)*dlog(lkp) + (lv(i,1)-lv(i,2))*dlog(1.0D0-lkp)
"""
return locals()
import pymc as mc
# We define a simple model of a survey with one data point. We use a $Beta$
# distribution for the $p$ parameter in a binomial. We would like to know both
# the posterior distribution for p, as well as the predictive posterior
# distribution over the survey parameter.
alpha = 4
beta = 4
n = 20
yes = 15
with mc.Model() as model:
p = mc.Beta('p', alpha, beta)
surv_sim = mc.Binomial('surv_sim', n=n, p=p)
surv = mc.Binomial('surv', n=n, p=p, observed=yes)
# First let's try and use `find_MAP`.
with model:
print(mc.find_MAP())
# `find_map` defaults to find the MAP for only the continuous variables we have
# to specify if we would like to use the discrete variables.
with model:
print(mc.find_MAP(vars=model.vars, disp=True))
# We set the `disp` variable to display a warning that we are using a
# non-gradient minimization technique, as discrete variables do not give much
def cluster(sup,dep,cn_states,Nvar,sparams,cparams,phi_limit,norm,recluster=False):
'''
clustering model using Dirichlet Process
'''
Ndp = cparams['clus_limit'] if not recluster else 1
n_iter = cparams['n_iter'] if not recluster else cparams['merge_iter']
burn = cparams['burn'] if not recluster else cparams['merge_burn']
thin, use_map = cparams['thin'], cparams['use_map']
use_map = False if recluster else use_map
nclus_init = cparams['nclus_init']
purity, ploidy = sparams['pi'], sparams['ploidy']
fixed_alpha, gamma_a, gamma_b = cparams['fixed_alpha'], cparams['alpha'], cparams['beta']
sens = 1.0 / ((purity/ float(ploidy)) * np.mean(dep))
pval_cutoff = cparams['clonal_cnv_pval']
print('phi lower limit: %f; phi upper limit: %f' % (sens, phi_limit))
if fixed_alpha.lower() in ("yes", "true", "t"):
fixed = True
fixed_alpha = 0.75 / math.log10(Nvar) if Nvar > 10 else 1
else:
try:
fixed_alpha = float(fixed_alpha)
fixed = True
except ValueError:
fixed = False
if fixed:
print('Dirichlet concentration fixed at %f' % fixed_alpha)
h = pm.Beta('h', alpha=1, beta=fixed_alpha, size=Ndp)
else:
beta_init = float(gamma_a) / gamma_b
print("Dirichlet concentration gamma prior values: alpha = %f; beta= %f; init = %f" % (gamma_a, gamma_b, beta_init))
alpha = pm.Gamma('alpha', gamma_a, gamma_b, value = beta_init)
h = pm.Beta('h', alpha=1, beta=alpha, size=Ndp)
@pm.deterministic
def p(h=h):
value = [u*np.prod(1.0-h[:i]) for i,u in enumerate(h)]
#value /= np.sum(value)
value[-1] = 1-sum(value[:-1])
return value
z_init = np.zeros(Nvar, dtype=np.int)
phi_init = np.random.rand(Ndp) * phi_limit
# use smart initialisation if nclus_init specified
if not nclus_init.lower() in ("no", "false", "f"):
try:
nclus_init = nclus_init if not recluster else 1
nclus_init = int(nclus_init)
nclus_init = Ndp if nclus_init > Ndp else nclus_init
if nclus_init == 1:
phi_init[0] = 1.
else:
z_init, phi_init = get_initialisation(nclus_init, Ndp, sparams, sup, dep, norm,
cn_states, sens, phi_limit, pval_cutoff)
except ValueError:
pass
z = pm.Categorical('z', p = p, size = Nvar, value = z_init)
phi_init = np.array([sens if x < sens else x for x in phi_init])
phi_k = pm.Uniform('phi_k', lower = sens, upper = phi_limit, size = Ndp, value=phi_init)
@pm.deterministic
def p_var(z=z, phi_k=phi_k, z_init=z_init):
# if np.any(np.isnan(phi_k)):
# phi_k = phi_init
if np.any(z < 0):
z = z_init
# ^ some fmin optimization methods initialise this array with -ve numbers
most_lik_cn_states, pvs = \
get_most_likely_cn_states(cn_states, sup, dep, phi_k[z], purity, pval_cutoff, norm)
return np.array(pvs)-0.00000001
cbinom = pm.Binomial('cbinom', dep, p_var, observed=True, value=sup)
if fixed:
model = pm.Model([h, p, phi_k, z, p_var, cbinom])
else:
model = pm.Model([alpha, h, p, phi_k, z, p_var, cbinom])
mcmc, map_ = fit_and_sample(model, n_iter, burn, thin, use_map)
return mcmc, map_
if a <= 0 or b <= 0:
return -np.inf
else:
return np.log(np.power((a+b), -2.5))
a = beta_priors[0]
b = beta_priors[1]
#hidden true rate for each website
true_rates = pymc.Beta("true_rates", a, b, size=5)
#observed values
trials = np.array([1055, 1057, 1065, 1039, 1046])
successes = np.array([28, 45, 69, 58, 60])
observed_values = pymc.Binomial("observed_values", trials, true_rates, observed=True,
value=successes)
model = pymc.Model([a, b, true_rates, observed_values])
mcmc = pymc.MCMC(model)
#Generate 1,000,000 samples and throw out first 500,000
mcmc.sample(1000000, 500000)
diff_CA = mcmc.trace("true_rates")[:][:,2] - mcmc.trace("true_rates")[:][:,0]
sns.kdeplot(diff_CA, shade=True, label="Difference site C - site A")
plt.axvline(0.0, color="black")
print ("Probability that website A gets MORE sign-ups than website C: %0.3f" %
(diff_CA < 0).mean())
print ("Probability that website A gets LESS sign-ups than website C: %0.3f" %
@pm.deterministic
def observed_proportion(t_a=true_answers, fc=first_coin, sc=second_coin):
observed = fc * t_a + (1 - fc) * sc
return observed.sum() / float(N)
observed_proportion.value
# data generation
X = 35
observations = pm.Binomial("obs",
N,
observed_proportion,
observed=True,
value=X)
model = pm.Model([
p, true_answers, first_coin, second_coin, observed_proportion, observations
])
mcmc = pm.MCMC(model)
mcmc.sample(40000, 15000)
p_trace = mcmc.trace("freq_cheating")[:]
plt.hist(p_trace,
histtype="stepfilled",
normed=True,
alpha=0.85,
bins=30,
color="#348ABD")
32, 48, 36, 29, 37, 53, 55, 50, 47, 46, 44, 50, 56, 58, 42, 58, 54, 57, 54,
51, 49, 52, 51, 49, 51, 46, 46, 42, 49, 46, 56, 42, 53, 55, 51, 55, 49, 53,
55, 40, 46, 56, 47, 54, 54, 42, 34, 35, 41, 48, 46, 39, 55, 30, 49, 27, 51,
41, 36, 45, 41, 53, 32, 43, 33
])
condition = np.repeat([0, 1, 2, 3], nSubj)
# Specify the model in PyMC
with pm.Model() as model:
kappa = pm.Gamma('kappa', 1, 0.1, shape=ncond)
mu = pm.Beta('mu', 1, 1, shape=ncond)
theta = pm.Beta('theta',
mu[condition] * kappa[condition],
(1 - mu[condition]) * kappa[condition],
shape=len(z))
y = pm.Binomial('y', p=theta, n=N, observed=z)
start = pm.find_MAP()
step1 = pm.Metropolis([mu])
step2 = pm.Metropolis([theta])
step3 = pm.NUTS([kappa])
# samplers = [pm.Metropolis([rv]) for rv in model.unobserved_RVs]
trace = pm.sample(10000, [step1, step2, step3],
start=start,
progressbar=False)
## Check the results.
burnin = 5000 # posterior samples to discard
thin = 10 # posterior samples to discard
## Print summary for each trace
#pm.summary(trace[burnin::thin])
mu0 = pm.Beta('mu0', 1, 1)
a_Beta0 = mu0 * kappa[cond_of_subj]
b_Beta0 = (1 - mu0) * kappa[cond_of_subj]
mu1 = pm.Beta('mu1', 1, 1, shape=n_cond)
a_Beta1 = mu1[cond_of_subj] * kappa[cond_of_subj]
b_Beta1 = (1 - mu1[cond_of_subj]) * kappa[cond_of_subj]
#Prior on theta
theta0 = pm.Beta('theta0', a_Beta0, b_Beta0, shape=n_subj)
theta1 = pm.Beta('theta1', a_Beta1, b_Beta1, shape=n_subj)
# if model_index == 0 then sample from theta1 else sample from theta0
theta = pm.switch(pm.eq(model_index, 0), theta1, theta0)
# Likelihood:
y = pm.Binomial('y', p=theta, n=n_trl_of_subj, observed=n_corr_of_subj)
# Sampling
start = pm.find_MAP()
steps = [pm.Metropolis([i]) for i in model.unobserved_RVs[1:]]
steps.append(pm.ElemwiseCategoricalStep(var=model_index,values=[0,1]))
trace = pm.sample(20000, steps, start=start, progressbar=False)
# EXAMINE THE RESULTS.
burnin = 10000
thin = 10
## Print summary for each trace
#pm.summary(trace[burnin::thin])
#pm.summary(trace)
"""
A model for an MCMC model for batting average
"""
import pymc
import numpy as np
import pandas as pd
#load in the data
april_df = pd.read_table('./hw_11_data/laa_2011_april.txt',sep='\t')
at_bats = april_df['AB']
num_players = len(april_df.index)
num_hits = april_df['H']
#prior dist
mean_ba = .255
var_ba = .0011
a = ((1-mean_ba)/var_ba - 1/mean_ba)*mean_ba**2
b = a*(1/mean_ba -1)
ba = pymc.Beta('ba',alpha=a,beta=b,size=num_players)
#model
@pymc.deterministic(plot=False)
def modeled_ba(ba=ba):
return ba
#likelihood
hits = pymc.Binomial('hits',n=at_bats,p=modeled_ba,value=num_hits,observed =True)
#hits_i = pymc.Binomial('hits_i',n=1000,p=modeled_ba,value=800,observed =True)
# Import relevant modules
import pymc
import numpy as np
import pandas as pd
data = pd.read_csv('hw_11_data/laa_2011_april.csv',sep='\t')
# Priors on unknown parameters
alpha = pymc.Normal('alpha',mu=0.255,tau=1/float(0.0011))
beta = pymc.Normal('beta',mu=1-0.255,tau=1/float(0.0011))
avg = pymc.Beta('avg', alpha=alpha, beta=beta, size=len(data))
#def playeravg(a=alpha, b=beta):
# return pymc.Beta('avg',a,b, size=len(data))
#mus['mu'+ str(i)] = playeravg
xi = pymc.Binomial('xi',n=data.AB, p=avg, value=data.H)
author : ykita
date : Thu Feb 11 02:38:03 JST 2016
memo :
'''
import pymc as pm
import matplotlib.pyplot as plt
import numpy as np
observed = [1, 0, 1, 1, 0, 1, 0, 1, 0, 0]
h = sum(observed)
n = len(observed)
alpha, beta = 1, 1
niter = 10**6
with pm.Model() as model:
# define priors
p = pm.Beta('p', alpha=alpha, beta=beta)
# define likelihood
y = pm.Binomial('y', n=n, p=p, observed=h)
# inference
start = {'p': 0.5}
step = pm.Metropolis()
trace = pm.sample(niter, step, start)
pm.traceplot(trace)
plt.show()
N = 10000
p, bins = np.histogram(trace["p"], bins=N, density=True)
theta = np.linspace(np.min(bins), np.max(bins), N)
print "ML:" + str(h / float(n))
print "MCMC:" + str(np.dot(p, theta) / N)
name='s',
parents={
't_l': 1851,
't_h': 1962
},
random=s_rand,
trace=True,
value=1900,
dtype=int,
rseed=1.,
observed=False,
cache_depth=2,
plot=True,
verbose=0)
x = pm.Binomial('x', value=7, n=10, p=.8, observed=True)
x = pm.MvNormalCov('x', numpy.ones(3), numpy.eye(3))
y = pm.MvNormalCov('y', numpy.ones(3), numpy.eye(3))
print x + y
#<pymc.PyMCObjects.Deterministic '(x_add_y)' at 0x105c3bd10>
print x[0]
#<pymc.CommonDeterministics.Index 'x[0]' at 0x105c52390>
print x[1] + y[2]
#<pymc.PyMCObjects.Deterministic '(x[1]_add_y[2])' at 0x105c52410>
@pm.deterministic
def r(switchpoint=s, early_rate=e, late_rate=l):
pos_score = y_score[y_test == 1]
neg_score = y_score[y_test == 0]
# ranksums(pos_score, neg_score)
alldata = np.concatenate((pos_score, neg_score))
ranked = rankdata(alldata)
m1 = len(pos_score)
m2 = len(neg_score)
pos_rank = ranked[:m1]
neg_rank = ranked[m1:]
s = np.sum(pos_rank, axis=0)
count = s - m1 * (m1 + 1) / 2.0
# Binomal-Beta Conjugate
n_sample = 20000
p = pm.Beta("p", alpha=1, beta=1)
n = pm.Binomial("Bino", n=m1 * m2, p=p, value=count, observed=True)
mcmc = pm.MCMC([n, p])
trace = mcmc.sample(n_sample)
auc_trace = mcmc.trace("p")[:]
auc_mean = auc_trace.mean()
# 95% credible region
n_sample = auc_trace.shape[0]
lower_limits = np.sort(auc_trace)[int(0.025 * n_sample)]
upper_limits = np.sort(auc_trace)[int(0.975 * n_sample)]
# plot Posterior predictive distribution of auc measure
ax = plt.subplot(l, 2, i)
i += 1
# from pymc.Matplot import plot as mcplot
# mcplot(mcmc.trace("p"),common_scale=False)
with pymc.Model() as model:
### pp.228のBUGSコード相当
Y = df['y'].values
N = len(Y)
### hyperpriors
s = pymc.Uniform(name="s", lower=1.0e-2, upper=1.0e+2, testval=0.01)
b = pymc.Normal(name='b', mu=0.01, tau=1.0e+2)
### priors
r = [
pymc.Normal(name="r_{0}".format(i), mu=0., tau=s**-2) for i in range(N)
]
p = tinvlogit(b + r)
obs = pymc.Binomial(name="obs", n=8, p=p, observed=Y)
#H = model.fastd2logp()
with model:
start = pymc.find_MAP(vars=[s], fmin=optimize.fmin_l_bfgs_b)
# with model:
# step = pymc.NUTS(model.vars, scaling=start)
# かなり時間がかかるので実行時には注意すること！
def run(n=3000):
if n == "short":
n = 50
with model: