def toy_model(tau=10000, prior='Beta0.5'):
b_obs = 200
f_AB = 400
f_CB = 1000
f_CA = 600
A = np.array([0, f_AB, f_CA, 0, f_CB, 0])
if prior == 'Normal':
ABp = Normal('ABp', mu=0.5, tau=100, trace=True)
CBp = Normal('CBp', mu=0.5, tau=100, trace=True)
CAp = Normal('CAp', mu=0.5, tau=100, trace=True)
elif prior == 'Uniform':
ABp = Uniform('ABp', lower=0.0, upper=1.0, trace=True)
CBp = Uniform('CBp', lower=0.0, upper=1.0, trace=True)
CAp = Uniform('CAp', lower=0.0, upper=1.0, trace=True)
elif prior == 'Beta0.25':
ABp = Beta('ABp', alpha=0.25, beta=0.25, trace=True)
CBp = Beta('CBp', alpha=0.25, beta=0.25, trace=True)
CAp = Beta('CAp', alpha=0.25, beta=0.25, trace=True)
elif prior == 'Beta0.5':
ABp = Beta('ABp', alpha=0.5, beta=0.5, trace=True)
CBp = Beta('CBp', alpha=0.5, beta=0.5, trace=True)
CAp = Beta('CAp', alpha=0.5, beta=0.5, trace=True)
elif prior == 'Beta2':
ABp = Beta('ABp', alpha=2, beta=2, trace=True)
CBp = Beta('CBp', alpha=2, beta=2, trace=True)
CAp = Beta('CAp', alpha=2, beta=2, trace=True)
elif prior == 'Gamma':
ABp = Gamma('ABp', alpha=1, beta=0.5, trace=True)
CBp = Gamma('CBp', alpha=1, beta=0.5, trace=True)
CAp = Gamma('CAp', alpha=1, beta=0.5, trace=True)
AB1 = ABp
AB3 = 1 - ABp
CB4 = CBp
CB5 = 1 - CBp
CA42 = CAp
CA52 = 1 - CAp
b = Normal('b',
mu=f_AB * AB3 + f_CB * CB4 + f_CA * CA42,
tau=tau,
value=b_obs,
observed=True,
trace=True)
# print [x.value for x in [ABp,CBp,CAp]]
# print b.logp
return locals()
def test_mixture_list_of_poissons(self):
with Model() as model:
w = Dirichlet("w",
floatX(np.ones_like(self.pois_w)),
shape=self.pois_w.shape)
mu = Gamma("mu", 1.0, 1.0, shape=self.pois_w.size)
Mixture(
"x_obs",
w,
[Poisson.dist(mu[0]), Poisson.dist(mu[1])],
observed=self.pois_x)
step = Metropolis()
trace = sample(5000,
step,
random_seed=self.random_seed,
progressbar=False,
chains=1)
assert_allclose(np.sort(trace["w"].mean(axis=0)),
np.sort(self.pois_w),
rtol=0.1,
atol=0.1)
assert_allclose(np.sort(trace["mu"].mean(axis=0)),
np.sort(self.pois_mu),
rtol=0.1,
atol=0.1)
def generate_route_flows_from_incidence_matrix(M, alpha=1):
"""
Generate blocks of route flows/splits (x) from an incidence matrix
:param M: incidence matrix
:return:
"""
x_blocks = []
order, block_sizes = [], []
m, n = M.shape
assert M.getnnz() == n
# Construct a Gamma distribution for each row in the incidence matrix
for i in xrange(m):
block_ind = M.getrow(i).nonzero()[1]
order.extend(block_ind)
size = len(block_ind)
block_sizes.append(size)
block = Gamma('x%d' % i, np.array([alpha] * size), 1, shape=size)
x_blocks.append(block)
x_blocks_expanded = [[x[xi]/x.sum() for xi in range(i-1)] for (i,x) in \
zip(block_sizes,x_blocks)]
[x.append(1 - sum(x)) for x in x_blocks_expanded]
x_pri = list(chain(*x_blocks_expanded))
# reorder
x_pri = zip(*sorted(zip(x_pri, order), key=lambda x: x[1]))[0]
return x_pri
def test_normal_mixture(self):
with Model() as model:
w = Dirichlet("w", floatX(np.ones_like(self.norm_w)), shape=self.norm_w.size)
mu = Normal("mu", 0.0, 10.0, shape=self.norm_w.size)
tau = Gamma("tau", 1.0, 1.0, shape=self.norm_w.size)
NormalMixture("x_obs", w, mu, tau=tau, observed=self.norm_x)
step = Metropolis()
trace = sample(5000, step, random_seed=self.random_seed, progressbar=False, chains=1)
assert_allclose(np.sort(trace["w"].mean(axis=0)), np.sort(self.norm_w), rtol=0.1, atol=0.1)
assert_allclose(
np.sort(trace["mu"].mean(axis=0)), np.sort(self.norm_mu), rtol=0.1, atol=0.1
)
def test_find_MAP_issue_4488():
# Test for https://github.com/pymc-devs/pymc/issues/4488
with Model() as m:
x = Gamma("x", alpha=3, beta=10, observed=np.array([1, np.nan]))
y = Deterministic("y", x + 1)
map_estimate = find_MAP()
assert not set.difference({"x_missing", "x_missing_log__", "y"},
set(map_estimate.keys()))
np.testing.assert_allclose(map_estimate["x_missing"],
0.2,
rtol=1e-4,
atol=1e-4)
np.testing.assert_allclose(map_estimate["y"],
[2.0, map_estimate["x_missing"][0] + 1])
pathways, features, path_dict, reverse_path_dict, evidence, metfrag_evidence = data
for c,v in evidence.iteritems():
print c,v
for c,v in metfrag_evidence.iteritems():
print c,v
print "num_pathways:", len(pathways)
print "num_features:", len(features)
print "num_evidence:", len(evidence)
print "num_metfrag: ", len(metfrag_evidence)
rate_prior = 0.5
#eps = Beta('eps', 0.005, 1)
eps = 0.0001
ap = {p : Gamma('p_' + p, rate_prior, 1) for p in pathways}
bmp = {p : {feat : Gamma('b_{' + p + ',' + feat + '}', ap[p],1) for feat in path_dict[p]} for p in pathways}
y_bmp = {}
g = {}
def logp_f(f, b, eps):
if f in evidence:
return math.log(1 - math.e ** (-1 * b) + epsilon)
if f in metfrag_evidence:
a_p = (1.0 / (1 - metfrag_evidence[f])) - 1
return a_p * math.log(1 - math.e ** (-1 * b) + epsilon) - b
return math.log(eps) - b
psi = {}
for feat, pathways in reverse_path_dict.iteritems():
y_bmp[feat] = sum([bmp[pname][feat] for pname in pathways])
g[feat] = Bernoulli('g_' + feat, 1 - math.e ** (-y_bmp[feat]))
def create_model():
all_vars = []
# b = 0.02
# target_mean = 1/0.1**2
# a = b*target_mean
b = 0.001
target_mean = 10/0.1**2
a = b*target_mean
# print a/b
# print np.sqrt(a/(b**2))
# tau_qd = Normal('tau_qd', 0.05,1/(0.15**2))
# tau_qd = Exponential('tau_qd', 10)
tau_qd = Gamma('tau_qd', a, b)
plot_dist(tau_qd, transform=lambda x: 1/np.sqrt(x))
print np.mean([1/np.sqrt(tau_qd.random()) for i in xrange(1000)])
print np.std([1/np.sqrt(tau_qd.random()) for i in xrange(1000)])
# pot = TruncPotential('tau_qd_potential', 0, 0.2, tau_qd)
# all_vars.append(pot)
# tau_qd.value = 1/0.05**2
all_vars.append(tau_qd)
# plot_dist(tau_qd, 0, 0.2)
mu_sc = Normal('mu_sc', 0.5, 1/(0.25**2))
mu_sc.value=0.5
pot = TruncPotential('mu_sc_potential', 0, 1, mu_sc)
all_vars.append(pot)
# tau_sc = Normal('tau_sc', 0.2, 1/(0.25**2))
# tau_sc = Exponential('tau_sc', 10)
tau_sc = Gamma('tau_sc', a, b)
# plot_dist(tau_sc)
# tau_sc.value = 1/0.1**2
# pot = TruncPotential('tau_sc_potential', 0, 0.3, tau_sc)
# all_vars.append(pot)
# tau_bias = Normal('tau_bias', 0.05, 1/(0.25**2))
# tau_bias = Exponential('tau_bias', 10)
tau_bias = Gamma('tau_bias', a, b)
# pot = TruncPotential('tau_bias_potential', 0, 0.2, tau_bias)
# all_vars.append(pot)
# tau_bias.value = 1/0.01**2
# tau_student_handin_capabilities = Normal('tau_student_handin_capabilities', 0.05, 1/(0.15**2))
# tau_student_handin_capabilities = Exponential('tau_student_handin_capabilities', 10)
tau_student_handin_capabilities = Gamma('tau_student_handin_capabilities', a, b)
# tau_student_handin_capabilities.value = 1/0.05**2
# pot = TruncPotential('tau_student_handin_capabilities_potential', 0, 0.3, tau_student_handin_capabilities)
# all_vars.append(pot)
# tau_student_question_capabilities = Normal('tau_student_question_capabilities', 0.05,1/(0.15**2))
# tau_student_question_capabilities = Exponential('tau_student_question_capabilities', 10)
tau_student_question_capabilities = Gamma('tau_student_question_capabilities', a, b)
# plot_dist(tau_student_question_capabilities)
# tau_student_question_capabilities.value = 1/0.05**2
# pot = TruncPotential('tau_student_question_capabilities_potential', 0, 0.15, tau_student_question_capabilities)
# all_vars.append(pot)
# plot_dist(tau_student_question_capabilities, 0, 0.2)
all_vars.append(mu_sc)
all_vars.append(tau_sc)
all_vars.append(tau_bias)
all_vars.append(tau_student_handin_capabilities)
all_vars.append(tau_student_question_capabilities)
for i in xrange(num_assignments):
questions = []
for j in xrange(num_questions_pr_handin):
# tau = pymc.Lambda('tau_%i_%i'% (i,j), lambda a=tau_qd: 1/ (tau_qd.value*tau_qd.value))
tau = tau_qd
difficulty = Normal('difficulty_q_%i_%i'% (i,j), 0, tau)
q = Question(difficulty)
questions.append(q)
all_vars.append(difficulty)
assignment = Assignment(questions)
assignments.append(assignment)
for i in xrange(num_students):
# tau = pymc.Lambda('tau1_%i'%i, lambda a=tau_sc: 1/(tau_sc.value*tau_sc.value))
tau = tau_sc
student_capabilities = Normal('student_capabilities_s_%i'%i, mu_sc, tau)
# pot = TruncPotential('student_capabilities_potential_s_%i'%i, 0, 1, student_capabilities)
all_vars.append(student_capabilities)
# all_vars.append(pot)
# grading_bias = Normal('grading_bias_s_%i'%i, 0, 1/tau_bias)
# tau = pymc.Lambda('tau2_%i'%i, lambda a=tau_bias: 1/ (tau_bias.value*tau_bias.value))
tau = tau_bias
grading_bias = Normal('grading_bias_s_%i'%i, 0, tau)
all_vars.append(grading_bias)
s = Student(student_capabilities, grading_bias)
students.append(s)
for j, assignment in enumerate(assignments):
# student_handin_capabilities = Normal('student_handin_capabilities_sh_%i_%i' % (i,j), 0, 1/tau_student_handin_capabilities)
tau = tau_student_handin_capabilities
student_handin_capabilities = Normal('student_handin_capabilities_sh_%i_%i' % (i,j), 0, tau)
all_vars.append(student_handin_capabilities)
question_capabilities = []
for k, q in enumerate(assignment.questions):
tau = tau_student_question_capabilities
student_question_capabilities = Normal('student_question_capabilities_shq_%i_%i_%i' % (i,j,k ), 0, tau)
all_vars.append(student_question_capabilities)
question_capabilities.append(student_question_capabilities)
handins.append(Handin(s, assignment, student_handin_capabilities, question_capabilities))
# assign grader
all_grades = []
for handin in handins:
potential_graders = range(0, len(students))
potential_graders.remove(students.index(handin.student))
idx = np.random.randint(0, len(potential_graders), num_graders_pr_handin)
graders = [students[i] for i in idx]
grades = handin.grade(graders)
all_grades.append(grades)
grade_list = sum(sum(all_grades, []),[])
b = 1.0
target_mean = 1/np.sqrt(0.01)
a = b*target_mean
tau_exo_grade = Gamma('tau_exo_grade', a, b)
# plt.hist([1/tau_exo_grade.random()**2 for i in xrange(50000)])
# tau_exo_grade = Exponential('mu_exo_grade', 20)
# tau_exo_grade = Normal('mu_exo_grade', 0.05, 1/(0.1**2))
# pot = TruncPotential('tau_exo_grade', 0, 0.2, tau_exo_grade)
# all_vars.append(pot)
tau = tau_exo_grade
all_vars.append(tau_exo_grade)
print "Creating grade list"
# grade_list_real = [g.value for g in grade_list]
# print 1
# grade_list_real = [min(max((g), 0), 1) for g in grade_list_real]
# print 2
# grade_list = [Normal('grade_%i'%i, g, tau, value=g_real, observed=True) for i, (g_real, g) in enumerate(zip(grade_list_real, grade_list))]
# print 3
# grade_list_potentials = [TruncPotential('grade_potential_%i'%i, 0, 1, g) for i,g in enumerate(grade_list)]
# print 4
# take one MCMC step in order to make it more probable that all variables are in the allowed range
# var_dict = {str(v):v for v in all_vars}
# sampler = pymc.MCMC(var_dict)
# sampler.sample(iter=1)
grade_list_real = [g.value for g in grade_list]
# plt.hist(grade_list_real)
# plt.show()
print "Number of illegal grades: %i (out of %i)" % (len([g for g in grade_list_real if g > 1 or g < 0]), len(grade_list))
grade_list_real = [min(max((g), 0), 1) for g in grade_list_real]
# grade_list = Normal('grade_%i'%i, np.array(grade_list), np.array([tau]*len(grade_list)), value=grade_list_real, observed=True)
# grade_list = [Normal('grade_%i'%i, g, tau, value=g_real, observed=True) for i, (g_real, g) in enumerate(zip(grade_list_real, grade_list))]
grade_list_new = []
for i, (g_real, g) in enumerate(zip(grade_list_real, grade_list)):
grade_list_new.append(Normal('grade_%i'%i, g, tau, value=g_real, observed=True))
if i % 100 == 0:
print i
# grade_list_potentials = [TruncPotential('grade_potential_%i'%i, 0, 1, g) for i,g in enumerate(grade_list)]
grade_list = grade_list_new
print "Grade list created"
all_vars += grade_list
# all_vars += grade_list_potentials
all_vars = list(set(all_vars))
print len(all_vars)
# print [str(v) for v in all_vars]
return locals(), grade_list_real, all_vars
features = read.get_metabolites(path_dict)
evidence = read.metlin(observation_file)
evidence |= read.hmdb(observation_file)
evidence -= cofactors
features -= cofactors
evidence &= features
reverse_path_dict = read.reverse_dict(path_dict)
metfrag = read.metfrag(observation_file)
metfrag_evidence = read.dict_of_set(
read.metfrag_with_scores(observation_file, keep_zero_scores=False),
metfrag & features - cofactors - evidence)
evidence = {e: 1 for e in evidence}
rate_prior = 0.5
ap = {p: Gamma('p_' + p, rate_prior, 1) for p in pathways}
bmp = {
p: {
feat: Gamma('b_{' + p + ',' + feat + '}', ap[p], 1)
for feat in path_dict[p]
}
for p in pathways
}
y_bmp = {}
virtual = {}
se_count = 0
for feat, pathways in reverse_path_dict.iteritems():
#g_bmp[feat] = Poisson('g_' + feat, sum([bmp[pname][feat] for pname in pathways]))
y_bmp[feat] = Bernoulli(
'y_' + feat,
def test_normal_mixture_nd(self, nd, ncomp):
nd = to_tuple(nd)
ncomp = int(ncomp)
comp_shape = nd + (ncomp,)
test_mus = np.random.randn(*comp_shape)
test_taus = np.random.gamma(1, 1, size=comp_shape)
observed = generate_normal_mixture_data(
w=np.ones(ncomp) / ncomp, mu=test_mus, sd=1 / np.sqrt(test_taus), size=10
)
with Model() as model0:
mus = Normal("mus", shape=comp_shape)
taus = Gamma("taus", alpha=1, beta=1, shape=comp_shape)
ws = Dirichlet("ws", np.ones(ncomp), shape=(ncomp,))
mixture0 = NormalMixture("m", w=ws, mu=mus, tau=taus, shape=nd, comp_shape=comp_shape)
obs0 = NormalMixture(
"obs", w=ws, mu=mus, tau=taus, shape=nd, comp_shape=comp_shape, observed=observed
)
with Model() as model1:
mus = Normal("mus", shape=comp_shape)
taus = Gamma("taus", alpha=1, beta=1, shape=comp_shape)
ws = Dirichlet("ws", np.ones(ncomp), shape=(ncomp,))
comp_dist = [
Normal.dist(mu=mus[..., i], tau=taus[..., i], shape=nd) for i in range(ncomp)
]
mixture1 = Mixture("m", w=ws, comp_dists=comp_dist, shape=nd)
obs1 = Mixture("obs", w=ws, comp_dists=comp_dist, shape=nd, observed=observed)
with Model() as model2:
# Expected to fail if comp_shape is not provided,
# nd is multidim and it does not broadcast with ncomp. If by chance
# it does broadcast, an error is raised if the mixture is given
# observed data.
# Furthermore, the Mixture will also raise errors when the observed
# data is multidimensional but it does not broadcast well with
# comp_dists.
mus = Normal("mus", shape=comp_shape)
taus = Gamma("taus", alpha=1, beta=1, shape=comp_shape)
ws = Dirichlet("ws", np.ones(ncomp), shape=(ncomp,))
if len(nd) > 1:
if nd[-1] != ncomp:
with pytest.raises(ValueError):
NormalMixture("m", w=ws, mu=mus, tau=taus, shape=nd)
mixture2 = None
else:
mixture2 = NormalMixture("m", w=ws, mu=mus, tau=taus, shape=nd)
else:
mixture2 = NormalMixture("m", w=ws, mu=mus, tau=taus, shape=nd)
observed_fails = False
if len(nd) >= 1 and nd != (1,):
try:
np.broadcast(np.empty(comp_shape), observed)
except Exception:
observed_fails = True
if observed_fails:
with pytest.raises(ValueError):
NormalMixture("obs", w=ws, mu=mus, tau=taus, shape=nd, observed=observed)
obs2 = None
else:
obs2 = NormalMixture("obs", w=ws, mu=mus, tau=taus, shape=nd, observed=observed)
testpoint = model0.recompute_initial_point()
testpoint["mus"] = test_mus
testpoint["taus"] = test_taus
assert_allclose(model0.logp(testpoint), model1.logp(testpoint))
assert_allclose(mixture0.logp(testpoint), mixture1.logp(testpoint))
assert_allclose(obs0.logp(testpoint), obs1.logp(testpoint))
if mixture2 is not None and obs2 is not None:
assert_allclose(model0.logp(testpoint), model2.logp(testpoint))
if mixture2 is not None:
assert_allclose(mixture0.logp(testpoint), mixture2.logp(testpoint))
if obs2 is not None:
assert_allclose(obs0.logp(testpoint), obs2.logp(testpoint))
from pymc import Gamma, Poisson, InverseGamma
import pymc
import numpy as np
import gen
pathways = gen.pathways()
features = gen.features_dict()
detected = gen.detected_features()
evidence = gen.evidence()
ap = {p.name: Gamma('p_' + p.name, p.rate, 1) for p in pathways}
#bmp = [Gamma('b_{' + str(i) + '}', 1, ap[i]) for i in range(3)]
bmp = {
p.name: {
feat: Gamma('b_{' + p.name + ',' + str(feat) + '}', ap[p.name], 1)
for feat in p.mets
}
for p in pathways
}
print bmp
#g_bmp = {feat : Poisson('g_' + str(feat), sum([bmp[pname][feat] for pname in pathways])) for feat, pathways in features.iteritems()}
g_bmp = {}
for feat, pathways in features.iteritems():
if detected(feat):
print feat, "was detected"
g_bmp[feat] = Poisson('g_' + str(feat),
sum([bmp[pname][feat] for pname in pathways]),
value=1,
observed=True)
else:
print feat, "was not detected"
g_bmp[feat] = Poisson('g_' + str(feat),
def create_model():
all_vars = []
# b = 20
# target_mean = 0.1
b = 5
target_mean = 0.2
a = b*target_mean
# sigma_qd = Normal('sigma_qd', 0.05,1/(0.15**2))
# sigma_qd = Exponential('sigma_qd', 10)
sigma_qd = Gamma('sigma_qd', a, b)
# pot = TruncPotential('sigma_qd_potential', 0, 0.2, sigma_qd)
# all_vars.append(pot)
# sigma_qd.value = 0.05
all_vars.append(sigma_qd)
# plot_dist(sigma_qd, 0, 0.2)
# mu_sc = Normal('mu_sc', 0.5, 1/(0.25**2))
mu_sc = TruncNormal('mu_sc', 0, 1, 0.5, 1/(0.2**2))
mu_sc.value=0.5
# pot = TruncPotential('mu_sc_potential', 0, 1, mu_sc)
# all_vars.append(pot)
# sigma_sc = Normal('sigma_sc', 0.2, 1/(0.25**2))
# sigma_sc = Exponential('sigma_sc', 10)
sigma_sc = Gamma('sigma_sc', a, b)
# plot_dist(sigma_sc)
sigma_sc.value = 0.1
# pot = TruncPotential('sigma_sc_potential', 0, 0.3, sigma_sc)
# all_vars.append(pot)
# sigma_bias = Normal('sigma_bias', 0.05, 1/(0.25**2))
# sigma_bias = Exponential('sigma_bias', 10)
sigma_bias = Gamma('sigma_bias', a, b)
# pot = TruncPotential('sigma_bias_potential', 0, 0.2, sigma_bias)
# all_vars.append(pot)
sigma_bias.value = 0.1
b_c = 5
target_mean_c = 0.2
a_c = b_c*target_mean
# sigma_student_handin_capabilities = Normal('sigma_student_handin_capabilities', 0.05, 1/(0.15**2))
# sigma_student_handin_capabilities = Exponential('sigma_student_handin_capabilities', 10)
sigma_student_handin_capabilities = Gamma('sigma_student_handin_capabilities', a, b)
sigma_student_handin_capabilities.value = 0.05
# pot = TruncPotential('sigma_student_handin_capabilities_potential', 0, 0.3, sigma_student_handin_capabilities)
# all_vars.append(pot)
# sigma_student_question_capabilities = Normal('sigma_student_question_capabilities', 0.05,1/(0.15**2))
# sigma_student_question_capabilities = Exponential('sigma_student_question_capabilities', 10)
sigma_student_question_capabilities = Gamma('sigma_student_question_capabilities', a, b)
# plot_dist(sigma_student_question_capabilities)
sigma_student_question_capabilities.value = 0.05
# pot = TruncPotential('sigma_student_question_capabilities_potential', 0, 0.15, sigma_student_question_capabilities)
# all_vars.append(pot)
# plot_dist(sigma_student_question_capabilities, 0, 0.2)
all_vars.append(mu_sc)
all_vars.append(sigma_sc)
all_vars.append(sigma_bias)
all_vars.append(sigma_student_handin_capabilities)
all_vars.append(sigma_student_question_capabilities)
for i in xrange(num_assignments):
questions = []
for j in xrange(num_questions_pr_handin):
tau = pymc.Lambda('tau_%i_%i'% (i,j), lambda a=sigma_qd: 1/ (sigma_qd.value*sigma_qd.value))
difficulty = Normal('difficulty_q_%i_%i'% (i,j), 0, tau)
q = Question(difficulty)
questions.append(q)
all_vars.append(difficulty)
assignment = Assignment(questions)
assignments.append(assignment)
for i in xrange(num_students):
tau = pymc.Lambda('tau1_%i'%i, lambda a=sigma_sc: 1/(sigma_sc.value*sigma_sc.value))
# student_capabilities = Normal('student_capabilities_s_%i'%i, mu_sc, tau)
student_capabilities = TruncNormal('student_capabilities_s_%i'%i, 0, 1, mu_sc, tau)
all_vars.append(student_capabilities)
# pot = TruncPotential('student_capabilities_potential_s_%i'%i, 0, 1, student_capabilities)
# all_vars.append(pot)
# grading_bias = Normal('grading_bias_s_%i'%i, 0, 1/sigma_bias)
tau = pymc.Lambda('tau2_%i'%i, lambda a=sigma_bias: 1/ (sigma_bias.value*sigma_bias.value))
grading_bias = Normal('grading_bias_s_%i'%i, 0, tau)
all_vars.append(grading_bias)
s = Student(student_capabilities, grading_bias)
students.append(s)
for j, assignment in enumerate(assignments):
# student_handin_capabilities = Normal('student_handin_capabilities_sh_%i_%i' % (i,j), 0, 1/sigma_student_handin_capabilities)
tau = pymc.Lambda('tau2_%i_i%i'%(i, j), lambda a=sigma_student_handin_capabilities: 1/ (sigma_student_handin_capabilities.value*sigma_student_handin_capabilities.value))
student_handin_capabilities = Normal('student_handin_capabilities_sh_%i_%i' % (i,j), 0, tau)
all_vars.append(student_handin_capabilities)
question_capabilities = []
for k, q in enumerate(assignment.questions):
tau = pymc.Lambda('tau2_%i_i%i_%i'%(i, j,k), lambda a=sigma_student_question_capabilities: 1/ (sigma_student_question_capabilities.value*sigma_student_question_capabilities.value))
student_question_capabilities = Normal('student_question_capabilities_shq_%i_%i_%i' % (i,j,k ), 0, tau)
all_vars.append(student_question_capabilities)
question_capabilities.append(student_question_capabilities)
handins.append(Handin(s, assignment, student_handin_capabilities, question_capabilities))
# assign grader
all_grades = []
for handin in handins:
potential_graders = range(0, len(students))
potential_graders.remove(students.index(handin.student))
idx = np.random.randint(0, len(potential_graders), num_graders_pr_handin)
graders = [students[i] for i in idx]
grades = handin.grade(graders)
all_grades.append(grades)
grade_list = sum(sum(all_grades, []),[])
b = 50
target_mean = 0.05
a = b*target_mean
sigma_exo_grade = Gamma('sigma_exo_grade', a, b)
# sigma_exo_grade = Exponential('mu_exo_grade', 20)
# sigma_exo_grade = Normal('mu_exo_grade', 0.05, 1/(0.1**2))
# pot = TruncPotential('sigma_exo_grade', 0, 0.2, sigma_exo_grade)
# all_vars.append(pot)
tau = pymc.Lambda('tau3', lambda a=sigma_exo_grade: 1/ (sigma_exo_grade.value*sigma_exo_grade.value))
all_vars.append(sigma_exo_grade)
print "Creating grade list"
# grade_list_real = [g.value for g in grade_list]
# print 1
# grade_list_real = [min(max((g), 0), 1) for g in grade_list_real]
# print 2
# grade_list = [Normal('grade_%i'%i, g, tau, value=g_real, observed=True) for i, (g_real, g) in enumerate(zip(grade_list_real, grade_list))]
# print 3
# grade_list_potentials = [TruncPotential('grade_potential_%i'%i, 0, 1, g) for i,g in enumerate(grade_list)]
# print 4
# take one MCMC step in order to make it more probable that all variables are in the allowed range
# var_dict = {str(v):v for v in all_vars}
# sampler = pymc.MCMC(var_dict)
# sampler.sample(iter=1)
grade_list_real = [g.value for g in grade_list]
# plt.hist(grade_list_real)
# plt.show()
print "Number of illegal grades: %i (out of %i)" % (len([g for g in grade_list_real if g > 1 or g < 0]), len(grade_list))
grade_list_real = [min(max((g), 0), 1) for g in grade_list_real]
grade_list = [Normal('grade_%i'%i, g, tau, value=g_real, observed=True) for i, (g_real, g) in enumerate(zip(grade_list_real, grade_list))]
# grade_list = [Normal('grade_%i'%i, g, 1/(0.02^2), value=g_real, observed=True) for i, (g_real, g) in enumerate(zip(grade_list_real, grade_list))]
grade_list_potentials = [TruncPotential('grade_potential_%i'%i, 0, 1, g) for i,g in enumerate(grade_list)]
print "Grade list created"
all_vars += grade_list
all_vars += grade_list_potentials
all_vars = list(set(all_vars))
print len(all_vars)
# print [str(v) for v in all_vars]
return locals(), grade_list_real, all_vars
prior = 'Gamma'
if prior == 'Normal':
ABp = Normal('ABp', mu=0.5, tau=100)
CBp = Normal('CBp', mu=0.5, tau=100)
CAp = Normal('CAp', mu=0.5, tau=100)
elif prior == 'Uniform':
ABp = Uniform('ABp', lower=0.0, upper=1.0)
CBp = Uniform('CBp', lower=0.0, upper=1.0)
CAp = Uniform('CAp', lower=0.0, upper=1.0)
elif prior == 'Beta':
ABp = Beta('ABp', alpha=0.5, beta=0.5)
CBp = Beta('CBp', alpha=0.5, beta=0.5)
CAp = Beta('CAp', alpha=0.5, beta=0.5)
elif prior == 'Gamma':
ABp = Gamma('ABp', alpha=1, beta=0.5)
CBp = Gamma('CBp', alpha=1, beta=0.5)
CAp = Gamma('CAp', alpha=1, beta=0.5)
AB1 = ABp
AB3 = 1 - ABp
CB4 = CBp
CB5 = 1 - CBp
CA42 = CAp
CA52 = 1 - CAp
b = Normal('b',
mu=400 * AB3 + 1000 * CB4 + 600 * CA42,
tau=10000,
value=200,
observed=True)