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
from pymc import deterministic, Normal, Uniform, Model
from pymc.distributions import truncated_normal_like
import pymc
import numpy as np
from grade_model2 import *
import pydot_ng as pydot
from pymc.ScipyDistributions import stochastic_from_scipy_dist, stochastic_from_dist
from scipy.stats import truncnorm
import matplotlib.pyplot as plt
from distributions import TruncNormal
test = TruncNormal('test', 0, 1, 0.5, 0.2, 0.5)
x = np.linspace(-1,2, 100)
plt.hist([test.random() for i in xrange(1000)])
# plt.hist([test.random(0,1,0.5, 0.2) for i in xrange(1000)])
num_students = 120
num_assignments = 4
num_questions_pr_handin = 20
num_graders_pr_handin = 7
students = []
assignments = []
handins = []
def create_model():
all_vars = []
sigma_qd = Uniform('sigma_qd', 0,0.15)
