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
def create_model():
all_vars = []
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)
# target = 0.1**2
# a = 2
# b = target*(a+1)
target = 0.02**2
a = 0.7
b = target*(a+1)
tau_qd = InverseGamma('tau_qd', a, b)
tau_sc = InverseGamma('tau_sc', a, b)
tau_bias = InverseGamma('tau_bias', a, b)
# plot_dist(tau_qd, transform=lambda x: np.sqrt(x), high=0.5)
print np.mean([np.sqrt(tau_qd.random()) for i in xrange(10000)])
print np.std([np.sqrt(tau_qd.random()) for i in xrange(10000)])
target = 0.02**2
a = 0.9
b = target*(a+1)
tau_student_question_capabilities = InverseGamma('tau_student_question_capabilities', a, b)
tau_student_handin_capabilities = InverseGamma('tau_student_handin_capabilities', a, b)
# plot_dist(tau_student_handin_capabilities, transform=lambda x: np.sqrt(x), high=0.5)
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)
all_vars.append(tau_qd)
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, 1/tau)
q = Question(difficulty)
questions.append(q)
all_vars.append(difficulty)
assignment = Assignment(questions)
assignments.append(assignment)
for i in xrange(num_students):
tau = tau_sc
student_capabilities = Normal('student_capabilities_s_%i'%i, mu_sc, 1/tau)
all_vars.append(student_capabilities)
tau = tau_bias
grading_bias = Normal('grading_bias_s_%i'%i, 0, 1/tau)
all_vars.append(grading_bias)
s = Student(student_capabilities, grading_bias)
students.append(s)
for j, assignment in enumerate(assignments):
tau = tau_student_handin_capabilities
student_handin_capabilities = Normal('student_handin_capabilities_sh_%i_%i' % (i,j), 0, 1/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, 1/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 = []
num_grades_given = np.zeros((len(students),1))
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)+1, num_graders_pr_handin)
num_grades_given[idx] += 1
graders = [students[i] for i in idx]
grades = handin.grade(graders)
all_grades.append(grades)
# print num_grades_given
grade_list = sum(sum(all_grades, []),[])
tau = 1/0.02**2
print "Creating grade list"
grade_list_real = [g.value for g in grade_list]
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_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 % 10000 == 0:
print i
grade_list = grade_list_new
print "Grade list created"
all_vars += grade_list
all_vars = list(set(all_vars))
print len(all_vars)
return locals(), grade_list_real, all_vars
