decay = Uniform([[0], [1]], name='decay')
diffusion = Uniform([[0], [1]], name='diffusion')
liBufferRatio = Uniform([[0], [3]], name='liBufferRatio')
liBufferAngle = Uniform([[45], [90]], name='liBufferAngle')
diasA = Uniform([[0],[3]], name='diasA')
diasB = Uniform([[0],[3]], name='diasB')
diasP1 = Uniform([[0],[1]], name='diasP1')
diasP2 = Uniform([[0],[1]], name='diasP2')
# Define simulator and perturbation kernels
# Since each model use a different number of parameters different ifs are employed
# The same name is used for the simulator so that there is no need to distinguish hereafter
from abcpy.perturbationkernel import MultivariateNormalKernel, JointPerturbationKernel
if sim_model=='ff1':
ff = FFSimulator1([kS, kD, kW, decay, diffusion], name = 'ff')
kernelcontinuous = MultivariateNormalKernel([kS, kD, kW, decay, diffusion])
if sim_model=='ff2':
ff = FFSimulator2([kS, kD, kW, decay, diffusion, liBufferRatio, liBufferAngle], name = 'ff')
kernelcontinuous = MultivariateNormalKernel([kS, kD, kW, decay, diffusion, liBufferRatio, liBufferAngle])
if sim_model=='ff3':
ff = FFSimulator3([kS, kD, kW, decay, diffusion, diasA, diasB, diasP1, diasP2], name = 'ff')
kernelcontinuous = MultivariateNormalKernel([kS, kD, kW, decay, diffusion, diasA, diasB, diasP1, diasP2])
kernel = JointPerturbationKernel([kernelcontinuous])
# Example to Generate Data to check forward simulations work without problems
if sim_model=='ff1':
fftry = FFSimulator1([4.0, 1.0, 1.5, 0.1, 0.25], name = 'fftry')
resultfakeobs1 = fftry.forward_simulate([4.0, 1.0, 1.5, 0.1, 0.25], 10)
resultfakeobs2 = fftry.forward_simulate([5.0, 1.0, 1.5, 0.1, 0.25], 10)
if sim_model=='ff2':
fftry = FFSimulator2([4.0, 1.0, 1.5, 0.1, 0.25, 0.5, 50.0], name = 'fftry')
# Define Statistics
from abcpy.statistics import Identity
statistics_calculator = Identity(degree=1, cross=False)
# Define distance
from Distance import DistanceType1
distance_calculator = DistanceType1(statistics_calculator)
print('# Check whether the distance works')
print(distance_calculator.distance(resultfakeobs1, resultfakeobs1))
print(distance_calculator.distance(resultfakeobs1, resultfakeobs2))
# Define kernel
from abcpy.perturbationkernel import MultivariateNormalKernel, RandomWalkKernel, JointPerturbationKernel
# Join the defined kernels
kernelcontinuous = MultivariateNormalKernel(
[bufferRatio, kW, kS, kD, decay, diffusion])
kerneldiscrete = RandomWalkKernel([bufferAngle])
kernel = JointPerturbationKernel([kernelcontinuous, kerneldiscrete])
#
## APMCABC ##
from abcpy.inferences import APMCABC
sampler = APMCABC([ff], [distance_calculator], backend, kernel, seed=1)
steps, n_samples, n_samples_per_param, alpha, acceptance_cutoff, covFactor, full_output, journal_file = 4, 100, 1, 0.1, 0.03, 2, 1.0, None
print('APMCABC Inferring')
# We use resultfakeobs1 as our observed dataset
journal_apmcabc = sampler.sample([resultfakeobs1], steps, n_samples,
n_samples_per_param, alpha, acceptance_cutoff,
covFactor, full_output, journal_file)
print(journal_apmcabc.posterior_mean())
journal_apmcabc.save('apmcabc_fakeobs1.jrnl')
def infer_parameters():
# The data corresponding to model_1 defined below
grades_obs = [3.872486707973337, 4.6735380808674405, 3.9703538990858376, 4.11021272048805, 4.211048655421368, 4.154817956586653, 4.0046893064392695, 4.01891381384729, 4.123804757702919, 4.014941267301294, 3.888174595940634, 4.185275142948246, 4.55148774469135, 3.8954427675259016, 4.229264035335705, 3.839949451328312, 4.039402553532825, 4.128077814241238, 4.361488645531874, 4.086279074446419, 4.370801602256129, 3.7431697332475466, 4.459454162392378, 3.8873973643008255, 4.302566721487124, 4.05556051626865, 4.128817316703757, 3.8673704442215984, 4.2174459453805015, 4.202280254493361, 4.072851400451234, 3.795173229398952, 4.310702877332585, 4.376886328810306, 4.183704734748868, 4.332192463368128, 3.9071312388426587, 4.311681374107893, 3.55187913252144, 3.318878360783221, 4.187850500877817, 4.207923106081567, 4.190462065625179, 4.2341474252986036, 4.110228694304768, 4.1589891480847765, 4.0345604687633045, 4.090635481715123, 3.1384654393449294, 4.20375641386518, 4.150452690356067, 4.015304457401275, 3.9635442007388195, 4.075915739179875, 3.5702080541929284, 4.722333310410388, 3.9087618197155227, 4.3990088006390735, 3.968501165774181, 4.047603645360087, 4.109184340976979, 4.132424805281853, 4.444358334346812, 4.097211737683927, 4.288553086265748, 3.8668863066511303, 3.8837108501541007]
# The prior information changing the class size and the teacher student ratio, depending on the yearly budget of the school
from abcpy.continuousmodels import Uniform, Normal
school_budget = Uniform([[1], [10]], name = 'school_budget')
# The average class size of a certain school
class_size = Normal([[800*school_budget], [1]], name = 'class_size')
# The number of teachers in the school
no_teacher = Normal([[20*school_budget], [1]], name = 'no_teacher')
# The grade a student would receive without any bias
grade_without_additional_effects = Normal([[4.5], [0.25]], name = 'grade_without_additional_effects')
# The grade a student of a certain school receives
final_grade = grade_without_additional_effects - .001 * class_size + .02 * no_teacher
# The data corresponding to model_2 defined below
scholarship_obs = [2.7179657436207805, 2.124647285937229, 3.07193407853297, 2.335024761813643, 2.871893855192, 3.4332002458233837, 3.649996835818173, 3.50292335102711, 2.815638168018455, 2.3581613289315992, 2.2794821846395568, 2.8725835459926503, 3.5588573782815685, 2.26053126526137, 1.8998143530749971, 2.101110815311782, 2.3482974964831573, 2.2707679029919206, 2.4624550491079225, 2.867017757972507, 3.204249152084959, 2.4489542437714213, 1.875415915801106, 2.5604889644872433, 3.891985093269989, 2.7233633223405205, 2.2861070389383533, 2.9758813233490082, 3.1183403287267755, 2.911814060853062, 2.60896794303205, 3.5717098647480316, 3.3355752461779824, 1.99172284546858, 2.339937680892163, 2.9835630207301636, 2.1684912355975774, 3.014847335983034, 2.7844122961916202, 2.752119871525148, 2.1567428931391635, 2.5803629307680644, 2.7326646074552103, 2.559237193255186, 3.13478196958166, 2.388760269933492, 3.2822443541491815, 2.0114405441787437, 3.0380056368041073, 2.4889680313769724, 2.821660164621084, 3.343985964873723, 3.1866861970287808, 4.4535037154856045, 3.0026333138006027, 2.0675706089352612, 2.3835301730913185, 2.584208398359566, 3.288077633446465, 2.6955853384148183, 2.918315169739928, 3.2464814419322985, 2.1601516779909433, 3.231003347780546, 1.0893224045062178, 0.8032302688764734, 2.868438615047827]
# A quantity that determines whether a student will receive a scholarship
scholarship_without_additional_effects = Normal([[2], [0.5]], name = 'schol_without_additional_effects')
# A quantity determining whether a student receives a scholarship, including his social teacher_student_ratio
final_scholarship = scholarship_without_additional_effects + .03 * no_teacher
# Define a summary statistics for final grade and final scholarship
from abcpy.statistics import Identity
statistics_calculator_final_grade = Identity(degree = 2, cross = False)
statistics_calculator_final_scholarship = Identity(degree = 3, cross = False)
# Define a distance measure for final grade and final scholarship
from abcpy.distances import Euclidean
distance_calculator_final_grade = Euclidean(statistics_calculator_final_grade)
distance_calculator_final_scholarship = Euclidean(statistics_calculator_final_scholarship)
# Define a backend
from abcpy.backends import BackendDummy as Backend
backend = Backend()
# Define kernels
from abcpy.perturbationkernel import MultivariateNormalKernel, MultivariateStudentTKernel
kernel_1 = MultivariateNormalKernel([school_budget,\
scholarship_without_additional_effects, grade_without_additional_effects])
kernel_2 = MultivariateStudentTKernel([class_size, no_teacher], df=3)
# Join the defined kernels
from abcpy.perturbationkernel import JointPerturbationKernel
kernel = JointPerturbationKernel([kernel_1, kernel_2])
# Define sampling parameters
T, n_sample, n_samples_per_param = 3, 250, 10
eps_arr = np.array([.75])
epsilon_percentile = 10
# Define sampler
from abcpy.inferences import PMCABC
sampler = PMCABC([final_grade, final_scholarship], [distance_calculator, distance_calculator], backend, kernel)
# Sample
journal = sampler.sample([y_obs_grades, y_obs_scholarship], T, eps_arr, n_sample, n_samples_per_param, epsilon_percentile)
#
# Define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(statistics_calculator)
#
print('# Check whether the distance works')
print(distance_calculator.distance(resultfakeobs1, resultfakeobs1))
print(distance_calculator.distance(resultfakeobs1, resultfakeobs2))
# Define kernel
from abcpy.perturbationkernel import MultivariateNormalKernel, JointPerturbationKernel
# Join the defined kernels
kernel1 = MultivariateNormalKernel([theta1, theta2])
kernel = JointPerturbationKernel([kernel1])
#
## APMCABC ##
from abcpy.inferences import APMCABC
sampler = APMCABC([lorenz], [distance_calculator], backend, kernel, seed=1)
steps, n_samples, n_samples_per_param, alpha, acceptance_cutoff, covFactor, full_output, journal_file = 4, 100, 1, 0.1, 0.03, 2, 1.0, None
print('APMCABC Inferring')
# We use resultfakeobs1 as our observed dataset
journal_apmcabc = sampler.sample([resultfakeobs1], steps, n_samples,
n_samples_per_param, alpha, acceptance_cutoff,
covFactor, full_output, journal_file)
print(journal_apmcabc.posterior_mean())
journal_apmcabc.save('apmcabc_lorenz_fakeobs1.jrnl')