-
Notifications
You must be signed in to change notification settings - Fork 33
/
mpi_pmc_hierarchical_models.py
93 lines (67 loc) · 5.78 KB
/
mpi_pmc_hierarchical_models.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
import numpy as np
def setup_backend():
global backend
from abcpy.backends import BackendMPI as Backend
backend = Backend(process_per_model=2)
"""An example showing how to implement a bayesian network in ABCpy"""
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 social background, depending on school location
from abcpy.continuousmodels import Uniform, Normal
school_location = Uniform([[0.2], [0.3]], )
# The average class size of a certain school
class_size = Normal([[school_location], [0.1]], )
# The social background of a student
background = Normal([[school_location], [0.1]], )
# The grade a student would receive without any bias
grade_without_additional_effects = Normal([[4.5], [0.25]], )
# The grade a student of a certain school receives
final_grade = grade_without_additional_effects-class_size-background
# 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]], )
# A quantity determining whether a student receives a scholarship, including his social background
final_scholarship = scholarship_without_additional_effects + 3*background
# 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.approx_lhd import SynLiklihood
approx_lhd_final_grade = SynLiklihood(statistics_calculator_final_grade)
approx_lhd_final_scholarship = SynLiklihood(statistics_calculator_final_scholarship)
# Define a backend
# from abcpy.backends import BackendDummy as Backend
# backend = Backend()
setup_backend()
# Define a perturbation kernel
from abcpy.perturbationkernel import DefaultKernel
kernel = DefaultKernel([school_location, class_size, grade_without_additional_effects, \
background, scholarship_without_additional_effects])
# Define sampling parameters
T, n_sample, n_samples_per_param = 3, 250, 10
# Define sampler
from abcpy.inferences import PMC
sampler = PMC([final_grade, final_scholarship], \
[approx_lhd_final_grade, approx_lhd_final_scholarship], backend, kernel)
# Sample
journal = sampler.sample([grades_obs, scholarship_obs], T, n_sample, n_samples_per_param)
def analyse_journal(journal):
# output parameters and weights
print(journal.get_stored_output_values())
print(journal.weights)
# do post analysis
print(journal.posterior_mean())
print(journal.posterior_cov())
print(journal.posterior_histogram())
# print configuration
print(journal.configuration)
# save and load journal
journal.save("experiments.jnl")
from abcpy.output import Journal
new_journal = Journal.fromFile('experiments.jnl')
if __name__ == "__main__":
journal = infer_parameters()
analyse_journal(journal)