Implement beta_oddsratio

This commit is contained in:
RunasSudo 2022-10-07 16:52:51 +11:00
parent d3842e1645
commit cbb79207ae
Signed by: RunasSudo
GPG Key ID: 7234E476BF21C61A
3 changed files with 235 additions and 11 deletions

View File

@ -0,0 +1,94 @@
# scipy-yli: Helpful SciPy utilities and recipes
# Copyright © 2022 Lee Yingtong Li (RunasSudo)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
import numpy as np
from scipy import stats
import yli
def test_beta_ratio_cdf_vs_empirical():
"""Compare beta_ratio.cdf with empirical distribution"""
# Define the example beta distribution
beta1 = stats.beta(3, 6)
beta2 = stats.beta(12, 7)
dist = yli.beta_oddsratio.from_scipy(beta1, beta2)
# Compute empirical distribution
samples_p1 = beta1.rvs(10_000, random_state=31415)
samples_p2 = beta2.rvs(10_000, random_state=92653)
sample = (samples_p1 / (1 - samples_p1)) / (samples_p2 / (1 - samples_p2))
# Values to check
x = np.linspace(0, 2, 10)
y1 = dist.cdf(x)
y2 = [(sample < xx).sum()/sample.size for xx in x]
# Allow 0.01 tolerance
assert (np.abs(y1 - y2) < 0.01).all()
def test_beta_ratio_ppf_vs_empirical():
"""Compare beta_ratio.ppf with empirical distribution"""
# Define the example beta distribution
beta1 = stats.beta(3, 6)
beta2 = stats.beta(12, 7)
dist = yli.beta_oddsratio.from_scipy(beta1, beta2)
# Compute empirical distribution
samples_p1 = beta1.rvs(10_000, random_state=31415)
samples_p2 = beta2.rvs(10_000, random_state=92653)
sample = (samples_p1 / (1 - samples_p1)) / (samples_p2 / (1 - samples_p2))
# Values to check
x = np.linspace(0, 0.9, 10)
y1 = dist.ppf(x)
y2 = np.quantile(sample, x)
# Allow 0.01 tolerance
assert (np.abs(y1 - y2) < 0.01).all()
def test_beta_ratio_mean_vs_empirical():
"""Compare beta_ratio.mean (vs _munp) with empirical mean"""
# Define the example beta distribution
beta1 = stats.beta(3, 6)
beta2 = stats.beta(12, 7)
dist = yli.beta_oddsratio.from_scipy(beta1, beta2)
# Compute empirical mean
samples_p1 = beta1.rvs(10_000, random_state=31415)
samples_p2 = beta2.rvs(10_000, random_state=92653)
sample = (samples_p1 / (1 - samples_p1)) / (samples_p2 / (1 - samples_p2))
# Allow 0.01 tolerance
assert np.abs(dist.mean() - sample.mean()) < 0.01
def test_beta_ratio_var_vs_empirical():
"""Compare beta_ratio.var (vs _munp) with empirical variance"""
# Define the example beta distribution
beta1 = stats.beta(3, 6)
beta2 = stats.beta(12, 7)
dist = yli.beta_oddsratio.from_scipy(beta1, beta2)
# Compute empirical mean
samples_p1 = beta1.rvs(10_000, random_state=31415)
samples_p2 = beta2.rvs(10_000, random_state=92653)
sample = (samples_p1 / (1 - samples_p1)) / (samples_p2 / (1 - samples_p2))
# Allow 0.01 tolerance
assert np.abs(dist.var() - sample.var()) < 0.01

View File

@ -15,6 +15,7 @@
# along with this program. If not, see <https://www.gnu.org/licenses/>. # along with this program. If not, see <https://www.gnu.org/licenses/>.
import numpy as np import numpy as np
from scipy import stats
import yli import yli
@ -30,7 +31,7 @@ def test_beta_ratio_vs_jsaffer_pdf():
y = dist.pdf(x) y = dist.pdf(x)
# Compare with expected values from jsaffer implementation # Compare with expected values from jsaffer implementation
expected = np.load('beta_ratio_vs_jsaffer.npy', allow_pickle=False)[0] expected = np.load('tests/beta_ratio_vs_jsaffer.npy', allow_pickle=False)[0]
# Allow 1e-10 tolerance # Allow 1e-10 tolerance
diff = np.abs(y - expected) diff = np.abs(y - expected)
@ -48,7 +49,7 @@ def test_beta_ratio_vs_jsaffer_cdf():
y = dist.cdf(x) y = dist.cdf(x)
# Compare with expected values from jsaffer implementation # Compare with expected values from jsaffer implementation
expected = np.load('beta_ratio_vs_jsaffer.npy', allow_pickle=False)[1] expected = np.load('tests/beta_ratio_vs_jsaffer.npy', allow_pickle=False)[1]
# Allow 1e-10 tolerance # Allow 1e-10 tolerance
diff = np.abs(y - expected) diff = np.abs(y - expected)
@ -65,16 +66,36 @@ def _gen_beta_ratio_vs_jsaffer():
y1 = np.vectorize(lambda w: float(beta_quotient_distribution.pdf_bb_ratio(a1, a2, b1, b2, w)))(x) y1 = np.vectorize(lambda w: float(beta_quotient_distribution.pdf_bb_ratio(a1, a2, b1, b2, w)))(x)
y2 = np.vectorize(lambda w: float(beta_quotient_distribution.cdf_bb_ratio(a1, a2, b1, b2, w)))(x) y2 = np.vectorize(lambda w: float(beta_quotient_distribution.cdf_bb_ratio(a1, a2, b1, b2, w)))(x)
np.save('beta_ratio_vs_jsaffer.npy', np.array([y1, y2]), allow_pickle=False) np.save('tests/beta_ratio_vs_jsaffer.npy', np.array([y1, y2]), allow_pickle=False)
def test_beta_ratio_mean_vs_empirical(): def test_beta_ratio_mean_vs_empirical():
"""Compare beta_ratio.mean (via beta_ratio._munp) with empirical mean""" """Compare beta_ratio.mean (via beta_ratio._munp) with empirical mean"""
# Define the example beta distribution # Define the example beta distribution
dist = yli.beta_ratio(3, 6, 12, 7) beta1 = stats.beta(3, 6)
beta2 = stats.beta(12, 7)
dist = yli.beta_ratio.from_scipy(beta1, beta2)
# Compute empirical mean # Compute empirical distribution
sample = dist.rvs(1000, random_state=31415) samples_p1 = beta1.rvs(10_000, random_state=31415)
samples_p2 = beta2.rvs(10_000, random_state=92653)
sample = samples_p1 / samples_p2
# Allow 0.01 tolerance # Allow 0.01 tolerance
assert np.abs(dist.mean() - sample.mean()) < 0.01 assert np.abs(dist.mean() - sample.mean()) < 0.01
def test_beta_ratio_var_vs_empirical():
"""Compare beta_ratio.var (via beta_ratio._munp) with empirical variance"""
# Define the example beta distribution
beta1 = stats.beta(3, 6)
beta2 = stats.beta(12, 7)
dist = yli.beta_ratio.from_scipy(beta1, beta2)
# Compute empirical distribution
samples_p1 = beta1.rvs(10_000, random_state=31415)
samples_p2 = beta2.rvs(10_000, random_state=92653)
sample = samples_p1 / samples_p2
# Allow 0.01 tolerance
assert np.abs(dist.var() - sample.var()) < 0.01

View File

@ -16,7 +16,7 @@
import mpmath import mpmath
import numpy as np import numpy as np
from scipy import optimize, stats from scipy import integrate, optimize, stats
import collections import collections
@ -30,6 +30,8 @@ class betarat_gen(stats.rv_continuous):
2. Weekend Editor. On the ratio of Beta-distributed random variables. Some Weekend Reading. 2021 Sep 13. https://www.someweekendreading.blog/beta-ratios/ 2. Weekend Editor. On the ratio of Beta-distributed random variables. Some Weekend Reading. 2021 Sep 13. https://www.someweekendreading.blog/beta-ratios/
""" """
# TODO: _rvs based on stats.beta
def from_scipy(self, beta1, beta2): def from_scipy(self, beta1, beta2):
"""Construct a new beta_ratio distribution from two SciPy beta distributions""" """Construct a new beta_ratio distribution from two SciPy beta distributions"""
return self(*beta1.args, *beta2.args) return self(*beta1.args, *beta2.args)
@ -84,14 +86,121 @@ class betarat_gen(stats.rv_continuous):
def _munp_one(self, k, a1, b1, a2, b2): def _munp_one(self, k, a1, b1, a2, b2):
"""Moments of the distribution, given by Weekend Editor""" """Moments of the distribution, given by Weekend Editor"""
term1 = mpmath.rf(a1, k) / mpmath.rf(a1 + b1, k) term1 = mpmath.rf(a1, k) * mpmath.rf(a2 + b2 - k, k)
term2 = mpmath.rf(a2 + b2 - k, k) / mpmath.rf(a2 - k, k) term2 = mpmath.rf(a1 + b1, k) * mpmath.rf(a2 - k, k)
return float(term1 * term2) return float(term1 / term2)
def _munp(self, k, a1, b1, a2, b2): def _munp(self, k, a1, b1, a2, b2):
return self._do_vectorized(self._munp_one, k, a1, b1, a2, b2) return self._do_vectorized(self._munp_one, k, a1, b1, a2, b2)
beta_ratio = betarat_gen(name='beta_ratio', a=0) beta_ratio = betarat_gen(name='beta_ratio', a=0) # a = lower bound of support
class betaoddsrat_gen(stats.rv_continuous):
"""
Ratio of the odds of 2 independent beta-distributed variables
Ratio of (X/(1-X)) / (Y/(1-Y)), where X ~ Beta(a1, b1), Y ~ Beta(a2, b2)
Reference:
Hora SC, Kelley GD. Bayesian inference on the odds and risk ratios. Communications in Statistics: Theory and Methods. 1983;12(6):72538. doi: 10.1080/03610928308828491
"""
# TODO: _rvs based on stats.beta
def from_scipy(self, beta1, beta2):
"""Construct a new beta_ratio distribution from two SciPy beta distributions"""
return self(*beta1.args, *beta2.args)
def _do_vectorized(self, func, x, a1, b1, a2, b2):
"""Helper function to call the implementation over potentially multiple values"""
x = np.atleast_1d(x)
result = np.zeros(x.size)
for i, (x_, a1_, b1_, a2_, b2_) in enumerate(zip(x, np.pad(np.atleast_1d(a1), x.size, 'edge'), np.pad(np.atleast_1d(b1), x.size, 'edge'), np.pad(np.atleast_1d(a2), x.size, 'edge'), np.pad(np.atleast_1d(b2), x.size, 'edge'))):
result[i] = func(x_, a1_, b1_, a2_, b2_)
return result
def _pdf_one(self, w, a1, b1, a2, b2):
"""PDF for the distribution, given by Hora & Kelley"""
if w <= 0:
return 0
elif w < 1:
term1 = mpmath.beta(a1 + a2, b1 + b2) / (mpmath.beta(a1, b1) * mpmath.beta(a2, b2))
term2 = mpmath.power(w, a1 - 1)
term3 = mpmath.hyp2f1(a1 + b1, a1 + a2, a1 + a2 + b1 + b2, 1 - w)
else:
term1 = mpmath.beta(a1 + a2, b1 + b2) / (mpmath.beta(a1, b1) * mpmath.beta(a2, b2))
term2 = mpmath.power(w, -a2 - 1)
term3 = mpmath.hyp2f1(a2 + b2, a1 + a2, a1 + a2 + b1 + b2, 1 - mpmath.power(w, -1))
return float(term1 * term2 * term3)
def _pdf(self, w, a1, b1, a2, b2):
return self._do_vectorized(self._pdf_one, w, a1, b1, a2, b2)
def _cdf(self, w, a1, b1, a2, b2):
"""CDF for the distribution, computed by integrating the PDF"""
w = np.atleast_1d(w)
a1 = np.atleast_1d(a1)
b1 = np.atleast_1d(b1)
a2 = np.atleast_1d(a2)
b2 = np.atleast_1d(b2)
if not ((a1 == a1[0]).all() and (b1 == b1[0]).all() and (a2 == a2[0]).all() and (b2 == b2[0]).all()):
raise ValueError('Cannot compute CDF from different distributions')
if w.size == 1:
if w <= 0:
return 0
# Just compute an integral
if w < self.mean(a1, b1, a2, b2):
# Integrate normally
return integrate.quad(lambda x: self._pdf_one(x, a1[0], b1[0], a2[0], b2[0]), 0, w)[0]
else:
# Integrate on the distribution of 1/w (much faster)
return 1 - integrate.quad(lambda x: self._pdf_one(x, a2[0], b2[0], a1[0], b1[0]), 0, 1/w)[0]
else:
# Multiple points requested: use ODE solver
solution = integrate.solve_ivp(lambda x, _: self._pdf_one(x, a1[0], b1[0], a2[0], b2[0]), (0, w.max()), [0], t_eval=w, method='LSODA', rtol=1.5e-8, atol=1.5e-8)
return solution.y
def _ppf_one(self, p, a1, b1, a2, b2):
"""PPF for the distribution, using Newton's method"""
# Default SciPy implementation uses Brent's method
# This one is a bit faster
if p <= 0:
return 0
# Initial guess based on log-normal approximation
mean = self.mean(a1, b1, a2, b2)
se_log = self.std(a1, b1, a2, b2)/mean
initial_guess = np.exp(np.log(mean) + stats.norm.ppf(p) * se_log)
try:
return optimize.newton(lambda x: self.cdf(x, a1, b1, a2, b2) - p, x0=initial_guess, fprime=lambda x: self.pdf(x, a1, b1, a2, b2))
except RuntimeError:
# Failed to converge with Newton's method :(
# Use Brent's method instead
return super()._ppf(p, a1, b1, a2, b2)
def _ppf(self, p, a1, b1, a2, b2):
return self._do_vectorized(self._ppf_one, p, a1, b1, a2, b2)
def _munp_one(self, k, a1, b1, a2, b2):
"""Moments of the distribution, given by Hora & Kelley"""
term1 = mpmath.rf(a1, k) * mpmath.rf(b2, k)
term2 = mpmath.rf(b1 - k, k) * mpmath.rf(a2 - k, k)
return float(term1 / term2)
def _munp(self, k, a1, b1, a2, b2):
return self._do_vectorized(self._munp_one, k, a1, b1, a2, b2)
beta_oddsratio = betaoddsrat_gen(name='beta_oddsratio', a=0) # a = lower bound of support
ConfidenceInterval = collections.namedtuple('ConfidenceInterval', ['lower', 'upper']) ConfidenceInterval = collections.namedtuple('ConfidenceInterval', ['lower', 'upper'])