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July 19, 2016 22:07
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toy example of MCMC using (py)stan and (py)spark
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data { | |
int<lower=0> J; // number of schools | |
real y[J]; // estimated treatment effects | |
real<lower=0> sigma[J]; // s.e. of effect estimates | |
} | |
parameters { | |
real mu; | |
real<lower=0> tau; | |
real eta[J]; | |
} | |
transformed parameters { | |
real theta[J]; | |
for (j in 1:J) | |
theta[j] = mu + tau * eta[j]; | |
} | |
model { | |
eta ~ normal(0, 1); | |
y ~ normal(theta, sigma); | |
} |
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from pyspark import SparkContext, SparkConf | |
import pystan | |
import numpy as np | |
## TODO any advantage in compiling stan model once? possibly for local execution but maybe less for distributed mode. | |
## TODO how to decide which parameters to aggregate? all? for multiple parameters, make each parameter a key and reduceByKey. | |
## TODO Here I sometimes assume that parameter theta is 1-dimensional. | |
## TODO how to get prior covariances? | |
## 4.1: http://arxiv.org/pdf/1602.05221v2.pdf | |
appName = "ExampleConcensusMCMC" | |
SCHOOL_DATA = zip( | |
[28, 8, -3, 7, -1, 1, 18, 12], # y | |
[15, 10, 16, 11, 9, 11, 10, 18]) # sigma | |
if __name__ == "__main__": | |
def mcmc(sts): | |
## do MCMC... | |
sts = list(sts) | |
schools_dat = {'J': len(sts), # different J here! | |
'y': [d[0] for d in sts], | |
'sigma': [d[1] for d in sts]} | |
fit = pystan.stan(file="schools.stan", data=schools_dat, | |
iter=1000, chains=4) | |
return [np.array(fit["mu"])] | |
def consensus_avg(J): | |
## this was not designed to be a pairwse operation | |
## so it's a bit ugly | |
def c(f1, f2): | |
if np.isnan(f1).any() and np.isnan(f2).any(): | |
return 0 | |
if np.isnan(f1).any(): | |
return f2 | |
if np.isnan(f2).any(): | |
return f1 | |
# I ignore the prior covariance and assume theta is 1-d | |
# problem: need to know how many partitions there are | |
sigma_j = np.zeros(2) | |
fs = [f1, f2] | |
for j in [0, 1]: | |
sigma_j[j] = np.cov(fs[j]) | |
sigma = 1.0/(sum(1.0/(sigma_j))) | |
w_j = np.zeros(2) | |
for j in [0, 1]: | |
w_j[j] = sigma * (1/J + 1.0/sigma_j[j]) | |
return w_j[0] * f1 + w_j[1] * f2 | |
return c | |
conf = SparkConf().setAppName(appName) | |
sc = SparkContext(conf=conf) | |
subposteriors = sc.parallelize(SCHOOL_DATA, 3).mapPartitions(mcmc) | |
consensusSamples = subposteriors.reduce( | |
consensus_avg(subposteriors.getNumPartitions())) | |
print "----" | |
print "Combined posterior samples:" | |
print consensusSamples | |
print "----" |
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in case anybody every looks at this: I've started to turn this into more of a library: https://github.com/strongh/stark