With reference to chapter 7 of the book Statistical Rethinking Second Edition by Richard Mcelreath; I am getting a different lppd score using posteriors from Pymc3 and R. For convenience, I have Included all the codes from the book>> R code 7.1 sppnames <-c(“afarensis”,“africanus”,“habilis”,“boisei”, “rudolfensis”,“ergaster”,“sapiens”) brainvolcc <-c(438,452,612,521,752,871,1350) masskg <-c(37.0,35.5,34.5,41.5,55.5,61.0,53.5) d <-data.frame(species=sppnames,brain=brainvolcc,mass=masskg) Book uses R code: R Code 7.3 m7.1 <-quap( alist( brain_std ~dnorm(mu,exp(log_sigma)), mu <-a+b*mass_std, a ~dnorm(0.5,1), b ~dnorm(0,10), log_sigma ~dnorm(0,1) ), data=d) R code 7.13 set.seed(1) lppd( m7.1,n=1e4) We get average lppd score as below for each data point [1] 0.6098668 0.6483438 0.5496093 0.6234934 0.4648143 0.4347605 -0.8444633 And; Below this is my attempt to calculate lppd with pymc3 with pm.Model() as m_1: b_std=pm.Data(‘b_std’,brains[‘brain_std’]) m_std=pm.Data(‘m_std’,brains[‘mass_std’]) a=pm.Normal(‘a’,0.5,1) bM=pm.Normal(‘bM’,0,10) mu=pm.Deterministic(‘mu’,a+bM*m_std) log_sigma=pm.Normal(‘log_sigma’,0,1) brain=pm.Normal(‘brain’,mu=mu,sigma=pm.math.exp(log_sigma),observed=b_std) trace_1=pm.sample(chains=4) posterior_1=pm.sample_posterior_predictive(trace_1,var_names=[‘mu’,‘log_sigma’]) With reference to code (7.14) which has only OLS lppd ; I wrote a similar which calculates lppd from the posteriors. def my_lppd(pred_mu,sigma): rows, cols = pred_mu.shape ll=np.zeros((rows,cols)) for i in range(cols): log_prob=stats.norm.logpdf(brains.brain_std,loc=pred_mu[:,i],scale=sigma[i]) ll[:,i]=log_prob lppd = np.zeros(rows) for i in range(rows): lppd[i] = logsumexp(ll[i])-np.log(cols) return lppd But then I get different lppds, but the ordering is same my_lppd(pred_mu=posterior_1[‘mu’].T,sigma=np.exp(posterior_1[‘log_sigma’])) array([ 0.40075526, 0.42605526, 0.3376496 , 0.41475887, 0.28507802, 0.24066785, -0.61324239]) Am I missing something here? Also, the lppd score gets worse for higher-order regressions. Thanks in advance!

Is there any way to to calculate lppd (pymc3)?

ricardoV94 June 8, 2021, 8:32pm 2

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