def statistic_convergence(nsamples=5000,ncomputepoints=50,nruns=50,ndims=10):
# get samples
data = np.zeros((ndims,ndims))
data[np.roll(np.arange(ndims//2),1),np.arange(ndims//2)] = 10 # fill half the dims with data
alpha = 2. # Dirichlet prior hyperparameter
beta = 160. # MH proposal distribution parameter, set so acceptance rate is about 0.24 with ndims=10
mhsamples, auxsamples = map(np.array,
sampling.load_or_run_samples(nruns,nsamples,alpha,beta,data))
# compute statistics
(mhmeans, mhvars), (mh_truemean, mh_truevar), (mh_mean_ds, mh_var_ds) = \
tests.get_statistic_convergence(mhsamples,ncomputepoints)
(auxmeans, auxvars), (aux_truemean, aux_truevar), (aux_mean_ds, aux_var_ds) = \
tests.get_statistic_convergence(auxsamples,ncomputepoints)
# check that the estimated "true" statistics agree
assert ((mh_truemean - aux_truemean)**2).sum() < 1e-5 \
and ((mh_truevar - aux_truevar)**2).sum() < 1e-5
# get time scaling
aux_timing = timing.get_auxvar_timing(data=data,alpha=alpha)
mh_timing = timing.get_mh_timing(data=data,beta=beta,alpha=alpha)
# plot
for samplerds, statisticname in zip(((aux_mean_ds,mh_mean_ds),(aux_var_ds,mh_var_ds)),('mean','variance')):
# sample index scaling
plt.figure()
for ds, samplername, color in zip(samplerds, ['Aux. Var.','MH'],['b','g']):
plt.plot(np.array(tests.chunk_indices(nsamples,ncomputepoints)),
ds.mean(0),color+'-',label='%s Sampler' % samplername)
plt.plot(np.array(tests.chunk_indices(nsamples,ncomputepoints)),
scoreatpercentile(ds,per=10,axis=0),color+'--')
plt.plot(np.array(tests.chunk_indices(nsamples,ncomputepoints)),
scoreatpercentile(ds,per=90,axis=0),color+'--')
plt.legend()
plt.xlabel('sample index')
plt.title('%s Convergence' % statisticname.capitalize())
save('../writeup/figures/statisticconvergence_%dD_%s.pdf' % (ndims,statisticname))
# time scaling
plt.figure()
for ds, samplername, color, timescaling in zip(samplerds, ['Aux. Var.','MH'],['b','g'],
(aux_timing,mh_timing)):
plt.plot(np.array(tests.chunk_indices(nsamples,ncomputepoints))*timescaling,
ds.mean(0),color+'-',label='%s Sampler' % samplername)
plt.plot(np.array(tests.chunk_indices(nsamples,ncomputepoints))*timescaling,
scoreatpercentile(ds,per=10,axis=0),color+'--')
plt.plot(np.array(tests.chunk_indices(nsamples,ncomputepoints))*timescaling,
scoreatpercentile(ds,per=90,axis=0),color+'--')
plt.legend()
plt.xlabel('seconds')
plt.title('%s Convergence' % statisticname.capitalize())
save('../writeup/figures/statisticconvergence_timescaling_%dD_%s.pdf' % (ndims,statisticname))
def autocorrelation(nsamples=1000,nruns=50,ndims=10):
# get samples
data = np.zeros((ndims,ndims))
data[np.roll(np.arange(ndims//2),1),np.arange(ndims//2)] = 10 # fill half the dims with data
alpha = 2. # Dirichlet prior hyperparameter
beta = 160. # MH proposal distribution parameter, set so acceptance rate is about 0.24 with ndims=10
mhsamples, auxsamples = map(np.array,
sampling.load_or_run_samples(nruns,nsamples,alpha,beta,data))
# compute autocorrelations
aux_corrs = tests.get_autocorr(auxsamples)
mh_corrs = tests.get_autocorr(mhsamples)
# plot
for component, ordinalname in zip([0,1],['first','second']):
plt.figure()
for corrs, samplername, color in zip([aux_corrs, mh_corrs],['Aux. Var.','MH'],['b','g']):
plt.plot(corrs.mean(0)[:,component],color+'-',label='%s Sampler' % samplername)
plt.plot(scoreatpercentile(corrs[...,component],per=10,axis=0),color+'--')
plt.plot(scoreatpercentile(corrs[...,component],per=90,axis=0),color+'--')
plt.legend()
plt.xlabel('lag')
plt.xlim(0,np.where(mh_corrs.mean(0)[:,component] < 0.01)[0][0])
plt.title('%s Component Autocorrelations' % ordinalname.capitalize())
save('../writeup/figures/autocorrelations_%dD_%s.pdf' % (ndims,ordinalname))
def Rhatp(nsamples=1000,ncomputepoints=25,nruns=50,ndims=10):
# get samples
data = np.zeros((ndims,ndims))
data[np.roll(np.arange(ndims//2),1),np.arange(ndims//2)] = 10 # fill half the dims with data
alpha = 2. # Dirichlet prior hyperparameter
beta = 160. # MH proposal distribution parameter, set so acceptance rate is about 0.24 with ndims=10
mhsamples, auxsamples = map(np.array,
sampling.load_or_run_samples(nruns,nsamples,alpha,beta,data))
# get Rhatps
aux_R = tests.get_Rhat(auxsamples,ncomputepoints=ncomputepoints)
mh_R = tests.get_Rhat(mhsamples,ncomputepoints=ncomputepoints)
### plot without time scaling
plt.figure()
# plt.subplot(2,1,1)
plt.plot(tests.chunk_indices(nsamples,ncomputepoints),aux_R,'bx-',label='Aux. Var. Sampler')
plt.plot(tests.chunk_indices(nsamples,ncomputepoints),mh_R,'gx-',label='MH Sampler')
plt.ylim(0,1.1*mh_R.max())
plt.xlim(0,1000)
plt.xlabel('sample index')
plt.legend()
plt.title('MH and Aux. Var. Samplers MSPRF vs Sample Indices')
# plt.subplot(2,1,2)
# plt.plot(tests.chunk_indices(nsamples,ncomputepoints),aux_R,'bx-')
# plt.ylim(0,1.1*aux_R.max())
# plt.xlim(0,closeindex)
# plt.xlabel('sample index')
# plt.title('Aux. Var. Sampler MSPRF vs Sample Indices')
save('../writeup/figures/MSPRF_sampleindexscaling_%dD.pdf' % ndims)
### plot with time scaling
plt.figure()
# compute time per sample
aux_timing = timing.get_auxvar_timing(data=data,alpha=alpha)
mh_timing = timing.get_mh_timing(data=data,beta=beta,alpha=alpha)
plt.plot(np.array(tests.chunk_indices(nsamples,ncomputepoints))*aux_timing,
aux_R,'bx-',label='Aux. Var. Sampler')
plt.plot(np.array(tests.chunk_indices(nsamples,ncomputepoints))*mh_timing,
mh_R,'gx-',label='MH Sampler')
plt.ylim(0,1.1*mh_R.max())
plt.xlim(0,mh_timing*nsamples)
plt.xlabel('seconds')
plt.legend()
plt.title('MH and Aux. Var. Sampler MSPRF vs Computation Time')
save('../writeup/figures/MSPRF_timescaling_%dD.pdf' % ndims)