# correlated gaussian
def logp(x, y):
icov = np.linalg.inv(np.array([[1., .8], [.8, 1.]]))
d = np.array([x, y])
return -.5 * np.dot(np.dot(d, icov), d)
#logp_xy = lambda(th): logp(th[0], th[1])
start = {'x': 1., 'y': 1.}
# compare the performance of NUTS and Metropolis by effective sample size
nuts = smp.NUTS(logp, start)
nuts_trace = nuts.sample(1000)
met = smp.Metropolis(logp, start)
met_trace = met.sample(1000)
# compute effective sample size based on autocorrelation
nuts_eff = diagnostics.compute_n_eff_acf(nuts_trace.x)
met_eff = diagnostics.compute_n_eff_acf(met_trace.x)
print("NUTS effective sample size: {:0.2f}".format(nuts_eff))
print("MH effective sample size: {:0.2f}".format(met_eff))
# graphically compare samples
fig, axarr = plt.subplots(1, 2)
axarr[0].scatter(nuts_trace.x, nuts_trace.y)
axarr[0].set_title("NUTS samples")
axarr[1].scatter(met_trace.x, met_trace.y)
axarr[1].set_title("MH samples")
plt.show()
return -.5 * np.dot(np.dot(d, icov), d)
logp_xy = lambda(th): logp(th[0], th[1])
# compare slice samplers, metropolis hastings, and the two variable
# slice sampler
ssamp = smp.Slice(logp, start={'x': 4., 'y': 4.} )
slice_trace = ssamp.sample(1000)
met = smp.Metropolis(logp, start={'x': 4., 'y': 4.})
met_trace = met.sample(1000)
bslice = smp.Slice(logp_xy, start={'th': np.array([4., 4.])})
btrace = bslice.sample(1000)
# compute effective sample size based on autocorrelation
slice_eff = diagnostics.compute_n_eff_acf(slice_trace.x)
met_eff = diagnostics.compute_n_eff_acf(met_trace.x)
b_eff = diagnostics.compute_n_eff_acf(btrace.th[:,0])
print "Slice effective sample size: %2.2f"%slice_eff
print "MH effective sample size: %2.2f"%met_eff
print "two var slice effective sample size: %2.2f"%b_eff
print " ----- "
print "Slice sampler evals per sample: ", ssamp.evals_per_sample
# graphically compare samples
fig, axarr = plt.subplots(1, 3, figsize=(12,4))
axarr[0].scatter(slice_trace.x, slice_trace.y)
axarr[0].set_title("Slice samples")
axarr[1].scatter(met_trace.x, met_trace.y)
axarr[1].set_title("MH samples")
# correlated gaussian
def logp(x, y):
icov = np.linalg.inv(np.array([[1., .8], [.8, 1.]]))
d = np.array([x, y])
return -.5 * np.dot(np.dot(d, icov), d)
#logp_xy = lambda(th): logp(th[0], th[1])
start = {'x': 1., 'y': 1.}
# compare the performance of NUTS and Metropolis by effective sample size
nuts = smp.NUTS(logp, start)
nuts_trace = nuts.sample(1000)
met = smp.Metropolis(logp, start)
met_trace = met.sample(1000)
# compute effective sample size based on autocorrelation
nuts_eff = diagnostics.compute_n_eff_acf(nuts_trace.x)
met_eff = diagnostics.compute_n_eff_acf(met_trace.x)
print("NUTS effective sample size: {:0.2f}".format(nuts_eff))
print("MH effective sample size: {:0.2f}".format(met_eff))
# graphically compare samples
fig, axarr = plt.subplots(1, 2)
axarr[0].scatter(nuts_trace.x, nuts_trace.y)
axarr[0].set_title("NUTS samples")
axarr[1].scatter(met_trace.x, met_trace.y)
axarr[1].set_title("MH samples")
plt.show()
logp_xy = lambda (th): logp(th[0], th[1])
# compare slice samplers, metropolis hastings, and the two variable
# slice sampler
ssamp = smp.Slice(logp, start={'x': 4., 'y': 4.})
slice_trace = ssamp.sample(1000)
met = smp.Metropolis(logp, start={'x': 4., 'y': 4.})
met_trace = met.sample(1000)
bslice = smp.Slice(logp_xy, start={'th': np.array([4., 4.])})
btrace = bslice.sample(1000)
# compute effective sample size based on autocorrelation
slice_eff = diagnostics.compute_n_eff_acf(slice_trace.x)
met_eff = diagnostics.compute_n_eff_acf(met_trace.x)
b_eff = diagnostics.compute_n_eff_acf(btrace.th[:, 0])
print "Slice effective sample size: %2.2f" % slice_eff
print "MH effective sample size: %2.2f" % met_eff
print "two var slice effective sample size: %2.2f" % b_eff
print " ----- "
print "Slice sampler evals per sample: ", ssamp.evals_per_sample
# graphically compare samples
fig, axarr = plt.subplots(1, 3, figsize=(12, 4))
axarr[0].scatter(slice_trace.x, slice_trace.y)
axarr[0].set_title("Slice samples")
axarr[1].scatter(met_trace.x, met_trace.y)
axarr[1].set_title("MH samples")