import pymc as mc
import pandas
import numpy as np

cpus = pandas.read_csv('cpus.csv') # from R's MASS package - available in gist c212194ecbd2ee050192
cpus.head()

	name	syct	mmin	mmax	cach	chmin	chmax	perf	estperf
0	ADVISOR 32/60	125	256	6000	256	16	128	198	199
1	AMDAHL 470V/7	29	8000	32000	32	8	32	269	253
2	AMDAHL 470/7A	29	8000	32000	32	8	32	220	253
3	AMDAHL 470V/7B	29	8000	32000	32	8	32	172	253
4	AMDAHL 470V/7C	29	8000	16000	32	8	16	132	132

with mc.Model() as model:
    mc.glm.glm('perf ~ syct + mmin + mmax + cach + chmin + chmax', cpus)
    trace = mc.sample(200, mc.NUTS())

 [-----------------100%-----------------] 200 of 200 complete in 1.9 sec

class Laplace(mc.glm.families.Family):
    sm_family = mc.glm.families.Gaussian # TODO: check into the correct sm_family
    link = mc.glm.families.Identity
    likelihood = mc.Laplace
    parent = 'mu'
    priors = {'b': ('sigma', mc.Uniform.dist(0, 100))}

with mc.Model() as model_laplace:
    mc.glm.glm('perf ~ syct + mmin + mmax + cach + chmin + chmax', cpus, family=Laplace())
    trace_laplace = mc.sample(200, mc.NUTS())
# note: quite slow, so only 200 samples for now

 [-----------------100%-----------------] 201 of 200 complete in 9597.9 sec

for v in trace.varnames:
    print '{v}:\n\tNormal:\t{normal}\n\tLaplace:\t{laplace}'.format(v=v, normal=np.mean(trace.samples[v].vals), laplace=np.mean(trace_laplace.samples[v].vals))

Intercept:
	Normal: 	-55.8440754817
	Laplace:	-20.2074181573
syct:
	Normal: 	0.0486123276765
	Laplace:	0.0153899700386
mmin:
	Normal: 	0.0154247020762
	Laplace:	0.0155863267598
mmax:
	Normal: 	0.00556234346402
	Laplace:	0.00346221718791
cach:
	Normal: 	0.635439823768
	Laplace:	0.567473469829
chmin:
	Normal: 	-0.276933454985
	Laplace:	2.08713603599
chmax:
	Normal: 	1.49145192411
	Laplace:	0.360122961875
sigma:
	Normal: 	60.0888469755
	Laplace:	37.9504574424