#model
sd =pymc.Uniform('sd', lower = 5, upper = 100, value = 55.0)
a = pymc.Uniform('a', lower = 0, upper = 100, value = 10.0)
b = pymc.Uniform('b', lower = .05, upper = 2.0, value = .5)
h = pymc.Normal('h', mu = a * Re ** b, tau = sd **-2, value = h_measured, observed = True)
model = (sd, a, b)
#fit
M = pymc.MCMC(model)
M.use_step_method(gs.HMCStep, model, step_size_scaling = .3)
#M.use_step_method(pymc.AdaptiveMetropolis, model) #compare to without HMCStep
M.isample(iter=1000, burn=0, thin=1)
acceptance = M.trace('HMC' + '_acceptr' )()
print mean(acceptance)
#plot
gs.show_samples(gs.plot,a.trace())
gs.show_samples(gs.plot,b.trace())
gs.show_samples(gs.plot,sd.trace())
gs.show_samples(gs.hist,a.trace())
gs.show_samples(gs.hist,b.trace())
gs.show_samples(gs.hist,sd.trace())
pl.figure()
pl.hexbin(a.trace(), b.trace(), gridsize = 30)
pl.show()