Drawing from a 2-D prior that is only available as samples in pymc2 - pymc

Question

I'm trying to play around with Bayesian updating, and have a situation in which I am using a posterior from previous runs as a prior. This is a 2D prior on alpha and beta, for which I have traces, alphatrace and betatrace. So I stack them and use code adopted from https://gist.github.com/jcrudy/5911624 to make a KDE based stochastic.
#from https://gist.github.com/jcrudy/5911624
def KernelSmoothing(name, dataset, bw_method=None, observed=False, value=None):
'''Create a pymc node whose distribution comes from a kernel smoothing density estimate.'''
density = gaussian_kde(dataset, bw_method)
def logp(value):
#print "VAL", value
d = density(value)
if d == 0.0:
return float('-inf')
return np.log(d)
def random():
result = None
sample=density.resample(1)
#print sample, sample.shape
result = sample[0][0],sample[1][0]
return result
if value == None:
value = random()
dtype = type(value)
result = pymc.Stochastic(logp = logp,
doc = 'A kernel smoothing density node.',
name = name,
parents = {},
random = random,
trace = True,
value = None,
dtype = dtype,
observed = observed,
cache_depth = 2,
plot = True,
verbose = 0)
return result
Note that the critical thing here is to obtain 2-values from the joint prior: this is why i need a 2-D prior and not two 1-D priors.
The model itself is so:
ctrace=np.vstack((alphatrace, betatrace))
cnew=KernelSmoothing("cnew", ctrace)
#pymc.deterministic
def alphanew(cnew=cnew, name='alphanew'):
return cnew[0]
#pymc.deterministic
def betanew(cnew=cnew, name='betanew'):
return cnew[1]
newtheta=pymc.Beta("newtheta", alphanew, betanew)
newexp = pymc.Binomial('newexp', n=[14], p=[newtheta], value=[4], observed=True)
model3=pymc.Model([cnew, alphanew, betanew, newtheta, newexp])
mcmc3=pymc.MCMC(model3)
mcmc3.sample(20000,5000,5)
In case you are wondering, this is to do the 71st experiment in the hierarchical Rat Tumor example in Chapter 5 in Gelman's BDA. The "prior" I am using is the posterior on alpha and beta after 70 experiments.
But, when I sample, things blow up with the error:
ValueError: Maximum competence reported for stochastic cnew is <= 0... you may need to write a custom step method class.
Its not cnew I care about updating as a stochastic, but rather alphanew and betanew. How ought I be structuring the code to make this error go away?
EDIT: initial model which gave me the posteriors I wish to use as the prior:
tumordata="""0 20
0 20
0 20
0 20
0 20
0 20
0 20
0 19
0 19
0 19
0 19
0 18
0 18
0 17
1 20
1 20
1 20
1 20
1 19
1 19
1 18
1 18
3 27
2 25
2 24
2 23
2 20
2 20
2 20
2 20
2 20
2 20
1 10
5 49
2 19
5 46
2 17
7 49
7 47
3 20
3 20
2 13
9 48
10 50
4 20
4 20
4 20
4 20
4 20
4 20
4 20
10 48
4 19
4 19
4 19
5 22
11 46
12 49
5 20
5 20
6 23
5 19
6 22
6 20
6 20
6 20
16 52
15 46
15 47
9 24
"""
tumortuples=[e.strip().split() for e in tumordata.split("\n")]
tumory=np.array([np.int(e[0].strip()) for e in tumortuples if len(e) > 0])
tumorn=np.array([np.int(e[1].strip()) for e in tumortuples if len(e) > 0])
N = tumorn.shape[0]
mu = pymc.Uniform("mu",0.00001,1., value=0.13)
nu = pymc.Uniform("nu",0.00001,1., value=0.01)
#pymc.deterministic
def alpha(mu=mu, nu=nu, name='alpha'):
return mu/(nu*nu)
#pymc.deterministic
def beta(mu=mu, nu=nu, name='beta'):
return (1.-mu)/(nu*nu)
thetas=pymc.Container([pymc.Beta("theta_%i" % i, alpha, beta) for i in range(N)])
deaths = pymc.Binomial('deaths', n=tumorn, p=thetas, value=tumory, size=N, observed=True)
I use the joint-posterior from this model on alpha, beta as input to the "new model" at top. This also begs the question if I ought to be including theta1..theta70 in the model at top as they will update along with alpha and beta thanks to the new data which is a binomial with n=14, y=4. But I cant even get the little model with only a prior as a 2d sample array working :-(

Answer 1

I found your question since I ran into a similar proble. According to the documentation of pymc.StepMethod.competence, the problem is that none of the built-in samplers handle the dtype associated with the stochastic variable.
I am not sure what needs to be done to actually resolve that. Maybe one of the sampler methods can be extended to handle special types?
Hopefully someone with more pymc mojo can shine a light on what needs to be done..
def competence(s):
"""
This function is used by Sampler to determine which step method class
should be used to handle stochastic variables.
Return value should be a competence
score from 0 to 3, assigned as follows:
0: I can't handle that variable.
1: I can handle that variable, but I'm a generalist and
probably shouldn't be your top choice (Metropolis
and friends fall into this category).
2: I'm designed for this type of situation, but I could be
more specialized.
3: I was made for this situation, let me handle the variable.
In order to be eligible for inclusion in the registry, a sampling
method's init method must work with just a single argument, a
Stochastic object.
If you want to exclude a particular step method from
consideration for handling a variable, do this:
Competence functions MUST be called 'competence' and be decorated by the
'#staticmethod' decorator. Example:
#staticmethod
def competence(s):
if isinstance(s, MyStochasticSubclass):
return 2
else:
return 0
:SeeAlso: pick_best_methods, assign_method
"""