Hello everybody,

In the last days I have been working with PyMC3. I am new using it and I am interested in make my own model for parameter estimation. Basically, my problem is that I am interested in using a different Likelihood that the ones I have seen PyMC3 has implemented. The Likelihood that I am interested to use is given in “arXiv:astro-ph/0203259”, eq. (35) (see the image).

Here k is the k-dataset at our dispossal, n_k is the number of data inside a k-dataset, $\chi^2_k$ is the chi-square for the k-dataset.

I think I know how to add this kind of likelihoods, it is via pm.DensityDist(). I have been trying to programing it, but I have been having some problems. I am trying to fit a straight line for 3 datasets, first i did it with the typical approximation, which is with a Gaussian-like likelihood, but now I want to use the hyperparameter formalism. Could someone tell my what is the problem in my code? The code basically is:

```
import theano.tensor as T
import theano as TT
def ymodel(a,b,x):
return a+b*x
def chi2(a,b,x,data,sigma2,n):
D = ymodel(a,b,x)-data
sigma2_mat = T.nlinalg.AllocDiag()(sigma2*T.ones(n))
return T.dot(D,T.dot(sigma2_mat,D))
def log_Like1D(a,b,x1,y1,sigma2,n1):
N1 = 1*n1/2+1
return T.log(T.gamma(N1))+N1*(T.log(2)-T.log(chi2(a,b,x1,y1,sigma2,n1)+2))
with pm.Model() as model1:
# Priors for unknown model parameters
a = pm.Uniform('a', lower=-5., upper=5.)
b = pm.Uniform('b', lower=0., upper=4.)
sigma2 = pm.Uniform('sigma', lower = 0.001, upper = 0.5)
Lik = pm.DensityDist('Lik',lambda value: log_Like1D(a,b,x1,y1,sigma2,size)+log_Like1D(a,b,x2,y2,sigma2,size)+log_Like1D(a,b,x3,y3,sigma2,size))
```

But when I do:

```
niter=5000
with model1:
start = pm.find_MAP() #Compute a maximum a posteriori estimates
step = pm.Metropolis()
db = SQLite('H13Dataprue.db')
trace = pm.sample(niter, trace=db, step=step, start=start,njobs=5,temp = 2,thin=50, random_seed=123)
```

I have the following error:

```
ValueError Traceback (most recent call last)
in ()
2 with model1:
3 start = pm.find_MAP() #Compute a maximum a posteriori estimates
----> 4 step = pm.Metropolis()
5 db = SQLite('H13Dataprue.db')
6 trace = pm.sample(niter, trace=db, step=step, start=start,njobs=5,temp = 2,thin=50, random_seed=123)
/home/enriques/Downloads/yes/lib/python2.7/site-packages/pymc3/step_methods/arraystep.pyc in new(cls, *args, **kwargs)
63 # If we don't return the instance we have to manually
64 # call init
---> 65 step.init([var], *args, **kwargs)
66 # Hack for creating the class correctly when unpickling.
67 step.__newargs = ([var], ) + args, kwargs
/home/enriques/Downloads/yes/lib/python2.7/site-packages/pymc3/step_methods/metropolis.pyc in init(self, vars, S, proposal_dist, scaling, tune, tune_interval, model, mode, **kwargs)
134
135 shared = pm.make_shared_replacements(vars, model)
--> 136 self.delta_logp = delta_logp(model.logpt, vars, shared)
137 super(Metropolis, self).init(vars, shared)
138
/home/enriques/Downloads/yes/lib/python2.7/site-packages/pymc3/step_methods/metropolis.pyc in delta_logp(logp, vars, shared)
606 inarray1 = tensor_type('inarray1')
607
--> 608 logp1 = pm.CallableTensor(logp0)(inarray1)
609
610 f = theano.function([inarray1, inarray0], logp1 - logp0)
/home/enriques/Downloads/yes/lib/python2.7/site-packages/pymc3/theanof.pyc in call(self, input)
270 input : TensorVariable
271 """
--> 272 oldinput, = inputvars(self.tensor)
273 return theano.clone(self.tensor, {oldinput: input}, strict=False)
274
ValueError: need more than 0 values to unpack
```

I suppose that it is because I never say to PyMC3 what are my observables. How could I say to PyMC3 which ones are my observanbles? or/and how could I fix this problem?

Thank you for your time,

LP