I am using PyMC3 for parameter estimation using a particular likelihood function which has to be defined. I googled it and found out that I should use the densitydist
method for implementing the user defined likelihood functions but it is not working. How to incorporate a user defined likelihood function in PyMC3 and to find out the maximum a posteriori
(MAP) estimate for my model? My code is given below. Here L
is the analytic form of my Likelihood function. I have some observational data for the radial velocity(vr) and postion (r) for some objects, which is imported from excel file.
data_ = np.array(pandas.read_excel('aaa.xlsx',header=None))
gamma=3.77;
G = 4.302*10**-6;
rmin = 3.0;
R = 95.7;
vr=data_[:,1];
r= data_[:,0];
h= np.pi;
class integrateOut(theano.Op):
def __init__(self,f,t,t0,tf,*args,**kwargs):
super(integrateOut,self).__init__()
self.f = f
self.t = t
self.t0 = t0
self.tf = tf
def make_node(self,*inputs):
self.fvars=list(inputs)
try:
self.gradF = tt.grad(self.f,self.fvars)
except:
self.gradF = None
return theano.Apply(self,self.fvars,[tt.dscalar().type()])
def perform(self,node, inputs, output_storage):
args = tuple(inputs)
f = theano.function([self.t]+self.fvars,self.f)
output_storage[0][0] = quad(f,self.t0,self.tf,args=args)[0]
def grad(self,inputs,grads):
return [integrateOut(g,self.t,self.t0,self.tf)(*inputs)*grads[0] \
for g in self.gradF]
basic_model = pm.Model()
with basic_model:
M=[]
beta=[]
interval=0.01*10**12
M=pm.Uniform('M',
lower=0.5*10**12,upper=3.50*10**12,transform='interval')
beta=pm.Uniform('beta',lower=2.001,upper=2.999,transform='interval')
gamma=3.77
logp=[]
arr=[]
vnew=[]
rnew=[]
theta = tt.scalar('theta')
beta = tt.scalar('beta')
z = tt.cos(theta)**(2*( (gamma/(beta - 2)) - 3/2) + 3)
intZ = integrateOut(z,theta,-(np.pi)/2,(np.pi)/2)(beta)
gradIntZ = tt.grad(intZ,[beta])
funcIntZ = theano.function([beta],intZ)
funcGradIntZ = theano.function([beta],gradIntZ)
for j in np.arange(0,59,1):
vnew.append(vr[j]+(0.05*vr[j]*float(dm.Decimal(rm.randrange(1,
20))/10)));
rnew.append(r[j]+(0.05*r[j]*float(dm.Decimal(rm.randrange(1,
20))/10)));
vn=np.array(vnew)
rn=np.array(rnew)
for beta in np.arange (2.01,2.99,0.01):
for M in np.arange (0.5,2.50,0.01):
i=np.arange(0,59,1)
q =( gamma/(beta - 2)) - 3/2
B = (G*M*10**12)/((beta -2 )*( R**(3 - beta)))
K = (gamma - 3)/((rmin**(3 - gamma))*funcIntZ(beta)*m.sqrt(2*B))
logp= -np.log(K*((1 -(( 1/(2*B) )*((vn[i]**2)*rn[i]**(beta -
2))))**(q+1))*(rn[i]**(1-gamma +(beta/2))))
arr.append(logp.sum())
def logp_func(rn,vn):
return min(np.array(arr))
logpvar = pm.DensityDist("logpvar", logp_func, observed={"rn": rn,"vn":vn})
start = pm.find_MAP(model=basic_model)
step = pm.Metropolis()
basicmodeltrace = pm.sample(10000, step=step,
start=start,random_seed=1,progressbar=True)
print(pm.summary(basicmodeltrace))
map_estimate = pm.find_MAP(model=basic_model)
print(map_estimate)
I am getting the following error message:
ValueError: Cannot compute test value: input 0 (theta) of Op
Elemwise{cos,no_inplace}(theta) missing default value.
Backtrace when that variable is created:
I am unable to get the output since the numerical integration is not working. I have used custom theano op for numerical integration code which i got from Custom Theano Op to do numerical integration . The integration works if I run it seperately inputting a particular value of beta, but not within the model.