I want to specify an array of random variables where random variable at index i has a sigma that is a function of random variable i-1, for i=2, 3, 4, ... N. I cannot see how to do this in pymc3.Here is my shot at it:
import pymc3 as pm
with pm.Model() as model:
mu=pm.Normal('mu',-10,5)
phi=pm.Beta('phi',1,1)
tausq=pm.InverseGamma('tausq', 0,10000)
tau=pm.Deterministic('tau', pm.math.sqrt(tausq))
h0=pm.Normal('h0', 0,10000)
h=pm.Normal('h',mu+phi*(h0-mu),tau, shape=len(returns))
for i in range(2,len(returns)):
h[i]=pm.Normal('h'+str(i),mu+phi*(h[i-1]-mu), tau)
for i in range(1,len(returns)):
r[i]=pm.Normal('r'+str(i),0, pm.math.exp(h[i]/2), observed=returns[i])
trace_mdl=pm.sample(draws=2000,tune=2000,cores=10,init='adapt_diag')
This fails with error:
Traceback (most recent call last):
File "<ipython-input-7-011e4fcf40bd>", line 11, in <module>
h[i]=pm.Normal('h'+str(i),mu+phi*(h[i-1]-mu), tau)
TypeError: 'FreeRV' object does not support item assignment
I kinda understand that Pymc3 has the model specification component that I'm using here and perhaps I should be using the FreeRV class but that's as far as I can get. FWIW, this is how the original paper says its done in rstan:
parameters {
real mu;
real<lower=0,upper=1> phi;
real<lower=0.01> tausq;
real h0;
vector[T] h;
}
transformed parameters {
real<lower=0> tau;
tau <- sqrt(tausq);
}
model {
mu ~ normal(-10,5);
phi ~ beta(1, 1);
tausq ~ inv_gamma(2.5, 0.025);
h0 ~ normal(0, 10000);
h[1] ~ normal(mu + phi*(h0-mu), tau);
for (t in 2:T)
h[t] ~ normal(mu + phi*(h[t-1]-mu), tau);
for (t in 1:T)
y[t] ~ normal(0,exp(h[t]/2));
}