I am implementing a model which is similar to the stochastic volatility example in the documentation. The model is as follows:

`alpha ~ Normal(mu_alpha, sigma_alpha**2)`

`delta ~ Truncated-Normal(mu_delta, sigma_delta**2, a=-1, b=1)`

`beta_variance ~ InverseGamma(a_2, b_2)`

`stock_variance ~ InverseGamma(a_1, b_2)`

`beta_t ~ Normal( mu= alpha + delta * (beta_t-1 - alpha), beta_variance)`

`returns_obs_t ~ Normal(mu=beta_t * returns_market_t, stock_variance)`

Here is what I have so far:

```
with pm.Model() as model:
beta_variance = pm.InverseGamma('beta_var',1000, 200)
sym_variance = pm.InverseGamma('sym_var', 1000, 100)`
alpha = pm.Normal('steady_state_beta', mu=1.0, sd=10.0)
delta = pm.TruncatedNormal('mean_reversion_coeff', mu=0.3, sd=10.0, a=-1, b=1)
beta = pm.GaussianRandomWalk('beta', mu=alpha + delta * (beta - alpha), sd=math.sqrt(beta_variance), shape = len(returns_df.index))
returns = pm.Normal('stock_returns', mu = returns_df['excess_market'] * beta, sd = math.sqrt(sym_variance), observed = returns_df['excess_symbol', 'excess_market'])
```

Using a deterministic function for the mean of beta seems appropriate but it’s unclear how to combine the two concepts (deterministic functions of the mean of Guassian Random Walk). Any thoughts?