Time-series regression - shape error / Input dimension mis-match

Questions
3

Thank you!

Setting the alpha_zero’s as starting values via init or initval is throwing this error:

TypeError: can’t turn [Subtensor{int64}.0] and {} into a dict. Length of Subtensor{int64}.0 cannot be determined

How can I set the starting point of the time-varying process for the RandomGaussianWalk?
Also I am assuming I don’t need to specify the expected value as the previous alpha, given this is the whole point of the RGW?

I am trying to model the following time-varying process:

\theta_{t} = invlogit(\vec{\alpha_t} * x_{t}+ \beta + Ha)

with values:

\alpha_0 \sim N(0,2), \alpha_t \sim N(\alpha_{t-1},2)

\beta \sim N(0,2), Ha \sim N(0,2)

where \alpha_t are time-varying coefficients, \beta and Ha are constants.

This is my latest code.

def home_intensity_model(data, sample_shape=None):
    with pm.Model(coords={"time": data["timedelta"]}) as model:
        
        
        # how often do we update alpha? 
        # set this to every timedelta/row
        interval = len(data["timedelta"])

        
        # instantiate stochastic RV for global parameters                               
        beta = pm.Normal('beta',mu=0,sigma=np.sqrt(2))
        ha = pm.Normal('Ha',mu=0,sigma=np.sqrt(2))
                                       
        #vector of time varying parameters as random walk
        alpha_zero = pm.Normal("alpha_zero",mu=0,sigma=np.sqrt(2), shape=(sample_shape,1))  

        
        alpha= pm.GaussianRandomWalk("alpha",init=alpha_zero,sigma=np.sqrt(2),shape=(sample_shape,interval))   
        

        
        
        # Finally, define our deterministic prior variable theta
        #To ensure that deterministic variables' values are accumulated during sampling, they should be instantiated 
        #using the named deterministic interface; this uses the Deterministic function to create the variable. 
        #Two things happen when a variable is created this way:
        # 1- The variable is given a name (passed as the first argument)
        # 2- The variable is appended to the model's list of random variables, which ensures that its values are tallied.
       
        theta = pm.Deterministic("theta",pm.invlogit(pm.math.dot(data[pred_cols], alpha)+beta+ha))
        
        
        # finally we define our likelihood, i.e. our sampling distribution of values we are trying to fit
        # our observed thetas are between 0 and 1 but tilted towards 0 
        # try to fit Gamma distribution instead. Note that expected value of Gamma is alpha/beta, so set alpha as our theta and beta=1
        
        
        #now define our likelihood
        Y_obs =pm.Gamma("Y_obs", alpha=theta, beta =1 , observed= data[y])
        
        
        # Can sample and look at distribution of our priors and thetas
        trace = pm.sample(2, chains=1, cores=4)
        pm.traceplot(trace)
        plt.show()
                
    return model