 # Combining AR/Negative Binomial with Gaussian Random Walk

Hello,

First of all thank you to everyone who spends their time developing and maintaining this fantastic library! I’ve been trying to implement my first Bayesian model and I’ve become stuck. The original idea was to implement the paper cited in this post: Vectorized autoregressive model

However, my data is unstationary and highly dependent on time, and also is divided into categories, so I thought to utilize the GaussianRandomWalk as seen here: https://twiecki.io/blog/2017/03/14/random-walk-deep-net/

Here is my best attempt, drawing heavily from those two sources:

``````with  pm.Model() as stochastic_model:
#global hyperprior for alpha parameter used in Negative Binomial
alpha = pm.Uniform("alpha", lower=0.001, upper=0.1)
#attemping to make coefficients that depend on time
step_size = pm.HalfNormal('step_size', sd=np.ones(df.shape), shape=df.shape)
w = pm.GaussianRandomWalk('w', sd=step_size, shape=(df.shape, df.shape))
#hyperpriors for the precision, tau
kappa_tau = pm.Uniform("kappa_tau", lower=5, upper=10)
beta_tau = pm.Uniform("beta_tau", lower=2, upper=25)
tau_l = pm.Gamma("tau_l", kappa_tau, beta_tau, shape=df.shape)
alpha_l = pm.Exponential("alpha_l", alpha, shape=df.shape)
#The class AR2d comes from the first link above that allows pm.AR to accept multidimensional rho
eta_l = AR2d("eta_l", rho=w, tau=tau_l, constant=False,shape=(df.shape,df.shape))
y_t_l = pm.NegativeBinomial("y_t_l", tt.exp(eta_l), alpha_l, observed=df)

trace = pm.sample(5000, cores=4)
``````

My dataframe is 101 rows and 5 columns (time series with 101 observations of counts data for 5 different categories) and I hope to bring in more categories eventually. The sampling did not converge (“The chain contains only diverging samples. The model is probably misspecified”) and acceptance probabilities were rounding errors from 0. I’m trying to understand if the problem is in the ranges I choose for hyperpriors, whether the priors should be different distributions, if I’m getting the shape wrong in some instances, or if the model is conceptually flawed.