Hello. I have ran a simple uni-variate model and would like to do the Bayesian equivalent to a hypothesis test.

The model is below but at a high level, I have a dependent variable ‘claim count’ and predictor ‘repair_letter’. I have fit the model. I am asking guidance on showing the difference in claim count based on if an observation gets a repair letter (variable denoted by a 1 or 0)

```
#model code
model_cod = """
data {
int<lower=0> N;
int<lower=0> clmcnt[N];
vector[N] repair_flag;
}
parameters {
real beta;
}
model {
beta ~ normal(0,1);
clmcnt~poisson_log(repair_flag*beta);
}
"""
sm = StanModel(model_code = model_cod)
data1 = {'N': df_join.shape[0], 'repair_flag':df_join['repair_flag'].values
, 'clmcnt':df_join['clmcnt'].values}
sm_fit = sm.sampling(data = data1, init = .3, chains = 3, iter = 5000, warmup = 1000)
print(sm_fit)
```

Print

```
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
beta -2.81 3.1e-4 0.02 -2.85 -2.82 -2.81 -2.8 -2.77 4067 1.0
lp__ -5.5e6 0.01 0.72 -5.5e6 -5.5e6 -5.5e6 -5.5e6 -5.5e6 4742 1.0
```

Any guidance on analyzing and visualizing would be great.

1 Like

Code your `repair_flag`

variable as `-.5`

and `+.5`

, then you can interpret the beta parameter as the difference. See this lecture.

1 Like

Actually, are you sure you have your model coded as you intend? with `repair_flag`

as a 0/1 coded variable, you’re conveying perfect certainty that the entries coded with 0 have an alpha of 1 (`log(0)`

). I suspect that you want an intercept in your model as well.

ooo. Didn’t think about that. Could you point me to sampling from a posterior as well?

Sorry, I don’t know what you mean.

Here’s your model with an intercept:

```
data {
int<lower=0> N;
int<lower=0> clmcnt[N];
vector[N] repair_flag;
}
parameters {
real intercept;
real beta;
}
model {
intercept ~ normal(0,1);
beta ~ normal(0,1);
clmcnt ~ poisson_log( intercept + repair_flag*beta );
}
```

If you code your repair flag with -.5/+.5, beta will be the difference between conditions and intercept will be the average across conditions. Be sure to modify the priors to convey your actual beliefs.

Thank you. I think i’m trying to do what generated quantities does. Does this look correct?

```
generated quantities {
vector[N_new] y_new;
for (n in 1:N_new)
y_new[n] = poisson_rng(alpha[n] + repair_flag*beta[n])
}
```

This will generate new count observations given the posterior.