Bernoulli regression

Modeling
1

why i have different results in the estimated coefficients?

data {                          
int<lower=0> N;                       // number of observations
int<lower=0,upper=1> y[N];            // setting the dependent variable (damage) as binary
vector[N] x;                          // independent variable 

}
parameters {
real alpha;                           // intercept
real beta;                            // beta for thermal

}

model {
beta ~ normal(0,1);
for (n in 1:N)
      y[n] ~ bernoulli(inv_logit(alpha + beta * x[n]));
}
'

thermal = c(53,57,58,63,66,67,67,67,68,69,70,70,70,70,72,73,75,75,76,76,78,79,81)
damage  = c(1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0)
rings   = data.frame(thermal,damage);head(rings)
data    = list(N = nrow(rings), y = rings$damage, x= rings$thermal)
fit =  stan(model_code = nasa, data = data, iter = 4000, chains = 4,
            seed = sample.int(.Machine$integer.max, 1),
            control = list(max_treedepth = 15))

print(fit, digits = 3)
plot(fit)


fit1 <- stan_glm(damage ~ thermal, data = rings, 
                 family = binomial(link = "logit"))
print(fit1)
}
2

Not sure that this is the only difference, but stan_glm uses different priors than your first model. See here for priors in rstanarm: http://mc-stan.org/rstanarm/reference/priors.html

3

the rstan model is correct for bernoulli regression ?