Greetings all,

I have a rather naive question about CI with zero. As a part of my learning process, I do apply some data of mine to Bayesian framework. In the traditional framework, confidence intervals with zero are stated as ‘non significant’. How about Bayesian Framework? Honestly, I am not sure how to interpret the term ‘non significant’. Does it mean ‘the analysis is all wrong/useless and we should not use it’ or ‘since it is non significant, no relationship between predictors and outcome’. In the second case, how do we explain differences between different predictors?

Meanwhile I applied Neg_binominal:

```
check_distribution(m1)
# Distribution of Model Family
Predicted Distribution of Residuals
Distribution Probability
normal 75%
bernoulli 6%
beta 6%
Predicted Distribution of Response
Distribution Probability
neg. binomial (zero-infl.) 56%
beta-binomial 22%
lognormal 19%
```

For instance;

```
stan_glm(n~ 1 + groups, neg_binomial_2(link = "log"), iter = 10000, QR = TRUE, data = alternation_freq)
describe_posterior(m1, ci = 0.89)
```

```
Parameter | Median | 89% CI | pd | ROPE | % in ROPE | Rhat | ESS
-----------------------------------------------------------------------------------------------------------------
(Intercept) | 4.94 | [ 3.43, 6.80] | 100% | [-0.10, 0.10] | 0% | 1.001 | 7194.00
Group1 | -0.38 | **[-2.86, 2.28]** | 61.91% | [-0.10, 0.10] | 6.47% | 1.001 | 10819.00
Group2 | 1.13 | **[-1.35, 3.72]** | 80.28% | [-0.10, 0.10] | 3.86% | 1.001 | 10686.00
Group3 | 0.01 | [-2.63, 2.48] | 50.43% | [-0.10, 0.10] | 6.68% | 1.000 | 10852.00
Group4 | 0.22 | [-2.42, 2.69] | 56.89% | [-0.10, 0.10] | 6.35% | 1.000 | 10841.00
Group5 | -0.49 | [-3.12, 1.93] | 64.91% | [-0.10, 0.10] | 6.15% | 1.000 | 11083.00
Group6 | -0.18 | [-2.60, 2.42] | 55.92% | [-0.10, 0.10] | 7.14% | 1.001 | 11625.00
Group7 | 0.28 | [-2.16, 2.95] | 58.74% | [-0.10, 0.10] | 6.54% | 1.000 | 10902.00
Group8 | 0.35 | [-2.21, 2.83] | 60.67% | [-0.10, 0.10] | 6.55% | 1.001 | 12263.00
Group9 | -0.28 | [-2.81, 2.26] | 59.14% | [-0.10, 0.10] | 6.71% | 1.001 | 10009.00
Group10 | -0.07 | [-2.68, 2.46] | 52.39% | [-0.10, 0.10] | 6.99% | 1.000 | 10405.00
```