Hello! Iβm fitting the data using two component mixture model `ππ ~ πΎπππ(.|πππ)+ πΎπππ(.|πππ)`

. Where `π0π`

and `π1π`

represent the mixing probability, and `π(.|π)`

represent the Poisson distribution. After I pass through some processes using Stan package, I got like the following output:

yi | W1i |
---|---|

5 | 0.4 |

2 | 0.7 |

10 | 0.6 |

2 | 0.4 |

Finally, I define the new latent variable `ππ, π = 1,β¦,π`

that indicates the category of observation group, i.e., whether it is in the first or second category. The indicator variable has two outcomes (0 and 1), and it follows Bernoulli distribution, ππ~π΅πππππ’πππ(π1π), for π = 1, 2,β¦, π and it is concluded that the observation π is in the second group (I call it significant observations) whenever π(ππ = 1|π) is bigger than a cutoff value, say 0.5.

my question is that:

**is it need to use statistical significance or FDR to select significant observations, instead of using one ad hoc number (cutoff of the posterior probability of π1π > 0.5)?**