Hi all,

I am just beginning to work with mixture models. I have serological data that are negative and non-negative MFI values that range from -67.75 to 2759.50 (n = 1469), that are skewed heavily to the left. The values come from two different processes. I would like to estimate the two distributions using a mixture model. The following model runs fine, rhat and ESS values are good.

```
mix <- mixture(gaussian, gaussian)
prior <- c(prior(normal(0,0.5), Intercept, dpar = mu1),
prior(normal(0,0.5), Intercept, dpar = mu2))
fit <- brm(NiV ~ 1,
data = NiV,
family = mix,
prior = prior,
chains = 1, backend = "cmdstanr")
Family: mixture(gaussian, gaussian)
Links: mu1 = identity; sigma1 = identity; mu2 = identity; sigma2 = identity; theta1 = identity; theta2 = identity
Formula: NiV ~ 1
Data: NiV (Number of observations: 1469)
Draws: 1 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 1000
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
mu1_Intercept 0.04 0.49 -0.88 0.99 1.01 418 437
mu2_Intercept 1.62 0.43 0.80 2.47 1.00 918 381
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma1 521.70 36.56 457.91 594.91 1.01 832 645
sigma2 28.18 0.65 26.98 29.45 1.00 1014 863
theta1 0.07 0.01 0.06 0.09 1.00 724 623
theta2 0.93 0.01 0.91 0.94 1.00 723 623
```

I am at a lost on how to interpret the results. I would like to estimate cutoffs for the original data. For example, is the value 2759.5 in the 80th percentile of mu2? Or what are the cutoffs for mu2 in real terms. To add a little more explanation, mu1 are participants that are negative for a virus and mu2 participants are positive for a virus. I would like to associate the data values to a mu1 or mu2 (negative or positive - high MFI values are positive).

Thanks in advance for your help.

Alan