 Operating System: Windows 10
 brms Version: 2.9.0
Dear all,
Problem:

I performed a series of Bayesian MLM analyses on difference scores using
brms.
I evaluated my models using posterior predictive checks viapp_check()
, indicating kurtosis and skew in my data, both of which not captured by my models. 
My first impression is that this discrepancy could be potentially tackled by changing the family from Gaussian to sth like (skewed) hyperbolic secant. I might be wrong though.
Questions:
 What is your take on this?
 How would you tackle these discrepancies?
Posterior predictive checks:
General model details + context:
Family: gaussian
Links: mu = identity; sigma = identity
Formula: BetaDiff ~ 0 + intercept + VisROI + (1 + VisROI  ID)
Data: Data[Data$Contrasts == CurrContrast & Data$Area == (Number of observations: 20381)
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total postwarmup samples = 4000
 BetaDiff: Differential brain activity
 VisROI: Visual field region of interest (i.e. a particular subregion of the visual field); categorical with 4 levels: segments, corners, background, center; dummycoded with â€śsegmentsâ€ť as a reference category
 ID: Participant ID with 5 levels corresponding to 5 human observers
 The number of data points for each observer per level of VisROI is at minimum 10 but can be as much as ~3600
 The above model specs were used to fit 6 models, one for each contrast of interest (i.e. D vs Fix, ND vs Fix, D vs ND) and brain area (i.e., V1, V2). D and ND reflect different precepts of a visual stimulus and Fix is a fixation baseline where the stimulus was not presented
Priors
> prior_summary(ListFits$ListModels$Segments$`D vs Fix`$V1)
prior class coef group resp dpar nlpar bound
1 b
2 normal( 0,7) b intercept
3 normal( 0,7) b VisROIBackground
4 normal( 0,7) b VisROICenter
5 normal( 0,7) b VisROICorners
6 lkj_corr_cholesky(4) L
7 L ID
8 normal(0, 5) sd
9 sd ID
10 sd Intercept ID
11 sd VisROIBackground ID
12 sd VisROICenter ID
13 sd VisROICorners ID
14 normal(0, 5) sigma
> prior_summary(ListFits$ListModels$Segments$`D vs ND`$V1)
prior class coef group resp dpar nlpar bound
1 b
2 normal( 0,3) b intercept
3 normal( 0,3) b VisROIBackground
4 normal( 0,3) b VisROICenter
5 normal( 0,3) b VisROICorners
6 lkj_corr_cholesky(4) L
7 L ID
8 normal(0, 5) sd
9 sd ID
10 sd Intercept ID
11 sd VisROIBackground ID
12 sd VisROICenter ID
13 sd VisROICorners ID
14 normal(0, 5) sigma
 The priors for V2 were as for V1 and the priors for ND vs Fix as for D vs Fix
 Given that I have only 5 subjects per model, I tightened the default priors on the grouplevel standard deviations and correlations quite a bit. Please do also note that I ran into problems of divergent transitions with the defaults.
Many thanks in advance for your help!