I used latent variable GP to implement a regression problem in my data which is the acceleration of a object that lowering to the sea water. Near the sea level there is high variation in the acceleration. The model seems that cannot predict well the uncertainty that reach to this level (i.e. near sea level).
The observation of the data are set based on simple normal distribution, while its mean and deviation have Gaussian process prior on both of them. I tried to keep my priro for hyper-parameters of the kernel as alpha with large number and lengthsacle very small to help me detect these sharp variation well:
lengthscale ~ lognormal(-2.5, .2);
sigma ~ normal(5, 2);
I checked different prior options, these two one give me a better prediction on the data at least.
Here I uploaded the results for your valubel considerations.
As it is shown, the model cannot predict high values in the middle of the time and also it also cannot predict the negative accelerations. Couls you kindly help with your advice?
Having said that, I have four different data set, in which for one of them i got one chain diverged from others. However, the results are the same particulary I can say.