Hello, I want to maximize P(ATR(t+1) | G(t)) i.e compute the most probable ATR for next period t+1. G is gaussian distributed with known mean m and std s. Beside G and ATR are not independant. How should I proceed? Thank you

IV should work too, but I think ATR gives better results. There are probably also other metrics that can be used as input but in any case the question would be the same.

G is a normally distributed random variable with known parameters. I can see the dependence empirically.

Solving this analytically using the normal distribution sounds hard and maybe impossible. I think your best bet is to divide t into multiple steps and run a Monte-Carlo simulation. Another idea is to build a binomial tree for the price like those used in option pricing. For each path through the tree calculate the ATR and a probability of the path. Then find the probability of each ATR across all paths. If you calibrate the tree correctly and use enough steps you approach the properties of the normal distribution.