Let's assume I want to train a binary naive Bayes classifier, with classes $y_0, y_1$ and $n$-dimensional data. For this one needs to calculate the conditional probabilities $P(x_i | y_j) $ for all pairs $i,j$.
When the distribution is discrete it's pretty straightforward, but let's assume I need to fit a continuous probability density function. Suppose I consider Gaussian and Poisson distributions, and would like to choose the more probable (use the ML principle). How do I choose which distribution is a better fit and what the parameters ($\lambda, \mu, \sigma)$ for those distributions should be?