How to construct a reasonable prior and likelihood for Bayes modelling?

Question

To apply Bayes inference for data analysis or machine learning, we have to construct prior and likelihood, right? But if I fail to come up with a reasonable prior and likelihood, then the Bayes model will not be meaningful, right?

I wonder is there any technique could be utilized to construct reasonable Bayes models?

Let me make it concrete by an example, given a dataest with features $X$ and target $y$, where $y=\{0,1\}$ and $X$ is composed of $p$ variables. This is an ordinary binary classification problem, to do Bayes inference, what and how should I specify for the prior and likelihood?

One more question, if we could not specify a reasonable prior, then what's the point of using Bayes modelling?

Answer 1

You would specify a prior for parameters. You haven't mentioned any!

You need to write some model for how the distribution of $Y$ relates to $X$, so your first step is to identify a distribution for $Y$ (it's 0-1, so there's an obvious first choice there) and then write a model for its parameters in terms of $X$.

Once you have that model, you need to think about priors on the parameters. Again, a first attempt should be relatively simple, then make it more complicated if you think it needs to be.