Intuition about conjugate priors and parameter estimation

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I have a problem that I am starting to work in a field where I need lots of non-rigorous probability theory for modelling.One large stumbling block for me is concept of conjugate Priors of random variables and Parameter estimation.Wherever I look the concepts are explained blurilly,with complete disregard for any kind of mathematical rigor.

I would like an explanation of conjugate priors and parameter estimation techniques, but such that rigor is not disregarded and all steps are laid out so that a complete novice can follow.

Mathematical rigor is wanted,but measure-theoretic arguments are not really welcome since I had no chance to acquainte myself with the theory at all.

Resource recomandations are more then welcome.

Thanks in advance