Understanding Bayesian Inference & Gaussian Distribution

[sensitive]

I am reading a topic on Bayesian Inference.I read books from different authors but they are all the same. I cannot see how the terms are derived.

Could anyone briefly explain what is going on and what is it that we are trying to find using this Bayesian. Bayesian is a combination of belief from past data. So I am thinking that we are making the prediction. But I am not sure of what sort of prediction. Is ther an example to this.

I need help in understanding the 1) Bayesian formalism and
2) the mean of a gaussian distribution - how are the parameters; mu and the variance are derived and how is the posterior distri bution derived as well.

By the way could anyone suggest any recommended books for this topic. Thx

 

[Chris Hillman]

Kapur and Kesevan.

 

[EnumaElish]

In practice Bayesian inference comes down to a weighting of prior beliefs vs. actual observations. I.e. the posterior mean is a weighted average of the prior beliefs (e.g. $\mu_0$) and the data average.