I have a set of points $(x,y)$ with the goal of predicting $y$. I am fitting a regression model of the form $\ln(y-1) = A + B\ln(x)$.
I am reading an article that gives me the following information: "using Bayes credibility, Bayes' formula would be used: $$f(\text{Parameters}\mid\text{Data}) \sim f(\text{Data}\mid\text{Parameters}) \cdot f(\text{Parameters})\cdots,$$ and later on, "the regression parameters would be used for calculating this prior likelihood component, which is the credibility component of the likelihood". The article also mentions complement curves, non-weighted curves, and credibility weighted curves.
I am not familiar with how to apply credibility as described in this article. I only understand the basic fitting of the regression. Given the following
I have fit the regression model to this as described initially (without Credibility). I would like to know how to create the points for the complement and the points for the credibility weighted portion. I think that seeing an example would help me understand the concept. On this graph I want to ultimately show all curves leading to the credibility weighted portion.
The author provided a similar graph that I would like to eventually replicate on the full dataset:
As a side note, if anyone can suggest a good reading on this topic for a novice like myself it would also be appreciated. Thank you.