Bayesian regression

it's a actually an informatics math related question. But i want to start here to get a first opinion.
As a software engineer and cryptographer, I'm developing an application to predict to price of certain alt-coin. I have read a paper about the math behind the algorithm.
I have a more then basic knowledge about math, I have seen some prediction methods in my math classes, but noting as advanced as I have read in the paper.
I'm just not so sure what regression to use, I have read about multi variable regressions, linear and logistics.
It's also that I use pré made libraries and tool that have implemented all the math I would need, but I need to have a specific one that is perfect for the job. I know it's bayesian, but all the formulas and theorems in the paper, can't figure it out.
I have a historic collection of data points, I would need to calculate the average price movement, I have also a variable 'w' for the learned parameters. The 2 (I think important formulas are present as attachment), please help me if you can