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1st question,

I recently learnt bayesian linear regression, but I'm confused that in what situation we should use bayesian linear regression, and when to use standard linear regression? What is the advantage of bayesian linear regression over standard one?


2nd question,

Also, another thing I'm confused with is that for a simple linear regression whose formula is $๐‘ฆ_๐‘–=ฮฑ+ฮฒ๐‘ฅ_๐‘–+๐œ€$, why the bayesian version is as:

$๐‘ข_๐‘–=ฮฑ+ฮฒ๐‘ฅ_๐‘–$

$๐‘ฆ_๐‘–โˆผ\mathcal{N}(๐œ‡_๐‘–,๐œŽ)$

I read from other place that $ฮผ_๐‘–$ corresponds to $๐‘ฆ_๐‘–=ฮฑ+ฮฒ๐‘ฅ_๐‘–$, what does ฯƒ correspond to? And how is the version transformation realize?


3nd question,

Last question, does $๐‘ฆ_๐‘–โˆผ\mathcal{N}(๐œ‡_๐‘–,๐œŽ)$

mean that each value y $\in๐‘Œ$ is a normal distribution, instead of the observed data is a normal distribution?


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  • $\begingroup$ $ฮผ_๐‘–$ is the mean of each $๐‘ฆ_๐‘–$ and $\sigma $ it's just the variance of $๐‘ฆ_๐‘–$. So $\sigma$ 'corresponds' to $y_i$ aswell. $\endgroup$ – Isa Feb 21 at 5:48
  • $\begingroup$ It would be a good idea if you could post the definitions of bayesian linear regression and standard linear regression or the source of these terms. $\endgroup$ – Isa Feb 21 at 5:53

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