# What is a tight prior?

In a paper that I was reading Bayesian stats, they are talking about a "tight" prior.

We control the “tightness” of the Minnesota prior by adjusting the values of parameter $b1$. A tight version of the Minnesota prior is de ned by $b1 = 0.2^2$, and a loose version sets $b1 = 0.9^2$.

Is a tight prior the same thing as an "informative prior"?

Is it saying that the variance of a distribution, if we take the example of a normal distribution, is smaller?

• They say directly in the article: "We control the “tightness” of the Minnesota prior by adjusting the values of parameter b1. A tight version of the Minnesota prior is defined by b1 = 0.2^2, and a loose version sets b1 = 0.9^2. Here the words “tight” or “loose” are used in relative terms. One can certainly argue that b1 = 0.9^2 represents a tight prior compared to the case b1 = 10^2." You can say one is more "informative" than the other, but it's equally loose and informal. – AdamO Oct 17 '17 at 18:03

A tight prior is indeed a concentrated prior, so a Normal(0, 1) prior for a parameter is more tight than a Normal(0, 10) prior. This is a relative statement, it depends on the scale of your parameter.