The dashed curve is meant to regularize. Since there is more probability around 0, the estimate of 0 shrinks. The other 2 curves are narrower priors and therefore are more skeptical of values further from 0. The thin curve has a standard deviation of 0.5 and the thick curve has a standard distribution of 0.2. 

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A "skeptical" prior that, when tuned properly,  slows the rate of learning from the sample. This reduces overfitting while allowing the model to learn the regular features of the sample.



Regularization Priors

McElreath, R. (2020). Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd ed.). Chapman and Hall/CRC.

Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd edition)

Regularization is a modification made to a learning algorithm with the goal of reducing generalization error, but not training error.

Linear Regression is useful for modeling outputs whose relation to their inputs is linear. However, linear regression performs poorly when trying to model non-linear relationships. We can use regularization to help learning algorithms select certain models over others, particularly to avoid overfitting. 

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