Bayesian Linear Regression

Bayesian linear regression is a form of linear regression that uses the information about the variances of the input variables to produce a probability distribution for outputs.

While ordinary linear regression predicts a single output value based on a range of input values, Bayesian linear regression predicts a probable value and a standard distribution around that probable value. This approach incorporates prior knowledge about the variances of input variables, which can improve the model’s accuracy and robustness.

In situations where the variances of input variables are known prior to training, this information can also be incorporated into the model. Bayesian linear regression is particularly useful in cases where it is important to quantify the uncertainty of predictions, such as in financial forecasting, risk assessment, and scientific research. By providing a distribution of probable outcomes, it allows for more informed decision-making and better understanding of the model’s confidence in its predictions.