Bayesian Regression

Simulate data

Number of data points:

Model definition

\[model(x, \beta) = \beta_1 + \beta_2 x\]

Inference

Prior

Prior β₁ mean Prior β₁ sd Prior β₂ mean Prior β₂ sd Prior β₃ lower Prior β₃ range

Likelihood

\[\log p(y \mid \beta, x) = \sum_i \log \mathrm{Normal}(y_i \mid \beta_1 + \beta_2 x_i, \beta_3)\]

Sampling from Posterior

Sampling...

Posterior prediction

The idea is that we propagate the uncertainty represented by the parameter posterior p(β | data) through the model. The prediction interval also takes the measurement uncertainty into account.