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As an example, let’s say you want to fit a linear regression model y=ax+by = a x + by=ax+b to some data (xi,yi)(x_i, y_i)(xi,yi). In a Bayesian approach, we first define priors for the parameters aaa, bbb. Since all parameters are continuous real numbers, a wide Normal distribution prior is a good choice. For the likelihood, we can focus on the residuals ri=yi−(axi+b)r_i = y_i - (a x_i + b)ri=yi−(axi+b) which we model via a normal distribution ri∼N(0,σ2)r_i \sim \mathcal{N}(0, \sigma^2)ri∼N(0,σ2) (we also provide priors for σ\sigmaσ). In pymc, this can be implemented as follows: