Writing a Custom Prior

Impulso uses typing.Protocol for extensibility. You can write your own prior by implementing the Prior protocol.

The Prior protocol

from impulso.protocols import Prior

class MyPrior:
    def build_priors(self, n_vars: int, n_lags: int) -> dict:
        ...

Your build_priors method must return a dictionary with keys "B_mu" and "B_sigma", both NumPy arrays of shape (n_vars, n_vars * n_lags).

• B_mu: Prior mean for VAR coefficient matrix
• B_sigma: Prior standard deviation for VAR coefficient matrix

Example: Flat prior

import numpy as np

class FlatPrior:
    def build_priors(self, n_vars: int, n_lags: int) -> dict:
        n_coeffs = n_vars * n_lags
        return {
            "B_mu": np.zeros((n_vars, n_coeffs)),
            "B_sigma": np.ones((n_vars, n_coeffs)) * 10.0,
        }

Using your custom prior

from impulso import VAR

spec = VAR(lags=2, prior=FlatPrior())
fitted = spec.fit(data)