def METHOD_NAME(T, q=1, r=1, phi=0.0, beta=0.0):
    def transition(state, i):
        x, mu = state
        x = numpyro.sample("x", dist.LogNormal(phi * x, q))
        mu = beta * mu + x
        numpyro.sample("y", dist.Normal(mu, r))
        return (x, mu), None
    scan(transition, (0.0, 0.0), jnp.arange(T))