def defaultModel(t, alpha=3.0, beta=None):
    """
    See ebisu's defaultModel function documentation.

    Note: This app's init_model function provides default alpha=2
    instead of alpha=3.0, but it's a small difference, and this
    function goes with default alpha=3.0.
    """
    if beta is None:
        beta = alpha
    return (alpha, beta, t)