allow different lambda functions (besides logistic)?

[mathause]

We have a TODO on allowing other lambda functions:

mesmer/mesmer/stats/_power_transformer.py

Line 256 in 8f8c8a0

# TODO allow passing func instead of our fixed lambda_function?

E.g. logistic, constant, linear. I think we could maybe do this by collecting the necessary info in a class for each covariate function:

class LogisticLambda:
    
    bounds = np.array([[0, np.inf], [-0.1, 0.1]])
    first_guess = np.array([1, 0])

    @staticmethod
    def lambdas_from_covariates(coeffs, covariate):
        return 2 / (1 + coeffs[0] * np.exp(covariate * coeffs[1]))

class ConstantLambda:
    
    bounds = None
    first_guess = np.array([1])

    @staticmethod
    def lambdas_from_covariates(coeffs, covariate):
        return np.full_like(covariate, fill_value=coeffs)

def _get_lambda_cls(function):

    if function == "logistic":
        return LogisticLambda()
    elif function == "constant":
        return ConstantLambda()
    else:
        raise ValueError()

...

- lambdas = lambda_function(coeffs, yearly_pred)
+ lambda_cls = _get_lambda_cls("constant")
+ lambdas = lambda_cls.lambdas_from_covariates(coeffs, yearly_pred)

---

As a side note: we have similar goals and challenges as for MESMER-X: extending standard statistical methods with covariates...

[mathause]

1. A constant lambda would be much faster to estimate - good to have an interactive example on rtd.
2. As we found out that lambda does not need to be in 0..2, a linear function could also be attractive