Scaling factors
===============

Interpretation of the DUBFI results
-----------------------------------

DUBFI optimizes coefficients for basis vectors that span the state space of interest.
DUBFI does not know (or care) about the basis vectors, but only knows how a set of coefficients translate to a model prediction for the observations.

In the default configuration, we assume that DUBFI shall compute a (small) correction to a given reference state.
In this case, all coefficients are initially zero: :math:`s_0=0`, defined in the configuration entry ``inversion.prior_scaling=0``.
For the interpretation it is necessary to know the reference state.
In this case, the a priori probability density function :math:`P(s_0)` must be a Gaussian.

In other cases, one may have a log-normal probability or try to prevent negative coefficients.
The coefficients are then interpreted as prefactors for components of the total state.
The a priori then usually consists of ones, defined in the configuration by ``inversion.prior_scaling=1``.

It is the responsibility of the user to check that the correct interpretation of the posterior coefficients, for example by comparison to the prior.
The input data are the same for both cases. Only the configuration differs.