An Ay-Lê-Jost-Schwachhöfer Type Characterization of Quantitatively Weakly Sufficient Statistics

We explain the notion of a \(\delta \) -almost sufficient statistic, which is a quantitative weak version of sufficient statistics introduced in [11], based on the example of coin tosses. We review the basic notions in information geometry, e.g., parametrized measure models, statistics and Fisher quadratic forms. Then we state characterizations of sufficient statistics due to Ay-Jost-Lê-Schwachhöfer and an analogous characterizations of sufficient statistics due to [11].