Maximum Fidelity
Ali Kinkhabwala (Max Planck Institute of Molecular Physiology)

TL;DR
Maximum fidelity is a unified, frequentist approach for univariate data that improves parameter estimation and goodness-of-fit assessment by directly measuring model concordance with observed data.
Contribution
It introduces the maximum fidelity statistic, a novel information measure based on cumulative distributions, providing a more optimal and unified framework for statistical inference.
Findings
Maximum fidelity outperforms maximum likelihood in parameter estimation.
The method offers a direct way to compute p-values for model concordance.
Extensions to various data types and tests are feasible with this approach.
Abstract
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation: Which candidate distribution provides the best fit to the observed data?, (2) Goodness-of-fit: How concordant is this distribution with the observed data?, and (3) Uncertainty: How concordant are other candidate distributions with the observed data? A simple unified approach for univariate data that addresses these traditionally distinct statistical notions is presented called "maximum fidelity". Maximum fidelity is a strict frequentist approach that is fundamentally based on model concordance with the observed data. The fidelity statistic is a general information measure based on the coordinate-independent cumulative distribution and critical yet…
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Taxonomy
TopicsStatistical Methods and Bayesian Inference · Meta-analysis and systematic reviews · Statistical Methods in Clinical Trials
