# Estimation of experimental data redundancy and related statistics

## TL;DR

This paper introduces an efficient approximation method to estimate data redundancy and related statistics from experimental data, aiding in understanding complexity and optimal experiment number.

## Contribution

It derives a practical approximation for data redundancy based on experimental data, enabling easier estimation of complexity and experiment requirements.

## Key findings

- Approximate redundancy formula simplifies entropy calculation.
- Method effectively estimates data complexity from experimental data.
- Demonstrated on 2D normal distribution data.

## Abstract

Redundancy of experimental data is the basic statistic from which the complexity of a natural phenomenon and the proper number of experiments needed for its exploration can be estimated. The redundancy is expressed by the entropy of information pertaining to the probability density function of experimental variables. Since the calculation of entropy is inconvenient due to integration over a range of variables, an approximate expression for redundancy is derived that includes only a sum over the set of experimental data about these variables. The approximation makes feasible an efficient estimation of the redundancy of data along with the related experimental information and information cost function. From the experimental information the complexity of the phenomenon can be simply estimated, while the proper number of experiments needed for its exploration can be determined from the minimum of the cost function. The performance of the approximate estimation of these statistics is demonstrated on two-dimensional normally distributed random data.