Binomial Prediction Using the Frequent Outcome Approach

TL;DR

This paper analyzes a prediction method for binomial sequences based on the most frequent outcome, demonstrating its convergence to optimal accuracy as more data is observed.

Contribution

It introduces and evaluates the frequent outcome approach for binomial prediction, providing theoretical probability bounds and convergence results.

Findings

The method's prediction accuracy converges to the optimal level.

Probability bounds for correct predictions are derived.

The approach is effective for sequences with nearly uniform distributions.

Abstract

Within the context of the binomial model, we analyse sequences of values that are almost-uniform and we discuss a prediction method called the frequent outcome approach, in which the outcome that has occurred the most in the observed trials is the most likely to occur again. Using this prediction method we derive probability statements for the prior probability of correct prediction, conditional on the underlying parameter value in the binomial model. We show that this prediction method converges to a level of accuracy that is equivalent to ideal prediction based on knowledge of the model parameter.