We propose a simple model-free solution to compute any confidence interval and to extrapolate these intervals beyond the observations available in your data set. In addition we propose a mechanism to sharpen the confidence intervals, to reduce their width by an order of magnitude. The methodology works with any estimator (mean, median, variance, quantile, correlation and so on) even when the data set violates the classical requirements necessary to make traditional statistical techniques work. In particular, our method also applies to observations that are auto-correlated, non identically distributed, non-normal, and even non-stationary.

No statistical knowledge is required to understand, implement, and test our algorithm, nor to interpret the results. Its robustness makes it suitable for black-box, automated machine learning technology. It will appeal to anyone dealing with data on a regular basis, such as data scientists, statisticians, software engineers, economists, quants, physicists, biologists, psychologists, system and business analysts, and industrial engineers.

In particular, we provide a confidence interval (CI) for the width of confidence intervals without using Bayesian statistics. The width is modeled as

Despite the apparent simplicity of our approach, we are dealing here with martingales. But you don't need to know what a martingale is to understand the concepts and use our methodology.

*L*=*A*/*n*^*B*and we compute, using Excel alone, a 95% CI for*B*in the classic case where*B*= 1/2. We also exhibit an artificial data set where*L*= 1 / (log*n*)^Pi. Here*n*is the sample size.Despite the apparent simplicity of our approach, we are dealing here with martingales. But you don't need to know what a martingale is to understand the concepts and use our methodology.