Displaying Uncertainty With Shading

Abstract

A new technique is presented for illustrating several probability distributions on the same axes. The density strip is a shaded monochrome strip whose darkness at a point is proportional to the probability density of the quantity at that point. These are ideal for comparing distributions arising from parameter estimation, such as posterior distributions from Bayesian multiple regression or meta-analysis. Such distributions are more commonly illustrated as a point and line representing point and interval estimates. This may give the false perception that all points within the line are equally likely, and that points outside the line are impossible. The density strip represents the entire distribution in one dimension, giving a fuller description of the uncertainty surrounding the quantity. The strips fade gradually to white in the tails of a typical distribution, in contrast with line plots and strips whose thickness is proportional to the density, which terminate at a clear limit. This discourages casual significance testing based on comparing an arbitrary point in the tail of the distribution to a threshold. Shaded strips can also be generalized to shaded regions, which illustrate the uncertainty surrounding a continuously varying unknown quantity, such as a survival curve or a forecast from a time series.