Confidence Interval

The estimation variance itself is not enough to establish a confidence interval for the proposed estimate, the distribution of the errors must also be known. In mining applications however, the standard 95% Gaussian confidence interval $[/pm 2/sigma_E]$ is used, where $/sigma_E^2$ is the estimation variance.

Experimental observation of a large number of experimental histograms of estimation errors has shown that the Gaussian distribution tends to underestimate the proportion of low errors (within $[/pm /sigma_E/2]$) and of high errors (outside the range $[/pm 3/sigma_E]$). However, the standard Gaussian confidence interval $[/pm 2/sigma_E]$ in general correctly estimates the 95% experimental confidence interval. Figure 1.4 should illustrate this.

Figure 1.4: Comparison of Empirical Distributions to the Gaussian One.