# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: On LOPs**

**From:**Trevor Kenchington

**Date:**2002 Apr 16, 11:50 -0300

Steven Wepster wrote: >Let me add one cent. I don't understand what _the_ _true_ form of a >confidence region should mean. IMO a confidence region is a region that >contains the MPP with a specified probability, often taken as 95%. It can >be circular, elliptical, square, heart-shaped or whatever you prefer, for >whatever theoretical, practical, or other reasons are important to you. > Steven, My use of statistical terminology is probably not what it should be (comes of picking up stats as a biologist with little formal training!) and I have no idea of whatever conventions may have developed in the application of statistics to navigation. My lack of the right words should not, however, hide the existence of the thing I was trying to refer too. Given an MPP and sufficient information on the associated uncertainties, one could draw any number of boundaries around it, each defined so that there was a 95% probability (or any other probability one might select) that the true position lay within the boundary. Each boundary would encompass some areas where there was a high probability that the true position would lie and other areas where there would be a low probability. But there would only be one such boundary that not only met the criterion of a 95% probability of the true position lying within it but also had, at all points along the boundary, an equal probability of the true position lying at that point. That boundary (and only that boundary) would encompass the smallest area that had a 95% probability of containing the true position. It would also be the only boundary which did not exclude some areas where there was a relatively high probability of the true position lying -- all other boundaries excluding small high-probability areas but taking in larger low-probability ones to maintain the 95% encompassed. It is the area surrounded by that one boundary (for any chosen probability of enclosing the true position) which is also a "contour" (or isopleth, if you prefer) of constant probability which I meant by the "true" confidence region. I would contend that it, rather than the area with some other boundary, is the confidence region that we would like to have when using an MPP in practical navigation. The problem, of course, is that we do not have complete information on the shape of the boundary and thus must fall back on estimates from the available data. Moreover, we do not (at least, I do not) go to sea with the sort of computing power needed to make statistically-optimal estimates from such data as we do have. Hence, in practical applications, we fall back on assuming that our true position is somewhere inside a cocked hat, a circle around the MPP, an ellipse or some other simple figure that we can plot. My only reason in seeking to go beyond that, in a discussion of theory, is to explore the reliability or otherwise of such simple approximations to a complex topic. If, for example, George was right that the true position falls within the cocked hat only 25% of times (and I have yet to see his defence of that conclusion), navigators should know not to rely on that old rule of thumb. The same would be true of computed ellipses if they fail us too often. Trevor Kenchington