Sir,

The devil tries to hide in every statistical study. He did not do a good job hiding in Reference JudsonJudson (1983) which concludes that an avalanche on an “index path” is “of little diagnostic value” as a predictor of another avalanche the same day on a “physically similar” path.

In Judson’s study, the conditional probability that avalanche A will occur given a “paired” avalanche B is designated P[A∣B], which Judson finds is ≤ 0.2 in 90% of his cases. Although that finding seems plausible, what is the “diagnostic” significance of 0.2, and where does that number come from? It is surely reason for concern even if P[A∣B] = 0.1, where A threatens life or property. Protective measures (artificial release, road closures, warnings) are in order. The minimum value of P[A∣B] at which the risk is acceptable will vary from case to case, but it is usually well below 0.1, perhaps even below 0.01 depending on the number of lives and economic value at risk. Moreover, even if P[A∣B] has a low value it may be relatively high compared with the “unconditional” P[A]. Although it is not feasible to show in detail all his cases, why has Judson displayed only his highest P[A∣B] values? It is equally important to see a summary of how his poorer cases distribute. From the high values in his table I, one suspects that P[A∣B] has great “diagnostic value”, given the right choice of pairs.

It would also be interesting to see how the ratio R = P[A∣B]/P[A] varies across his entire sample, for this ratio reflects the probability increase given the event B. The computation of R for the 40 pairs in table I shows that l.5 ≤ R ≤ 7.4 and R = 3.8. This seems to confirm that P[A∣B] has “diagnostic value” compared with p[A] for the pairs in table I. Also, R varies randomly as P[A∣B] varies over its range (0.74 to 0.26) in table I. Only Judson can tell us if R drops for the majority of his data (not summarized in table I), or if the low values of P[A∣B] correlate with a correspondingly low P[A].

The irony of Judson’s paper is that avalanche forecasters do not usually think in terms of “paired paths”. They usually reason qualitatively that if there is an event B in a group of n paths then the probability increases that there will be another event somewhere else in the remaining n−1 paths. Depending on n and many other factors the conditional probability of an event A or C or D or… given event B may be well above P[A∣B]. Protective measures are distributed over these n−1 paths, but compromises are sometimes necessary in order to cover all paths. Given Judson’s paper, and without seeing the complete summary mentioned above, the more probable conclusion is that indexing one path against another may have “diagnostic value”.

National Hydrology Research Institute,

Box 313,

Canmore, Alberta TOL OMO, Canada

29 August 1983

RON PERLA