Some approaches to statistical analysis of a weather modification experiment

Data from a weather modification experiment are examined and a number of statistical analyses reported. The validity of earlier inferences is studied as are the utilities of various statistical methods. The experiment is described. The original analysis of North American Weather Consultants, who conducted the experiment, is reviewed. Data summarization is reported. A major approach to analysis is through the use of cloud-physics covari-ates in regression analyses. Finally, a multivariate analysis is discussed. It appears that the covariates may have been affected by treatment (cloud seeding) and that their use is invalid, not only reducing error variances but removing treatment effect. Some recommendations for improved design of similar future experiments are given in a concluding section, including preliminary trial use of blocking by storms.     

Some statistical issues in weather experimentation

A number of topics of statistical methodology in weather modification are discussed. The time sequence of unit definition, classification and randomization is shown to affect the types of units that can be used validly, and this casts doubt on the value of blocking. Re-randomization (permutation) tests are recommended as the only reliable method of confirmatory inference for weather experiments. Some aspects of such tests are examined, including a procedure for multiple comparisons. The plague of multiplicity of tests is discussed and warned against. Doubts about cumulative evaluations of "all" experiment's are expressed. A case is argued for examination of some non-randomized seeding operations. Consid¬ering the dearth of randomized data, it is argued that careful evaluation of seeding operations should be undertaken.     

Developments in probability and mathematical statistics generated by studies in meteorology and weather modification

Invariably, a persistent study of a category of natural phenomena generates novel mathematical developments, occasionally including sophisticated mathematical concepts. Of the mathematical developments generated by meteorology and efforts to modify weather, the most sophisticated seems to be the concept of characteristic functional. It was first published by A. N. Kolmogorov to be unnoticed for twelve years. It was reintroduced in 1947 by L. M. LeCam, inspired by studies of meteorology. Substantially less sophisticated mathematical concepts stem from cloud seeding experiments. They include (i) “outlier prone” and “outlier resistant” distributions,(ii) two mechanisms of response to cloud seeding. and (iii) the concept of variability of response to cloudseeding.     

A glimpse of the impact of pál erd#ous on probability and statistics

The title of this article notwithstanding, it is the author's aspiration here to provide a bit more than merely a glimpse of some of Erdõs's contributions per se to probability‐statistics. He hopes to have succeeded in providing a guided tour of, and whenever it has appeared feasible, an introduction to, a few selected areas that have been strongly influenced by the work of Erdõs. The author also hopes to have succeeded in facilitating a glimpse of the impact of these contributions by presenting them in their historical context.