This research is concerned with statistical models and methods for circular data, including inference for wrapped stable family of circular distributions, tests for multimodality, predictive inference for directional data and application of Bayesian methods when appropriate prior information is available. When a circular variable depends on other linear or circular covariates, multifactor designs as well as regression approaches are used to assess such dependence.Correlation and regression for circular variables and related optimal-design issues involve novel statistical problems and form an essential part of this investigation.
One primary motivation for this research comes from the study of biorhythms which control our biological clock and include such important things as the sleep-wake cycle, hormonal pulsatility, reproductive cycles etc. Proper statistical analysis of such rhythms should take account of the fact that cyclical phenomena should be represented as data on a circle of suitable circumference rather than as more traditional "linear" data. Appropriate modeling of such rhythmicity and its proper statistical analysis is an intended outcome of this research. The regression models tell us how this rhythmicity might be affected by other covariates such as age, sex, time at which certain treatment is administered, dosage etc. Using these models, one can hope to determine optimal timing for medications or surgery to achieve greatest impact as well as help quantify the benefits of newly emerging approaches such as "Chronotherapeutics". Although the presence of circadian-time keeping mechanisms at both the neurophysiologic and molecular genetic levels have been known to scientists, the present research will provide methods for comprehensive statistical validation of such findings and especially in any future efforts to relate the biological clock to covariates like age etc.
This research on circular statistics is also closely related to some current investigations on the Environment and Global Change that utilize the directional spectra of wind and sea currents.
