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Title: A comparison of analytic and bayesian approaches for characterizing thermal hysteresis in cattle using algebraic and geometric distances

Author
item YANG, F. - University Of Nebraska
item PARKHURST, ANNE - University Of Nebraska
item ZHANG, S. - University Of Nebraska
item LEE, C - University Of Hawaii
item Brown-Brandl, Tami
item GEBREMEDHIN, K - Cornell University
item HILLMAN, P - Cornell University

Submitted to: Applied Statistics In Agriculture Conference Proceedings
Publication Type: Proceedings
Publication Acceptance Date: 1/20/2013
Publication Date: 4/1/2013
Citation: Yang, F., Parkhurst, A.M., Zhang, S., Lee, C.N., Brown-Brandl, T.M., Gebremedhin, K.G., Hillman, P.E. 2013. A comparison of analytic and bayesian approaches for characterizing thermal hysteresis in cattle using algebraic and geometric distances. In: Proceedings of Twenty-Fourth Annual Kansas State University Conference on Applied Statistics in Agriculture, April 29-May 1, 2012, Manhattan, Kansas. CDROM.

Interpretive Summary: High ambient temperature poses a serious threat to cattle. Above a certain environmental temperature, an animal's body temperature increases. This increase is affected by, not only the temperature, but the duration of time exposed to a higher temperature. A statistical analysis technique was developed to characterize an individual animal's response to these daily changes in temperatures. Data from a heat stress steer, during a summertime experiment, was used to test this new statistical method. This new procedure could be useful in determining differences in heat tolerance between animals.

Technical Abstract: A high ambient temperature poses a serious threat to cattle. Above a certain threshold, an animal’s body temperature (Tb) appears to be driven by the hot cyclic air temperature (Ta) and hysteresis occurs. Elliptical hysteresis describes the output of a process in response to a simple harmonic input, and the trajectory forms a closed loop. The hysteresis loop shows a rotated elliptical pattern which depends on the lag between Tb and Ta. The objectives of this study are 1)to characterize hysteresis using bootstrapped ellipse specific nonlinear least squares 2) to reformulate models using the Bayesian method, and 3) to assess the contribution of the Bayesian approach by comparing the risks using two metrics: algebraic and geometric. Comparisons and illustrations are made using simulations over three levels of signal strength. For each method; bootstrap and Bayes, both algebraic and geometric distances are compared based on the root mean square distance (RMSE) from fitting the hysteresis loop. Data from a heat stressed steer in a field experiment was analyzed to illustrate and compare the results from each method.