Applications of Catastrophe Theory for Statistical Modeling in the Biosciences
本文展示了统计突变论在实验数据分析中的应用，包括滞后效应、分叉效应和尖点突变模型，并讨论了参数估计、非线性时间序列分析和随机微分方程等方法。
Abstract Although catastrophe theory has been applied with mixed success to many problems in the biosciences, very few of these applications have used any form of statistical modeling. We present examples of the applications of statistical catastrophe theory in the analysis of experimental data. These include examples of hysteresis effects, bifurcation effects, and the full cusp catastrophe model. The methods of statistical catastrophe theory draw upon the theories of parameter estimation for multiparameter exponential families, nonlinear time-series analysis, and stochastic differential equations. We discuss the application of these methods to both canonical and noncanonical catastrophe models.