A controlled branching process is a stochastic growth population model in which the number of individuals with reproductive capacity in each generation is given by a random control function. The purpose of the present work was to examine the Approximate Bayesian Computation sequential Monte Carlo method, and to propose appropriate summary statistics for these processes. The method’s success is shown to rely on this latter issue, and its accuracy is illustrated and compared with a “likelihood free” Markov chain Monte Carlo technique by means of a simulated example. How to extend the method to a controlled multitype branching process is also illustrated, and an application is made to model real data from the cell kinetics field. Both illustrations are developed using the R statistical software environment.

中文翻译：

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受控分支过程中的近似贝叶斯计算：汇总统计的作用

受控分支过程是一种随机生长种群模型，其中每一代具有繁殖能力的个体数量由随机控制函数给出。目前工作的目的是检查近似贝叶斯计算顺序蒙特卡罗方法，并为这些过程提出适当的汇总统计。该方法的成功被证明依赖于后一个问题，并通过一个模拟例子说明了它的准确性并与“似然无”马尔可夫链蒙特卡罗技术进行了比较。还说明了如何将该方法扩展到受控的多类型分支过程，并应用到对来自细胞动力学领域的真实数据进行建模。两个插图都是使用 R 统计软件环境开发的。