Title: Goodness-of-fit testing for the stationary density of a size-structured PDE Show Chinese title

Title: 适合度检验用于尺寸结构PDE的平稳密度

Abstract: We consider two division models for structured cell populations, where cells can grow, age and divide. These models have been introduced in the literature under the denomination of `mitosis' and `adder' models. In the recent years, there has been an increasing interest in Biology to understand whether the cells divide equally or not, as this can be related to important mechanisms in cellular aging or recovery. We are therefore interested in testing the null hypothesis $H_0$ where the division of a mother cell results into two daughters of equal size or age, against the alternative hypothesis $H_1$ where the division is asymmetric and ruled by a kernel that is absolutely continuous with respect to the Lebesgue measure. The sample consists of i.i.d. observations of cell sizes and ages drawn from the population, and the division is not directly observed. The hypotheses of the test are reformulated as hypotheses on the stationary size and age distributions of the models, which we assume are also the distributions of the observations. We propose a goodness-of-fit test that we study numerically on simulated data before applying it on real data. Show Chinese abstract

Abstract: 我们考虑了两类用于描述结构化细胞群体分裂的模型，其中细胞可以生长、老化并分裂。 这些模型在文献中被称为“有丝分裂”和“加法器”模型。 近年来，在生物学领域对细胞是否均匀分裂的兴趣日益增加，因为这可能与细胞衰老或恢复的重要机制相关。 因此，我们感兴趣于检验零假设 $H_0$，即母细胞分裂产生的两个子细胞大小或年龄相等，而对立假设为 $H_1$，即分裂是不对称的，并由一个相对于勒贝格测度绝对连续的核函数所支配。 样本由从群体中抽取的独立同分布的细胞大小和年龄观测值组成，且分裂过程未被直接观察到。 我们将检验的假设重新表述为关于模型的稳态大小和年龄分布的假设，我们假定这些分布也对应于观测值的分布。 我们提出了一种拟合优度检验方法，并在模拟数据上进行数值研究后将其应用于真实数据。