Arianna Ceccarelli, Alexander P Browning, Ruth E Baker
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引用次数: 0
Abstract
Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time. These tracking data motivate the use of mathematical models to characterise the motion observed. In this paper, we aim to describe the solutions of velocity-jump models for single-agent motion in one spatial dimension, characterised by successive Markovian transitions within a finite network of n states, each with a specified velocity and a fixed rate of switching to every other state. In particular, we focus on obtaining the solutions of the model subject to noisy, discrete-time, observations, with no direct access to the agent state. The lack of direct observation of the hidden state makes the problem of finding the exact distributions generally intractable. Therefore, we derive a series of approximations for the data distributions. We verify the accuracy of these approximations by comparing them to the empirical distributions generated through simulations of four example model structures. These comparisons confirm that the approximations are accurate given sufficiently infrequent state switching relative to the imaging frequency. The approximate distributions computed can be used to obtain fast forwards predictions, to give guidelines on experimental design, and as likelihoods for inference and model selection.
实验技术的进步使我们能够收集高分辨率的时空数据,对单个运动实体进行长时间跟踪。这些跟踪数据促使我们使用数学模型来描述观察到的运动特征。在本文中,我们旨在描述速度跳跃模型在一个空间维度上的单体运动解,其特征是在一个由 n 个状态组成的有限网络中的连续马尔可夫转换,每个状态都有指定的速度和固定的转换到其他状态的速率。特别是,我们的重点是在无法直接访问代理状态的情况下,通过噪声、离散时间观测获得模型的解。由于缺乏对隐藏状态的直接观察,通常很难找到精确的分布。因此,我们推导出一系列数据分布的近似值。我们将这些近似值与通过模拟四个示例模型结构生成的经验分布进行比较,从而验证了这些近似值的准确性。这些比较证实,在相对于成像频率而言状态切换足够不频繁的情况下,近似值是准确的。计算出的近似分布可用于获得快速前瞻性预测,为实验设计提供指导,以及作为推理和模型选择的似然值。
期刊介绍:
The Bulletin of Mathematical Biology, the official journal of the Society for Mathematical Biology, disseminates original research findings and other information relevant to the interface of biology and the mathematical sciences. Contributions should have relevance to both fields. In order to accommodate the broad scope of new developments, the journal accepts a variety of contributions, including:
Original research articles focused on new biological insights gained with the help of tools from the mathematical sciences or new mathematical tools and methods with demonstrated applicability to biological investigations
Research in mathematical biology education
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Perspectives, and contributions that discuss issues important to the profession
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