论文标题
在异质介质中扩散的随机模型的轮廓可能性分析
Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media
论文作者
论文摘要
我们计算了由分层皮肤组织中热传导的实验观察到的扩散转运的随机模型的轮廓可能性。该过程被建模为在分层的一维材料中随机行走,在该材料中,每一层都具有独特的颗粒跳速。颗粒在某个位置释放,并记录每个粒子到达吸收边界的时间的持续时间。为了探索该数据是否可以用于识别每一层中的跳跃率,我们使用两种方法计算各种概况的可能性:首先,使用相对昂贵的Markov链方法评估了确切的可能性;第二,我们通过假设出口时间的分布是由伽马分布给出的,它的前两个矩与随机模型的连续限制描述相匹配。使用确切和近似的可能性,我们为各种问题构建了各种轮廓可能性。如果参数值无法识别,我们通过使用较少层的减少模型重新解释这些数据来取得进展。
We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether this data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the expected moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers.