重复时间序列中分段线性趋势的贝叶斯检测及其在增长数据建模中的应用
Bayesian detection of piecewise linear trends in replicated time-series with application to growth data modelling
摘要：
我们考虑的情况下，一个时间的过程是由连续的片段与不同的斜率和复制噪声损坏的时间序列测量观察。数据生成过程的未知均值被建模为具有未知数量的变点的时间的分段线性函数。我们发展了一个贝叶斯方法来推断联合后验分布的数量和位置的变化点，以及未知的平均参数。先验，所提出的模型使用过拟合的平均参数的数量，但有条件的一组变点，只有一个子集，他们影响的可能性。指数下降的变化点的数量的先验分布引起的后验分布集中在稀疏表示的基础序列。构造了一种用于逼近后验分布的Metropolis-Hastings马尔可夫链蒙特卡罗（MCMC）抽样器。我们的方法使用模拟数据进行基准测试，并应用于从不同菌株收集的成像时程数据中发现真菌生长动态的差异。源代码可以在CRAN上找到。
英文摘要：
We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as a piecewise linear function of time with an unknown number of change-points. We develop a Bayesian approach to infer the joint posterior distribution of the number and position of change-points as well as the unknown mean parameters. A-priori, the proposed model uses an overfitting number of mean parameters but, conditionally on a set of change-points, only a subset of them influences the likelihood. An exponentially decreasing prior distribution on the number of change-points gives rise to a posterior distribution concentrating on sparse representations of the underlying sequence. A Metropolis-Hastings Markov chain Monte Carlo (MCMC) sampler is constructed for approximating the posterior distribution. Our method is benchmarked using simulated data and is applied to uncover differences in the dynamics of fungal growth from imaging time course data collected from different strains. The source code is available on CRAN.
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