In many applications data is collected over time or can be ordered with respect to some other criteria (e.g. position along a chromosome). Often the statistical properties, such as mean or variance, of the data will change along data. This feature of data is known as non-stationarity. An important and challenging problem is to be able to model and infer how these properties change. Examples occur in environmental applications (e.g. detecting changes in ecological systems due to climatic conditions crossing some critical thresholds), signal processing (e.g. structural analysis of EEG signals), epidemiology (e.g. early detection of hospital infections from changes in patient’s antibody levels), bioinformatics (e.g. detecting changes in copy number variation), and finance (e.g. changing volatility). As technology advances, and ever larger and complex data are collected, the need to model changes in the statistical properties of the data, and the difficulty of making inference for these models increases.

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