Extending the Bayesian Dynamic Linear Model to changepoint problems
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Abstract
In this dissertation we develop a set of related methods for modeling a subset of time series data. Specifically, these models are designed for time series that contain a semi-regular pattern, but subject to outliers in the observations, as well as gradual and abrupt changes in pattern. We motivate these models and algorithms by an application to remote sensing reflectance data, which forces strong attention towards computational complexity due to the overwhelming abundance of data.
The models we introduce are based on the Bayesian Dynamic Linear Model (DLM), and we present them as a progression, in order of increasing model complexity and computational cost.
We start with a standard DLM implementation, with a simple outlier removal procedure. The focus of this work is in the application - we apply this model across tens of millions of time series, using the BU Shared Computing Cluster. We show that it performs favorably in comparison to existing methods in reflectance modeling.
Next, we use variance scales to more robustly accommodate both outliers and abrupt changes in pattern. Further, we develop a characterization of the tradeoff between downweighting outliers and rapidly adapting to changes in pattern, when using this model.
Finally, we propose a formal changepoint extension for the DLM. We combine the DLM with a Product Partition Model, allowing for rigorous inference on location of changepoints within a series, while preserving the DLM's capacity for gradual adaptation between changepoints.
We also provide implementations of each of these algorithms in an \textsf{R} package, with the core algorithms written in \textsf{C++} for efficient computation.
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Attribution 4.0 International