Tutorial Contents¶
Video Tutorial¶
Introduction¶
PaleoSTeHM background and data level modelling: Introduction to Bayesian Hierarchical modelling, consisting of data level, process level, and parameter level modelling. This notebook will cover data level modelling with an example of building a data level model for coral-based sea-level records from the Great Barrier Reef.
Process level and parameter level modelling: This tutorial covers process and parameter level modelling, including hand-drawn models, linear models, change-point models, Gaussian Process models, physical models, and mixed physical/statistical models.
Analysis Choice: This tutorial discusses the difference between deterministic models and probabilistic (Bayesian) models, optimization methods for deterministic models (least squares and gradient-based optimization), and inference methods for Bayesian models, such as MCMC, Variational Bayes, and Empirical Bayes.
Temporal Gaussian Process¶
Gaussian Process background: A tutorial covering the basics of Gaussian Process, including calculating squared distance matrices, covariance matrices, hyperparameter definitions, conditional probability, and hyperparameter optimization.
Gaussian Process kernels and kernel operations: Introduction to popular GP kernels and instructions on how to combine different kernels.
Incorporate temporal uncertainty in Gaussian Process: Two methods commonly used for Gaussian Process, including noisy-input GP and errors-in-variable GP.
Holocene sea-level analysis in New Jersey and Northern North Carolina: This tutorial replicates Gaussian Process modelling results from New Jersey and Northern North Carolina as seen in Ashe et al., 2019.
Spatio-temporal Gaussian Process¶
Spatio-temporal Gaussian Process Background: Introduction to building a Spatio-temporal Gaussian Process model.
Spatio-temporal Gaussian Process with multiple kernels Detailed instructions on kernel decomposition and building a Spatio-temporal GP model using multiple kernels.
Spatio-temporal Gassusian Process with Physical Models: Combining Spatio-temporal GP models with physical models.
Applications¶
Common Era Sea-Level Reconstruction: Reconstructing Common Era global sea-level change using the method introduced in Kopp et al., 2016.
Updating Common Era sea-level curve: Add your own data to update the Common Era global sea-level curve, following the methodology of Walker et al., 2022.
PaleoSTeHM User Interface¶
Automatic Spatiotemporal sea-level analysis: Automatic implementation/optimization/visulization of Holocene sea-level change using a spatiotemporal Gaussian Process model with a zero mean function.