simmonsja / bayes-lr-shoreline

Analysing storm erosion prediction uncertainty with Bayesian techniques

Bayesian Linear Regression

Written by Joshua Simmons 2022

Also available as a Streamlit web app!

In this notebook, we will fit a Bayesian Linear Regression to predict shoreline change due to coastal storms. This will mirror the simple empirical model developed by:

Harley, M. D., Turner, I. L., Short, A. D., & Ranasinghe, R. (2009). An empirical model of beach response to storms–SE Australia. In Coasts and Ports (pp. 600-606).

Paper available here.

This model is of the form: $\Delta W=aE^b$, where $\Delta W$ is the change in shoreline position, $E$ is the storm energy, and $a$ and $b$ are learnable model parameters.

To provide uncertainty alongside the model prediction, we will use the probabilistic programming language NumPyro to fit a Bayesian Linear Regression.

Disclaimers:

• This is an overly simplified analysis for the purpose of demonstrating uncertainty quantification (via Bayesian inference) with NumPyro and presentation via streamlit.
• Model predictions of shoreline change should not be relied upon for real-world applications.