Mathematics & Statistics Colloquium - Dr Erica Ashe, Rutgers University

Wednesday, April 21, 2021 - 16:00
MS Teams

Title: How Can Novel Statistical Methods Improve Analyses in Environmental Sciences

Speaker: Dr Erica Ashe, Rutgers University

The talks will be held virtually this semester via Microsoft Teams. Link to join the meeting is given below.  All are welcome.
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Characterizing the spatio-temporal variability of relative sea level (RSL) and estimating local, regional, and global RSL trends requires statistical analysis of RSL data. Formal statistical treatments are needed to account for the spatially and temporally sparse distribution of data and for geochronological and elevational uncertainties. I frame improvements in statistical methods by themes: Uncertainty, Correlations, and Progress.

First, I introduce a newly developed statistical framework to estimate past RSL change based on the modern distributions of RSL proxy elevations in relation to RSL, using corals as an illustrative example.  The new statistical model incorporates nonparametric empirical likelihoods through a distribution-fitting module, a sampling module, and a sample-wise prediction module. Using Markov chain Monte Carlo (MCMC) sampling, we approximate the posterior distributions on these parameters and RSL, conditioned on the observed data. Through the use of a robust set of validation and sensitivity tests, we show that the nonparametric model, while sometimes overestimating uncertainties, performs better than past methods in these tests.

Then, I outline the importance of Bayesian and empirical Bayesian hierarchical models, particularly in a spatio-temporal context, to analyze diverse, noisy observations with errors in both dependent and independent variables. The hierarchical frameworks employed improves upon past RSL models by more richly representing the correlation structure of RSL across space and time.  Bayesian hierarchical models are suitable for developing complex process-level models, accounting for uncertainties in model parameters, incorporating prior knowledge, and sharing information over various dimensions. My models are able to rigorously quantify spatial and temporal variability, combine geographically disparate data, and separate the RSL field into various components associated with different driving processes.

Last, I demonstrate the value of statistical emulation in environmental science through the emulation of an Antarctic Ice Sheet (AIS) model simulator. Gaussian process emulators easily mimic the behavior of the ice-sheet model and provide continuous probability distributions of past and future sea-level equivalents from AIS from discrete simulation ensembles. I present the results of two ice-sheet emulators (for the last interglacial period [LIG, 130kya] and the future [1950-2100]) to demonstrate the value of emulation and geological data for constraining projections of Antarctica’s role in future sea level rise.  I show that posterior estimates of future AIS sea-level equivalent are highly dependent on how geological data can constrain LIG contributions, and that statistical emulation is a powerful tool for incorporating physics into statistical models.

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