arXiv subjects

Samuel Baugh

Publications and source records attributed to Samuel Baugh.

3 recordsLinked to original sources

arXiv2022

Bayesian Quantification of Covariance Matrix Estimation Uncertainty in Optimal Fingerprinting

Regression-based optimal fingerprinting techniques for climate change detection and attribution require the estimation of the forced signal as well as the internal variability covariance matrix in order to distinguish between their influences in the observational record. While previously developed approaches have taken into account the uncertainty linked to the estimation of the forced signal, there has been less focus on uncertainty in the covariance matrix describing natural variability, despite the fact that the specification of this covariance matrix is known to meaningfully impact the results. Here we propose a Bayesian optimal fingerprinting framework using a Laplacian basis function parameterization of the covariance matrix. This parameterization, unlike traditional methods based on principal components, does not require the basis vectors themselves to be estimated from climate model data, which allows for the uncertainty in estimating the covariance structure to be propagated to the optimal fingerprinting regression parameter. We show through a CMIP6 validation study that this proposed approach achieves better-calibrated coverage rates of the true regression parameter than principal component-based approaches. When applied to HadCRUT observational data, the proposed approach detects anthropogenic warming with higher confidence levels, and with lower variability over the choice of climate models, than principal-component-based approaches.

stat.ME↗

arXiv2021

Hierarchical Bayesian Modeling of Ocean Heat Content and its Uncertainty

The accurate quantification of changes in the heat content of the world's oceans is crucial for our understanding of the effects of increasing greenhouse gas concentrations. The Argo program, consisting of Lagrangian floats that measure vertical temperature profiles throughout the global ocean, has provided a wealth of data from which to estimate ocean heat content. However, creating a globally consistent statistical model for ocean heat content remains challenging due to the need for a globally valid covariance model that can capture complex nonstationarity. In this paper, we develop a hierarchical Bayesian Gaussian process model that uses kernel convolutions with cylindrical distances to allow for spatial non-stationarity in all model parameters while using a Vecchia process to remain computationally feasible for large spatial datasets. Our approach can produce valid credible intervals for globally integrated quantities that would not be possible using previous approaches. These advantages are demonstrated through the application of the model to Argo data, yielding credible intervals for the spatially varying trend in ocean heat content that accounts for both the uncertainty induced from interpolation and from estimating the mean field and other parameters. Through cross-validation, we show that our model out-performs an out-of-the-box approach as well as other simpler models. The code for performing this analysis is provided as the R package BayesianOHC.

stat.AP↗

arXiv2020

Mapping unobserved item-respondent interactions: A latent space item response model with interaction map

Classic item response models assume that all items with the same difficulty have the same response probability among all respondents with the same ability. These assumptions, however, may very well be violated in practice, and it is not straightforward to assess whether these assumptions are violated, because neither the abilities of respondents nor the difficulties of items are observed. An example is an educational assessment where unobserved heterogeneity is present, arising from unobserved variables such as cultural background and upbringing of students, the quality of mentorship and other forms of emotional and professional support received by students, and other unobserved variables that may affect response probabilities. To address such violations of assumptions, we introduce a novel latent space model which assumes that both items and respondents are embedded in an unobserved metric space, with the probability of a correct response decreasing as a function of the distance between the respondent's and the item's position in the latent space. The resulting latent space approach provides an interaction map that represents interactions of respondents and items, and helps derive insightful diagnostic information on items as well as respondents. In practice, such interaction maps enable teachers to detect students from underrepresented groups who need more support than other students. We provide empirical evidence to demonstrate the usefulness of the proposed latent space approach, along with simulation results.

stat.ME↗