arXiv subjects

David Pollard

Publications and source records attributed to David Pollard.

18 recordsLinked to original sources

arXiv2020

Antarctic ice sheet - climate feedbacks under high future carbon emissions

Freshwater forcing from a retreating Antarctic Ice Sheet could have a wide range of impacts on future global climate. Here, we report on multi-century (present-2250) climate simulations performed using a fully coupled numerical model integrated under future greenhouse gas emissions scenarios IPCC RCP4.5 and 8.5, with meltwater discharge provided by a dynamic-thermodynamic ice sheet model. Accounting for Antarctica's meltwater contribution raises sub-surface ocean temperatures by 1 C at the ice margin, beyond rates currently projected. In contrast, 2-10 C cooler surface air and ocean temperatures in the Southern Ocean cause sea ice to expand and delay the increase of projected global mean anthropogenic warming. In addition, the projected loss of Arctic winter sea ice and weakening of the Atlantic Meridional Overturning Circulation are delayed be several decades. Our results demonstrate a clear need to more accurately account for meltwater input from ice sheets if we are to make confident climate predictions.

physics.ao-ph↗

arXiv2019

Rapid mixing of a Markov chain for an exponentially weighted aggregation estimator

The Metropolis-Hastings method is often used to construct a Markov chain with a given $\pi$ as its stationary distribution. The method works even if $\pi$ is known only up to an intractable constant of proportionality. Polynomial time convergence results for such chains (rapid mixing) are hard to obtain for high dimensional probability models where the size of the state space potentially grows exponentially with the model dimension. In a Bayesian context, Yang, Wainwright, and Jordan (2016) (=YWJ) used the path method to prove rapid mixing for high dimensional linear models. This paper proposes a modification of the YWJ approach that simplifies the theoretical argument and improves the rate of convergence. The new approach is illustrated by an application to an exponentially weighted aggregation estimator.

math.ST↗

arXiv2019

Fair quantile regression

Quantile regression is a tool for learning conditional distributions. In this paper we study quantile regression in the setting where a protected attribute is unavailable when fitting the model. This can lead to "unfair'' quantile estimators for which the effective quantiles are very different for the subpopulations defined by the protected attribute. We propose a procedure for adjusting the estimator on a heldout sample where the protected attribute is available. The main result of the paper is an empirical process analysis showing that the adjustment leads to a fair estimator for which the target quantiles are brought into balance, in a statistical sense that we call $\sqrt{n}$-fairness. We illustrate the ideas and adjustment procedure on a dataset of 200,000 live births, where the objective is to characterize the dependence of the birth weights of the babies on demographic attributes of the birth mother; the protected attribute is the mother's race.

math.ST↗

arXiv2019

A Fast Particle-Based Approach for Calibrating a 3-D Model of the Antarctic Ice Sheet

We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases. Here we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea level projections when we account for a larger number of uncertain parameters.

stat.AP↗

arXiv2017

Evolving understanding of Antarctic ice-sheet physics and ambiguity in probabilistic sea-level projections

Mechanisms such as ice-shelf hydrofracturing and ice-cliff collapse may rapidly increase discharge from marine-based ice sheets. Here, we link a probabilistic framework for sea-level projections to a small ensemble of Antarctic ice-sheet (AIS) simulations incorporating these physical processes to explore their influence on global-mean sea-level (GMSL) and relative sea-level (RSL). We compare the new projections to past results using expert assessment and structured expert elicitation about AIS changes. Under high greenhouse gas emissions (Representative Concentration Pathway [RCP] 8.5), median projected 21st century GMSL rise increases from 79 to 146 cm. Without protective measures, revised median RSL projections would by 2100 submerge land currently home to 153 million people, an increase of 44 million. The use of a physical model, rather than simple parameterizations assuming constant acceleration of ice loss, increases forcing sensitivity: overlap between the central 90% of simulations for 2100 for RCP 8.5 (93-243 cm) and RCP 2.6 (26-98 cm) is minimal. By 2300, the gap between median GMSL estimates for RCP 8.5 and RCP 2.6 reaches >10 m, with median RSL projections for RCP 8.5 jeopardizing land now occupied by 950 million people (vs. 167 million for RCP 2.6). The minimal correlation between the contribution of AIS to GMSL by 2050 and that in 2100 and beyond implies current sea-level observations cannot exclude future extreme outcomes. The sensitivity of post-2050 projections to deeply uncertain physics highlights the need for robust decision and adaptive management frameworks.

physics.ao-ph↗

arXiv2016

Inferring Ice Thickness from a Glacier Dynamics Model and Multiple Surface Datasets

The future behavior of the West Antarctic Ice Sheet (WAIS) may have a major impact on future climate. For instance, ice sheet melt may contribute significantly to global sea level rise. Understanding the current state of WAIS is therefore of great interest. WAIS is drained by fast-flowing glaciers which are major contributors to ice loss. Hence, understanding the stability and dynamics of glaciers is critical for predicting the future of the ice sheet. Glacier dynamics are driven by the interplay between the topography, temperature and basal conditions beneath the ice. A glacier dynamics model describes the interactions between these processes. We develop a hierarchical Bayesian model that integrates multiple ice sheet surface data sets with a glacier dynamics model. Our approach allows us to (1) infer important parameters describing the glacier dynamics, (2) learn about ice sheet thickness, and (3) account for errors in the observations and the model. Because we have relatively dense and accurate ice thickness data from the Thwaites Glacier in West Antarctica, we use these data to validate the proposed approach. The long-term goal of this work is to have a general model that may be used to study multiple glaciers in the Antarctic. Keywords: ice sheet, glacier dynamics, hierarchical Bayes, Gaussian process, Markov chain Monte Carlo, West Antarctic ice sheet.

stat.AP↗

arXiv2016

Assessing the Impact of Retreat Mechanisms in a Simple Antarctic Ice Sheet Model Using Bayesian Calibration

The response of the Antarctic ice sheet (AIS) to changing climate forcings is an important driver of sea-level changes. Anthropogenic climate change may drive a sizeable AIS tipping point response with subsequent increases in coastal flooding risks. Many studies analyzing flood risks use simple models to project the future responses of AIS and its sea-level contributions. These analyses have provided important new insights, but they are often silent on the effects of potentially important processes such as Marine Ice Sheet Instability (MISI) or Marine Ice Cliff Instability (MICI). These approximations can be well justified and result in more parsimonious and transparent model structures. This raises the question of how this approximation impacts hindcasts and projections. Here, we calibrate a previously published and relatively simple AIS model, which neglects the effects of MICI and regional characteristics, using a combination of observational constraints and a Bayesian inversion method. Specifically, we approximate the effects of missing MICI by comparing our results to those from expert assessments with more realistic models and quantify the bias during the last interglacial when MICI may have been triggered. Our results suggest that the model can approximate the process of MISI and reproduce the projected median melt from some previous expert assessments in the year 2100. Yet, our mean hindcast is roughly 3/4 of the observed data during the last interglacial period and our mean projection is roughly 1/6 and 1/10 of the mean from a model accounting for MICI in the year 2100. These results suggest that missing MICI and/or regional characteristics can lead to a low-bias during warming period AIS melting and hence a potential low-bias in projected sea levels and flood risks.

physics.ao-ph↗

arXiv2015

Improving Ice Sheet Model Calibration Using Paleoclimate and Modern Data

Human-induced climate change may cause significant ice volume loss from the West Antarctic Ice Sheet (WAIS). Projections of ice volume change from ice-sheet models and corresponding future sea-level rise have large uncertainties due to poorly constrained input parameters. In most future applications to date, model calibration has utilized only modern or recent (decadal) observations, leaving input parameters that control the long-term behavior of WAIS largely unconstrained. Many paleo-observations are in the form of localized time series, while modern observations are non-Gaussian spatial data; combining information across these types poses non-trivial statistical challenges. Here we introduce a computationally efficient calibration approach that utilizes both modern and paleo-observations to generate better-constrained ice volume projections. Using fast emulators built upon principal component analysis and a reduced dimension calibration model, we can efficiently handle high-dimensional and non-Gaussian data. We apply our calibration approach to the PSU3D-ICE model which can realistically simulate long-term behavior of WAIS. Our results show that using paleo observations in calibration significantly reduces parametric uncertainty, resulting in sharper projections about the future state of WAIS. One benefit of using paleo observations is found to be that unrealistic simulations with overshoots in past ice retreat and projected future regrowth are eliminated.

stat.AP↗

arXiv2015

Calibrating an ice sheet model using high-dimensional binary spatial data

Rapid retreat of ice in the Amundsen Sea sector of West Antarctica may cause drastic sea level rise, posing significant risks to populations in low-lying coastal regions. Calibration of computer models representing the behavior of the West Antarctic Ice Sheet is key for informative projections of future sea level rise. However, both the relevant observations and the model output are high-dimensional binary spatial data; existing computer model calibration methods are unable to handle such data. Here we present a novel calibration method for computer models whose output is in the form of binary spatial data. To mitigate the computational and inferential challenges posed by our approach, we apply a generalized principal component based dimension reduction method. To demonstrate the utility of our method, we calibrate the PSU3D-ICE model by comparing the output from a 499-member perturbed-parameter ensemble with observations from the Amundsen Sea sector of the ice sheet. Our methods help rigorously characterize the parameter uncertainty even in the presence of systematic data-model discrepancies and dependence in the errors. Our method also helps inform environmental risk analyses by contributing to improved projections of sea level rise from the ice sheets.

stat.AP↗

arXiv2014

Remarks on Kneip's linear smoothers

We were trying to understand the analysis provided by Kneip (1994, Ordered Linear Smoothers). In particular we wanted to persuade ourselves that his results imply the oracle inequality stated by Tsybakov (2014, Lecture 8). This note contains our reworking of Kneip's ideas.

math.ST↗

arXiv2011

Estimation in Functional Regression for General Exponential Families

This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed by constrained maximum likelihood estimation with parameters whose dimension grows with sample size. A change-of-measure argument, inspired by Le Cam's theory of asymptotic equivalence, is used to eliminate the bias caused by the non-linearity of exponential family models.

math.ST↗

arXiv2011

A note on insufficiency and the preservation of Fisher information

Kagan and Shepp (2005, Amer. Statist.) presented an elegant example of a mixture model for which an insufficient statistic preserves Fisher information. This note uses the regularity property of differentiability in quadratic mean to provide another explanation for the phenomenon they observed. Some connections with Le Cam's theory for convergence of experiments are noted.

math.ST↗

arXiv2011

Asymptotics for minimisers of convex processes

By means of two simple convexity arguments we are able to develop a general method for proving consistency and asymptotic normality of estimators that are defined by minimisation of convex criterion functions. This method is then applied to a fair range of different statistical estimation problems, including Cox regression, logistic and Poisson regression, least absolute deviation regression outside model conditions, and pseudo-likelihood estimation for Markov chains. Our paper has two aims. The first is to exposit the method itself, which in many cases, under reasonable regularity conditions, leads to new proofs that are simpler than the traditional proofs. Our second aim is to exploit the method to its limits for logistic regression and Cox regression, where we seek asymptotic results under as weak regularity conditions as possible. For Cox regression in particular we are able to weaken previously published regularity conditions substantially.

math.ST↗

arXiv2011

Some thoughts on Le Cam's statistical decision theory

The paper contains some musings about the abstractions introduced by Lucien Le Cam into the asymptotic theory of statistical inference and decision theory. A short, self-contained proof of a key result (existence of randomizations via convergence in distribution of likelihood ratios), and an outline of a proof of a local asymptotic minimax theorem, are presented as an illustration of how Le Cam's approach leads to conceptual simplifications of asymptotic theory.

math.ST↗

arXiv2011

Conditioned Poisson distributions and the concentration of chromatic numbers

The paper provides a simpler method for proving a delicate inequality that was used by Achlioptis and Naor to establish asymptotic concentration for chromatic numbers of Erdos-Renyi random graphs. The simplifications come from two new ideas. The first involves a sharpened form of a piece of statistical folklore regarding goodness-of-fit tests for two-way tables of Poisson counts under linear conditioning constraints. The second idea takes the form of a new inequality that controls the extreme tails of the distribution of a quadratic form in independent Poissons random variables.

cs.DM↗

arXiv2010

Estimation in functional regression for general exponential families

math.ST↗

arXiv2006

A note on Talagrand's convex hull concentration inequality

The paper reexamines an argument by Talagrand that leads to a remarkable exponential tail bound for the concentration of probability near a set. The main novelty is the replacement of a mysterious Calculus inequality by an application of Jensen's inequality.

math.PR↗

arXiv2005

Tusnady's inequality revisited

Tusnady's inequality is the key ingredient in the KMT/Hungarian coupling of the empirical distribution function with a Brownian bridge. We present an elementary proof of a result that sharpens the Tusnady inequality, modulo constants. Our method uses the beta integral representation of Binomial tails, simple Taylor expansion and some novel bounds for the ratios of normal tail probabilities.

math.ST↗