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Murali Haran

Publications and source records attributed to Murali Haran.

At least 37 records · Page 2Linked to original sources
arXiv2019

A Function Emulation Approach for Doubly Intractable Distributions

Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable normalising "constants" that are actually functions of the parameters of interest. Although several clever computational methods have been developed for these models, each method suffers from computational issues that makes it computationally burdensome or even infeasible for many problems. We propose a novel algorithm that provides computational gains over existing methods by replacing Monte Carlo approximations to the normalising function with a Gaussian process-based approximation. We provide theoretical justification for this method. We also develop a closely related algorithm that is applicable more broadly to any likelihood function that is expensive to evaluate. We illustrate the application of our methods to a variety of challenging simulated and real data examples, including an exponential random graph model, a Markov point process, and a model for infectious disease dynamics. The algorithm shows significant gains in computational efficiency over existing methods, and has the potential for greater gains for more challenging problems. For a random graph model example, we show how this gain in efficiency allows us to carry out accurate Bayesian inference when other algorithms are computationally impractical.

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arXiv2019

Computer model calibration based on image warping metrics: an application for sea ice deformation

Arctic sea ice plays an important role in the global climate. Sea ice models governed by physical equations have been used to simulate the state of the ice including characteristics such as ice thickness, concentration, and motion. More recent models also attempt to capture features such as fractures or leads in the ice. These simulated features can be partially misaligned or misshapen when compared to observational data, whether due to numerical approximation or incomplete physics. In order to make realistic forecasts and improve understanding of the underlying processes, it is necessary to calibrate the numerical model to field data. Traditional calibration methods based on generalized least-square metrics are flawed for linear features such as sea ice cracks. We develop a statistical emulation and calibration framework that accounts for feature misalignment and misshapenness, which involves optimally aligning model output with observed features using cutting edge image registration techniques. This work can also have application to other physical models which produce coherent structures.

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arXiv2018

Quantifying Spatio-Temporal Variation of Invasion Spread

The spread of invasive species can have far reaching environmental and ecological consequences. Understanding invasion spread patterns and the underlying process driving invasions are key to predicting and managing invasions. We combine a set of statistical methods in a novel way to characterize local spread properties and demonstrate their application using simulated and historical data on invasive insects. Our method uses a Gaussian process fit to the surface of waiting times to invasion in order to characterize the vector field of spread. Using this method we estimate with statistical uncertainties the speed and direction of spread at each location. Simulations from a stratified diffusion model verify the accuracy of our method. We show how we may link local rates of spread to environmental covariates for two case studies: the spread of the gypsy moth (Lymantria dispar), and hemlock wolly adelgid (Adelges tsugae) in North America. We provide an R-package that automates the calculations for any spatially referenced waiting time data.

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arXiv2018

A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models

Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain Monte Carlo (MCMC) algorithms for these models tend to be slow mixing. Moreover, spatial confounding inflates the variance of fixed effect (regression coefficient) estimates. Our approach addresses both the computational and confounding issues by replacing the high-dimensional spatial random effects with a reduced-dimensional representation based on random projections. Standard MCMC algorithms mix well and the reduced-dimensional setting speeds up computations per iteration. We show, via simulated examples, that Bayesian inference for this reduced-dimensional approach works well both in terms of inference as well as prediction, our methods also compare favorably to existing "reduced-rank" approaches. We also apply our methods to two real world data examples, one on bird count data and the other classifying rock types.

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arXiv2018

Bayesian Inference in the Presence of Intractable Normalizing Functions

Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference for these models is complicated because the normalizing functions of their probability distributions include the parameters of interest. In Bayesian analysis they result in so-called doubly intractable posterior distributions which pose significant computational challenges. Several Monte Carlo methods have emerged in recent years to address Bayesian inference for such models. We provide a framework for understanding the algorithms and elucidate connections among them. Through multiple simulated and real data examples, we compare and contrast the computational and statistical efficiency of these algorithms and discuss their theoretical bases. Our study provides practical recommendations for practitioners along with directions for future research for MCMC methodologists.

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arXiv2017

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.

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arXiv2017

An Ensemble Approach to Predicting the Impact of Vaccination on Rotavirus Disease in Niger

Recently developed vaccines provide a new way of controlling rotavirus in sub-Saharan Africa. Models for the transmission dynamics of rotavirus are critical both for estimating current burden from imperfect surveillance and for assessing potential effects of vaccine intervention strategies. We examine rotavirus infection in the Maradi area in southern Niger using hospital surveillance data provided by Epicentre collected over two years. Additionally, a cluster survey of households in the region allows us to estimate the proportion of children with diarrhea who consulted at a health structure. Model fit and future projections are necessarily particular to a given model; thus, where there are competing models for the underlying epidemiology an ensemble approach can account for that uncertainty. We compare our results across several variants of Susceptible-Infectious-Recovered (SIR) compartmental models to quantify the impact of modeling assumptions on our estimates. Model-specific parameters are estimated by Bayesian inference using Markov chain Monte Carlo. We then use Bayesian model averaging to generate ensemble estimates of the current dynamics, including estimates of $R_0$, the burden of infection in the region, as well as the impact of vaccination on both the short-term dynamics and the long-term reduction of rotavirus incidence under varying levels of coverage. The ensemble of models predicts that the current burden of severe rotavirus disease is 2.9 to 4.1% of the population each year and that a 2-dose vaccine schedule achieving 70% coverage could reduce burden by 37-43%.

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arXiv2017

A Spatially-Varying Stochastic Differential Equation Model for Animal Movement

Animal movement exhibits complex behavior which can be influenced by unobserved environmental conditions. We propose a model which allows for a spatially-varying movement rate and spatially-varying drift through a semiparametric potential surface and a separate motility surface. These surfaces are embedded in a stochastic differential equation framework which allows for complex animal movement patterns in space. The resulting model is used to analyze the spatially-varying behavior of ants to provide insight into the spatial structure of ant movement in the nest.

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arXiv2016

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.

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arXiv2016

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.

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arXiv2015

Dynamic Models of Animal Movement with Spatial Point Process Interactions

When analyzing animal movement, it is important to account for interactions between individuals. However, statistical models for incorporating interaction behavior in movement models are limited. We propose an approach that models dependent movement by augmenting a dynamic marginal movement model with a spatial point process interaction function within a weighted distribution framework. The approach is flexible, as marginal movement behavior and interaction behavior can be modeled independently. Inference for model parameters is complicated by intractable normalizing constants. We develop a double Metropolis-Hastings algorithm to perform Bayesian inference. We illustrate our approach through the analysis of movement tracks of guppies (Poecilia reticulata)

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arXiv2014

Fast dimension-reduced climate model calibration and the effect of data aggregation

How will the climate system respond to anthropogenic forcings? One approach to this question relies on climate model projections. Current climate projections are considerably uncertain. Characterizing and, if possible, reducing this uncertainty is an area of ongoing research. We consider the problem of making projections of the North Atlantic meridional overturning circulation (AMOC). Uncertainties about climate model parameters play a key role in uncertainties in AMOC projections. When the observational data and the climate model output are high-dimensional spatial data sets, the data are typically aggregated due to computational constraints. The effects of aggregation are unclear because statistically rigorous approaches for model parameter inference have been infeasible for high-resolution data. Here we develop a flexible and computationally efficient approach using principal components and basis expansions to study the effect of spatial data aggregation on parametric and projection uncertainties. Our Bayesian reduced-dimensional calibration approach allows us to study the effect of complicated error structures and data-model discrepancies on our ability to learn about climate model parameters from high-dimensional data. Considering high-dimensional spatial observations reduces the effect of deep uncertainty associated with prior specifications for the data-model discrepancy. Also, using the unaggregated data results in sharper projections based on our climate model. Our computationally efficient approach may be widely applicable to a variety of high-dimensional computer model calibration problems.

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arXiv2014

An attraction-repulsion point process model for respiratory syncytial virus infections

How is the progression of a virus influenced by properties intrinsic to individual cells? We address this question by studying the susceptibility of cells infected with two strains of the human respiratory syncytial virus (RSV-A and RSV-B) in an in vitro experiment. Spatial patterns of infected cells give us insight into how local conditions influence susceptibility to the virus. We observe a complicated attraction and repulsion behavior, a tendency for infected cells to lump together or remain apart. We develop a new spatial point process model to describe this behavior. Inference on spatial point processes is difficult because the likelihood functions of these models contain intractable normalizing constants; we adapt an MCMC algorithm called double Metropolis-Hastings to overcome this computational challenge. Our methods are computationally efficient even for large point patterns consisting of over 10,000 points. We illustrate the application of our model and inferential approach to simulated data examples and fit our model to various RSV experiments. Because our model parameters are easy to interpret, we are able to draw meaningful scientific conclusions from the fitted models.

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arXiv2013

A composite likelihood approach to computer model calibration using high-dimensional spatial data

Computer models are used to model complex processes in various disciplines. Often, a key source of uncertainty in the behavior of complex computer models is uncertainty due to unknown model input parameters. Statistical computer model calibration is the process of inferring model parameter values, along with associated uncertainties, from observations of the physical process and from model outputs at various parameter settings. Observations and model outputs are often in the form of high-dimensional spatial fields, especially in the environmental sciences. Sound statistical inference may be computationally challenging in such situations. Here we introduce a composite likelihood-based approach to perform computer model calibration with high-dimensional spatial data. While composite likelihood has been studied extensively in the context of spatial statistics, computer model calibration using composite likelihood poses several new challenges. We propose a computationally efficient approach for Bayesian computer model calibration using composite likelihood. We also develop a methodology based on asymptotic theory for adjusting the composite likelihood posterior distribution so that it accurately represents posterior uncertainties. We study the application of our new approach in the context of calibration for a climate model.

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arXiv2013

Emulating a gravity model to infer the spatiotemporal dynamics of an infectious disease

Probabilistic models for infectious disease dynamics are useful for understanding the mechanism underlying the spread of infection. When the likelihood function for these models is expensive to evaluate, traditional likelihood-based inference may be computationally intractable. Furthermore, traditional inference may lead to poor parameter estimates and the fitted model may not capture important biological characteristics of the observed data. We propose a novel approach for resolving these issues that is inspired by recent work in emulation and calibration for complex computer models. Our motivating example is the gravity time series susceptible-infected-recovered (TSIR) model. Our approach focuses on the characteristics of the process that are of scientific interest. We find a Gaussian process approximation to the gravity model using key summary statistics obtained from model simulations. We demonstrate via simulated examples that the new approach is computationally expedient, provides accurate parameter inference, and results in a good model fit. We apply our method to analyze measles outbreaks in England and Wales in two periods, the pre-vaccination period from 1944-1965 and the vaccination period from 1966-1994. Based on our results, we are able to obtain important scientific insights about the transmission of measles. In general, our method is applicable to problems where traditional likelihood-based inference is computationally intractable or produces a poor model fit. It is also an alternative to approximate Bayesian computation (ABC) when simulations from the model are expensive.

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arXiv2012

On automating Markov chain Monte Carlo for a class of spatial models

Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users still have to contend with several challenges with each implementation of the algorithm. These challenges include determining how to construct an efficient algorithm, finding reasonable starting values, deciding whether the sample-based estimates are accurate, and determining an appropriate length (stopping rule) for the Markov chain. We describe an approach for resolving these issues in a theoretically sound fashion in the context of spatial generalized linear models, an important class of models that result in challenging posterior distributions. Our approach combines analytical approximations for constructing provably fast mixing MCMC algorithms, and takes advantage of recent developments in MCMC theory. We apply our methods to real data examples, and find that our MCMC algorithm is automated and efficient. Furthermore, since starting values, rigorous error estimates and theoretically justified stopping rules for the sampling algorithm are all easily obtained for our examples, our MCMC-based estimation is practically as easy to perform as Monte Carlo estimation based on independent and identically distributed draws.

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arXiv2010

Dimension Reduction and Alleviation of Confounding for Spatial Generalized Linear Mixed Models

Non-gaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model (SGLMM) offers a very popular and flexible approach to modeling such data, but the SGLMM suffers from three major shortcomings: (1) uninterpretability of parameters due to spatial confounding, (2) variance inflation due to spatial confounding, and (3) high-dimensional spatial random effects that make fully Bayesian inference for such models computationally challenging. We propose a new parameterization of the SGLMM that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects. We illustrate the application of our approach to simulated binary, count, and Gaussian spatial datasets, and to a large infant mortality dataset.

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