arXiv subjects

Jake Carson

Publications and source records attributed to Jake Carson.

5 recordsLinked to original sources

arXiv2021

Efficient Bayesian model selection for coupled hidden Markov models with application to infectious diseases

Performing model selection for coupled hidden Markov models (CHMMs) is highly challenging, owing to the large dimension of the hidden state process. Whilst in principle the hidden state process can be marginalized out via forward filtering, in practice the computational cost of doing so increases exponentially with the number of coupled Markov chains, making this approach infeasible in most applications. Monte Carlo methods can be utilized, but despite many remarkable developments in model selection methodology, generic approaches continue to be ill-suited for such high-dimensional problems. Here we develop specialized solutions for CHMMs with weak inter-chain dependencies. Specifically we construct effective proposal distributions for the hidden state process that remain computationally viable as the number of chains increases, and that require little user input or tuning. This methodology is particularly applicable to individual-level infectious disease models characterized as CHMMs, in which each chain represents an individual, and the coupling represents contact between individuals. Since the only significant contacts are between susceptible and infectious individuals, and since multiple infection pathways are often possible, the resulting CHMMs naturally have low inter-chain dependencies. We demonstrate the utility of our methodology with an application to a study of highly pathogenic avian influenza in chickens.

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arXiv2018

Quantifying Age and Model Uncertainties in Paleoclimate Data and Dynamical Climate Models with a Joint Inferential Analysis

A major goal in paleoclimate science is to reconstruct historical climates using proxies for climate variables such as those observed in sediment cores, and in the process learn about climate dynamics. This is hampered by uncertainties in how sediment core depths relate to ages, how proxy quantities relate to climate variables, how climate models are specified, and the values of parameters in climate models. Quantifying these uncertainties is key in drawing well founded conclusions. Analyses are often performed in separate stages with, for example, a sediment core's depth-age relation being estimated as stage one, then fed as an input to calibrate climate models as stage two. Here, we show that such "multi-stage" approaches can lead to misleading conclusions. We develop a joint inferential approach for climate reconstruction, model calibration, and age model estimation. We focus on the glacial-interglacial cycle over the past 780 kyr, analysing two sediment cores that span this range. Our age estimates are largely in agreement with previous studies, but provides the full joint specification of all uncertainties, estimation of model parameters, and the model evidence. By sampling plausible chronologies from the posterior distribution, we demonstrate that downstream scientific conclusions can differ greatly both between different sampled chronologies, and in comparison with conclusions obtained in the complete joint inferential analysis. We conclude that multi-stage analyses are insufficient when dealing with uncertainty, and that to draw sound conclusions the full joint inferential analysis must be performed.

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arXiv2016

Bayesian modelling and quantification of Raman spectroscopy

Raman spectroscopy can be used to identify molecules such as DNA by the characteristic scattering of light from a laser. It is sensitive at very low concentrations and can accurately quantify the amount of a given molecule in a sample. The presence of a large, nonuniform background presents a major challenge to analysis of these spectra. To overcome this challenge, we introduce a sequential Monte Carlo (SMC) algorithm to separate the observed spectrum into a series of peaks plus a smoothly-varying baseline, corrupted by additive white noise. The peaks are modelled using Lorentzian or Gaussian broadening functions, while the baseline is estimated using a penalised cubic spline. This latent continuous representation accounts for differences in resolution between measurements. By incorporating this representation in a Bayesian model, we can quantify the relationship between molecular concentration and peak intensity, thereby providing an improved estimate of the limit of detection (LOD), which is of major importance in analytical chemistry.

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arXiv2016

Unbiased local solutions of partial differential equations via the Feynman-Kac Identities

The Feynman-Kac formulae (FKF) express local solutions of partial differential equations (PDEs) as expectations with respect to some complementary stochastic differential equation (SDE). Repeatedly sampling paths from the complementary SDE enables the construction of Monte Carlo estimates of local solutions, which are more naturally suited to statistical inference than the numerical approximations obtained via finite difference and finite element methods. Until recently, simulating from the complementary SDE would have required the use of a discrete-time approximation, leading to biased estimates. In this paper we utilize recent developments in two areas to demonstrate that it is now possible to obtain unbiased solutions for a wide range of PDE models via the FKF. The first is the development of algorithms that simulate diffusion paths exactly (without discretization error), and so make it possible to obtain Monte Carlo estimates of the FKF directly. The second is the development of debiasing methods for SDEs, enabling the construction of unbiased estimates from a sequence of biased estimates.

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arXiv2015

Bayesian model selection for the glacial-interglacial cycle

A prevailing viewpoint in palaeoclimate science is that a single palaeoclimate record contains insufficient information to discriminate between most competing explanatory models. Results we present here suggest the contrary. Using SMC^2 combined with novel Brownian bridge type proposals for the state trajectories, we show that even with relatively short time series it is possible to estimate Bayes factors to sufficient accuracy to be able to select between competing models. The results show that Monte Carlo methodology and computer power have now advanced to the point where a full Bayesian analysis for a wide class of conceptual climate models is now possible. The results also highlight a problem with estimating the chronology of the climate record prior to further statistical analysis, a practice which is common in palaeoclimate science. Using two datasets based on the same record but with different estimated chronologies results in conflicting conclusions about the importance of the orbital forcing on the glacial cycle, and about the internal dynamics generating the glacial cycle, even though the difference between the two estimated chronologies is consistent with dating uncertainty. This highlights a need for chronology estimation and other inferential questions to be addressed in a joint statistical procedure.

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