Likelihood informed dimension reduction for inverse problems in remote sensing of atmospheric constituent profiles

We use likelihood informed dimension reduction (LIS) (T. Cui et al. 2014) for inverting vertical profile information of atmospheric methane from ground based Fourier transform infrared (FTIR) measurements at Sodankyl\"a, Northern Finland. The measurements belong to the word wide TCCON network for greenhouse gas measurements and, in addition to providing accurate greenhouse gas measurements, they are important for validating satellite observations. LIS allows construction of an efficient Markov chain Monte Carlo sampling algorithm that explores only a reduced dimensional space but still produces a good approximation of the original full dimensional Bayesian posterior distribution. This in effect makes the statistical estimation problem independent of the discretization of the inverse problem. In addition, we compare LIS to a dimension reduction method based on prior covariance matrix truncation used earlier (S. Tukiainen et al. 2016)

Simulation and data processing of GOMOS measurements

In this paper the data simulation and data inversion studies for stellar occultation measurements are discussed. The specific application is the Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument which has been proposed for the first European Platform, Polar Orbiting Earth Mission (POEM-1)

On the flexibility of the design of Multiple Try Metropolis schemes

The Multiple Try Metropolis (MTM) method is a generalization of the classical Metropolis-Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities and show different numerical results

Kernel Sequential Monte Carlo

We propose kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities. KSMC is a family of sequential Monte Carlo algorithms that are based on building emulator models of the current particle system in a reproducing kernel Hilbert space. We here focus on modelling nonlinear covariance structure and gradients of the target. The emulator’s geometry is adaptively updated and subsequently used to inform local proposals. Unlike in adaptive Markov chain Monte Carlo, continuous adaptation does not compromise convergence of the sampler. KSMC combines the strengths of sequental Monte Carlo and kernel methods: superior performance for multimodal targets and the ability to estimate model evidence as compared to Markov chain Monte Carlo, and the emulator’s ability to represent targets that exhibit high degrees of nonlinearity. As KSMC does not require access to target gradients, it is particularly applicable on targets whose gradients are unknown or prohibitively expensive. We describe necessary tuning details and demonstrate the benefits of the the proposed methodology on a series of challenging synthetic and real-world examples

Estimation of ECHAM5 climate model closure parameters with adaptive MCMC

Climate models contain closure parameters to which the model climate is sensitive. These parameters appear in physical parameterization schemes where some unresolved variables are expressed by predefined parameters rather than being explicitly modeled. Currently, best expert knowledge is used to define the optimal closure parameter values, based on observations, process studies, large eddy simulations, etc. Here, parameter estimation, based on the adaptive Markov chain Monte Carlo (MCMC) method, is applied for estimation of joint posterior probability density of a small number (<i>n</i>=4) of closure parameters appearing in the ECHAM5 climate model. The parameters considered are related to clouds and precipitation and they are sampled by an adaptive random walk process of the MCMC. The parameter probability densities are estimated simultaneously for all parameters, subject to an objective function. Five alternative formulations of the objective function are tested, all related to the net radiative flux at the top of the atmosphere. Conclusions of the closure parameter estimation tests with a low-resolution ECHAM5 climate model indicate that (i) adaptive MCMC is a viable option for parameter estimation in large-scale computational models, and (ii) choice of the objective function is crucial for the identifiability of the parameter distributions

Parameter variations in prediction skill optimization at ECMWF

Peer reviewe

An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area which we feel deserves much further attention. Towards this aim, this paper proposes a general-purpose algorithm for automatic density exploration. The proposed exploration algorithm combines and expands upon components from various adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at its heart. Additionally, the algorithm is run on interacting parallel chains -- a feature which both decreases computational cost as well as stabilizes the algorithm, improving its ability to explore the density. Performance is studied in several applications. Through a Bayesian variable selection example, the authors demonstrate the convergence gains obtained with interacting chains. The ability of the algorithm's adaptive proposal to induce mode-jumping is illustrated through a trimodal density and a Bayesian mixture modeling application. Lastly, through a 2D Ising model, the authors demonstrate the ability of the algorithm to overcome the high correlations encountered in spatial models.Comment: 33 pages, 20 figures (the supplementary materials are included as appendices

Immune-mediated competition in rodent malaria is most likely caused by induced changes in innate immune clearance of merozoites

Malarial infections are often genetically diverse, leading to competitive interactions between parasites. A quantitative understanding of the competition between strains is essential to understand a wide range of issues, including the evolution of virulence and drug resistance. In this study, we use dynamical-model based Bayesian inference to investigate the cause of competitive suppression of an avirulent clone of Plasmodium chabaudi (AS) by a virulent clone (AJ) in immuno-deficient and competent mice. We test whether competitive suppression is caused by clone-specific differences in one or more of the following processes: adaptive immune clearance of merozoites and parasitised red blood cells (RBCs), background loss of merozoites and parasitised RBCs, RBC age preference, RBC infection rate, burst size, and within-RBC interference. These processes were parameterised in dynamical mathematical models and fitted to experimental data. We found that just one parameter μ, the ratio of background loss rate of merozoites to invasion rate of mature RBCs, needed to be clone-specific to predict the data. Interestingly, μ was found to be the same for both clones in single-clone infections, but different between the clones in mixed infections. The size of this difference was largest in immuno-competent mice and smallest in immuno-deficient mice. This explains why competitive suppression was alleviated in immuno-deficient mice. We found that competitive suppression acts early in infection, even before the day of peak parasitaemia. These results lead us to argue that the innate immune response clearing merozoites is the most likely, but not necessarily the only, mediator of competitive interactions between virulent and avirulent clones. Moreover, in mixed infections we predict there to be an interaction between the clones and the innate immune response which induces changes in the strength of its clearance of merozoites. What this interaction is unknown, but future refinement of the model, challenged with other datasets, may lead to its discovery

A generative approach for image-based modeling of tumor growth

22nd International Conference, IPMI 2011, Kloster Irsee, Germany, July 3-8, 2011. ProceedingsExtensive imaging is routinely used in brain tumor patients to monitor the state of the disease and to evaluate therapeutic options. A large number of multi-modal and multi-temporal image volumes is acquired in standard clinical cases, requiring new approaches for comprehensive integration of information from different image sources and different time points. In this work we propose a joint generative model of tumor growth and of image observation that naturally handles multi-modal and longitudinal data. We use the model for analyzing imaging data in patients with glioma. The tumor growth model is based on a reaction-diffusion framework. Model personalization relies only on a forward model for the growth process and on image likelihood. We take advantage of an adaptive sparse grid approximation for efficient inference via Markov Chain Monte Carlo sampling. The approach can be used for integrating information from different multi-modal imaging protocols and can easily be adapted to other tumor growth models.German Academy of Sciences Leopoldina (Fellowship Programme LPDS 2009-10)Academy of Finland (133611)National Institutes of Health (U.S.) (NIBIB NAMIC U54-EB005149)National Institutes of Health (U.S.) (NCRR NAC P41- RR13218)National Institutes of Health (U.S.) (NINDS R01-NS051826)National Institutes of Health (U.S.) (NIH R01-NS052585)National Institutes of Health (U.S.) (NIH R01-EB006758)National Institutes of Health (U.S.) (NIH R01-EB009051)National Institutes of Health (U.S.) (NIH P41-RR014075)National Science Foundation (U.S.) (CAREER Award 0642971

The academic backbone: longitudinal continuities in educational achievement from secondary school and medical school to MRCP(UK) and the specialist register in UK medical students and doctors

Background: Selection of medical students in the UK is still largely based on prior academic achievement, although doubts have been expressed as to whether performance in earlier life is predictive of outcomes later in medical school or post-graduate education. This study analyses data from five longitudinal studies of UK medical students and doctors from the early 1970s until the early 2000s. Two of the studies used the AH5, a group test of general intelligence (that is, intellectual aptitude). Sex and ethnic differences were also analyzed in light of the changing demographics of medical students over the past decades. Methods: Data from five cohort studies were available: the Westminster Study (began clinical studies from 1975 to 1982), the 1980, 1985, and 1990 cohort studies (entered medical school in 1981, 1986, and 1991), and the University College London Medical School (UCLMS) Cohort Study (entered clinical studies in 2005 and 2006). Different studies had different outcome measures, but most had performance on basic medical sciences and clinical examinations at medical school, performance in Membership of the Royal Colleges of Physicians (MRCP(UK)) examinations, and being on the General Medical Council Specialist Register. Results: Correlation matrices and path analyses are presented. There were robust correlations across different years at medical school, and medical school performance also predicted MRCP(UK) performance and being on the GMC Specialist Register. A-levels correlated somewhat less with undergraduate and post-graduate performance, but there was restriction of range in entrants. General Certificate of Secondary Education (GCSE)/O-level results also predicted undergraduate and post-graduate outcomes, but less so than did A-level results, but there may be incremental validity for clinical and post-graduate performance. The AH5 had some significant correlations with outcome, but they were inconsistent. Sex and ethnicity also had predictive effects on measures of educational attainment, undergraduate, and post-graduate performance. Women performed better in assessments but were less likely to be on the Specialist Register. Non-white participants generally underperformed in undergraduate and post-graduate assessments, but were equally likely to be on the Specialist Register. There was a suggestion of smaller ethnicity effects in earlier studies. Conclusions: The existence of the Academic Backbone concept is strongly supported, with attainment at secondary school predicting performance in undergraduate and post-graduate medical assessments, and the effects spanning many years. The Academic Backbone is conceptualized in terms of the development of more sophisticated underlying structures of knowledge ('cognitive capital’ and 'medical capital’). The Academic Backbone provides strong support for using measures of educational attainment, particularly A-levels, in student selection