Composite likelihood estimation for the Brown-Resnick process

Genton et al. (2011) investigated the gain in efficiency when triplewise, rather than pairwise, likelihood is used to fit the popular Smith max-stable model for spatial extremes. We generalize their results to the Brown-Resnick model and show that the efficiency gain is substantial only for very smooth processes, which are generally unrealistic in application

Differential Imaging of Biological Structures with Doubly-resonant Coherent Anti-stokes Raman Scattering (CARS)

Coherent Raman imaging techniques have seen a dramatic increase in activity over the past decade due to their promise to enable label-free optical imaging with high molecular specificity 1. The sensitivity of these techniques, however, is many orders of magnitude weaker than fluorescence, requiring milli-molar molecular concentrations 1,2. Here, we describe a technique that can enable the detection of weak or low concentrations of Raman-active molecules by amplifying their signal with that obtained from strong or abundant Raman scatterers. The interaction of short pulsed lasers in a biological sample generates a variety of coherent Raman scattering signals, each of which carry unique chemical information about the sample. Typically, only one of these signals, e.g. Coherent Anti-stokes Raman scattering (CARS), is used to generate an image while the others are discarded. However, when these other signals, including 3-color CARS and four-wave mixing (FWM), are collected and compared to the CARS signal, otherwise difficult to detect information can be extracted 3. For example, doubly-resonant CARS (DR-CARS) is the result of the constructive interference between two resonant signals 4. We demonstrate how tuning of the three lasers required to produce DR-CARS signals to the 2845 cm-1 CH stretch vibration in lipids and the 2120 cm-1 CD stretching vibration of a deuterated molecule (e.g. deuterated sugars, fatty acids, etc.) can be utilized to probe both Raman resonances simultaneously. Under these conditions, in addition to CARS signals from each resonance, a combined DR-CARS signal probing both is also generated. We demonstrate how detecting the difference between the DR-CARS signal and the amplifying signal from an abundant molecule's vibration can be used to enhance the sensitivity for the weaker signal. We further demonstrate that this approach even extends to applications where both signals are generated from different molecules, such that e.g. using the strong Raman signal of a solvent can enhance the weak Raman signal of a dilute solute

Geostatistics of Dependent and Asymptotically Independent Extremes

Spatial modeling of rare events has obvious applications in the environmental sciences and is crucial when assessing the effects of catastrophic events (such as heatwaves or widespread flooding) on food security and on the sustainability of societal infrastructure. Although classical geostatistics is largely based on Gaussian processes and distributions, these are not appropriate for extremes, for which max-stable and related processes provide more suitable models. This paper provides a brief overview of current work on the statistics of spatial extremes, with an emphasis on the consequences of the assumption of max-stability. Applications to winter minimum temperatures and daily rainfall are describe

Max-and-Smooth: a two-step approach for approximate Bayesian inference in latent Gaussian models

This is the final version. Available on open access from International Society for Bayesian Analysis (ISBA) via the DOI in this record. With modern high-dimensional data, complex statistical models are necessary, requiring computationally feasible inference schemes. We introduce Max-and-Smooth, an approximate Bayesian inference scheme for a flexible class of latent Gaussian models (LGMs) where one or more of the likelihood parameters are modeled by latent additive Gaussian processes. Max-and-Smooth consists of two-steps. In the first step (Max), the likelihood function is approximated by a Gaussian density with mean and covariance equal to either (a) the maximum likelihood estimate and the inverse observed information, respectively, or (b) the mean and covariance of the normalized likelihood function. In the second step (Smooth), the latent parameters and hyperparameters are inferred and smoothed with the approximated likelihood function. The proposed method ensures that the uncertainty from the first step is correctly propagated to the second step. Since the approximated likelihood function is Gaussian, the approximate posterior density of the latent parameters of the LGM (conditional on the hyperparameters) is also Gaussian, thus facilitating efficient posterior inference in high dimensions. Furthermore, the approximate marginal posterior distribution of the hyperparameters is tractable, and as a result, the hyperparameters can be sampled independently of the latent parameters. In the case of a large number of independent data replicates, sparse precision matrices, and high-dimensional latent vectors, the speedup is substantial in comparison to an MCMC scheme that infers the posterior density from the exact likelihood function. The proposed inference scheme is demonstrated on one spatially referenced real dataset and on simulated data mimicking spatial, temporal, and spatio-temporal inference problems. Our results show that Max-and-Smooth is accurate and fast.NER

Incidence of Arrhythmias and Myocardial Ischaemia During Haemodialysis and Haemofiltration

Thirty-two patients (10 male, 22 female; age 37-82 years) undergoing maintenance haemodialysis or haemofiltration were studied by means of Holter device capable of simultaneously analysing rhythm and ST changes in three leads. Twenty-five patients were on haemodialysis, seven on haemofiltration, mean duration of haemodialysis/haemofiltration being 3.4±3 years. Incidence of ventricular tachycardia was low, being detected only in 1 of 32 patients. Ventricular premature beats in excess of 10/h during a period of 2 h were found in 8 of 32 patients and 100 supraventricular premature beats for 2 h or more in 4 of 32 patients. Both ventricular premature beats and supraventricular premature beats were most frequently recorded during the last hour of haemodialysis/haemofiltration. ECG signs of ischaemia were detected in eight patients, four of whom were asymptomatic. Ischaemia also occurred predominantly during the last hour of haemodialysis/haemofiltration. Two symptomatic patients displayed neither arrhythmias nor ST-changes while being monitored. The study shows that silent ischaemia and arrhythmias in patients under going chronic haemodialysis/haemofiltration may not be infrequent. Recognition of these events could be of importance in the management of these patient

Space-time modelling of extreme events

Max-stable processes are the natural analogues of the generalized extreme-value distribution when modelling extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of independent replications of random fields, and they are also suitable for the modelling of extreme measurements over high thresholds. This paper shows how a pairwise censored likelihood can be used for consistent estimation of the extremes of space-time data under mild mixing conditions, and illustrates this by fitting an extension of a model of Schlather (2002) to hourly rainfall data. A block bootstrap procedure is used for uncertainty assessment. Estimator efficiency is considered and the choice of pairs to be included in the pairwise likelihood is discussed. The proposed model fits the data better than some natural competitors

Bayesian Networks for Max-linear Models

We study Bayesian networks based on max-linear structural equations as introduced in Gissibl and Kl\"uppelberg [16] and provide a summary of their independence properties. In particular we emphasize that distributions for such networks are generally not faithful to the independence model determined by their associated directed acyclic graph. In addition, we consider some of the basic issues of estimation and discuss generalized maximum likelihood estimation of the coefficients, using the concept of a generalized likelihood ratio for non-dominated families as introduced by Kiefer and Wolfowitz [21]. Finally we argue that the structure of a minimal network asymptotically can be identified completely from observational data.Comment: 18 page

Approximate Bayesian inference for analysis of spatiotemporal flood frequency data

This is the final version. Available from the Institute of Mathematical Statistics via the DOI in this recordExtreme floods cause casualties and widespread damage to property and vital civil infrastructure. Predictions of extreme floods, within gauged and ungauged catchments, is crucial to mitigate these disasters. In this paper a Bayesian framework is proposed for predicting extreme floods, using the generalized extreme-value (GEV) distribution. A major methodological challenge is to find a suitable parametrization for the GEV distribution when multiple covariates and/or latent spatial effects are involved and a time trend is present. Other challenges involve balancing model complexity and parsimony, using an appropriate model selection procedure and making inference based on a reliable and computationally efficient approach. We here propose a latent Gaussian modeling framework with a novel multivariate link function designed to separate the interpretation of the parameters at the latent level and to avoid unreasonable estimates of the shape and time trend parameters. Structured additive regression models, which include catchment descriptors as covariates and spatially correlated model components, are proposed for the four parameters at the latent level. To achieve computational efficiency with large datasets and richly parametrized models, we exploit a highly accurate and fast approximate Bayesian inference approach which can also be used to efficiently select models separately for each of the four regression models at the latent level. We applied our proposed methodology to annual peak river flow data from 554 catchments across the United Kingdom. The framework performed well in terms of flood predictions for both ungauged catchments and future observations at gauged catchments. The results show that the spatial model components for the transformed location and scale parameters as well as the time trend are all important, and none of these should be ignored. Posterior estimates of the time trend parameters correspond to an average increase of about 1.5% per decade with range 0.1% to 2.8% and reveal a spatial structure across the United Kingdom. When the interest lies in estimating return levels for spatial aggregates, we further develop a novel copula-based postprocessing approach of posterior predictive samples in order to mitigate the effect of the conditional independence assumption at the data level, and we demonstrate that our approach indeed provides accurate results.University of Iceland Research Fun

Approximate Bayesian inference for analysis of spatio-temporal flood frequency data

This is the final version. Available from the Institute of Mathematical Statistics via the DOI in this record. Extreme floods cause casualties, and widespread damage to property and vital civil infrastructure. We here propose a Bayesian approach for predicting extreme floods using the generalized extreme-value (GEV) distribution within gauged and ungauged catchments. A major methodological challenge is to find a suitable parametrization for the GEV distribution when covariates or latent spatial effects are involved. Other challenges involve balancing model complexity and parsimony using an appropriate model selection procedure, and making inference using a reliable and computationally efficient approach. Our approach relies on a latent Gaussian modeling framework with a novel multivariate link function designed to separate the interpretation of the parameters at the latent level and to avoid unreasonable estimates of the shape and time trend parameters. Structured additive regression models are proposed for the four parameters at the latent level. For computational efficiency with large datasets and richly parametrized models, we exploit an accurate and fast approximate Bayesian inference approach. We applied our proposed methodology to annual peak river flow data from 554 catchments across the United Kingdom (UK). Our model performed well in terms of flood predictions for both gauged and ungauged catchments. The results show that the spatial model components for the transformed location and scale parameters, and the time trend, are all important. Posterior estimates of the time trend parameters correspond to an average increase of about $1.5\%$ per decade and reveal a spatial structure across the UK. To estimate return levels for spatial aggregates, we further develop a novel copula-based post-processing approach of posterior predictive samples, in order to mitigate the effect of the conditional independence assumption at the data level, and we show that our approach provides accurate results.University of Iceland Research Fun