Measures of observation impact in non-Gaussian data assimilation

ABSTRACT Non-Gaussian/non-linear data assimilation is becoming an increasingly important area of research in the Geosciences as the resolution and non-linearity of models are increased and more and more non-linear observation operators are being used. In this study, we look at the effect of relaxing the assumption of a Gaussian prior on the impact of observations within the data assimilation system. Three different measures of observation impact are studied: the sensitivity of the posterior mean to the observations, mutual information and relative entropy. The sensitivity of the posterior mean is derived analytically when the prior is modelled by a simplified Gaussian mixture and the observation errors are Gaussian. It is found that the sensitivity is a strong function of the value of the observation and proportional to the posterior variance. Similarly, relative entropy is found to be a strong function of the value of the observation. However, the errors in estimating these two measures using a Gaussian approximation to the prior can differ significantly. This hampers conclusions about the effect of the non-Gaussian prior on observation impact. Mutual information does not depend on the value of the observation and is seen to be close to its Gaussian approximation. These findings are illustrated with the particle filter applied to the Lorenz ’63 system. This article is concluded with a discussion of the appropriateness of these measures of observation impact for different situations.

Persistence of a wild type Escherichia coli and its multiple antibiotic-resistant (MAR) derivatives in the abattoir and on chilled pig carcasses

The aim of this study was to evaluate the ability of an Escherichia coli with the multiple antibiotic resistance (MAR) phenotype to withstand the stresses of slaughter compared to an isogenic progenitor strain. A wild type E. coli isolate (345-2RifC) of porcine origin was used to derive 3 isogenic MAR mutants. Escherichia coli 345-2RifC and its MAR derivatives were inoculated into separate groups of pigs. Once colonisation was established, the pigs were slaughtered and persistence of the E. coli strains in the abattoir environment and on the pig carcasses was monitored and compared. No significant difference (P>0.05) was detected between the shedding of the different E. coli strains from the live pigs. Both the parent strain and its MAR derivatives persisted in the abattoir environment, however the parent strain was recovered from 6 of the 13 locations sampled while the MAR derivatives were recovered from 11 of 13 and the number of MAR E. coil recovered was 10-fold higher than the parent strain at half of the locations. The parent strain was not recovered from any of the 6 chilled carcasses whereas the MAR derivatives were recovered from 3 out of 5 (P<0.001). This study demonstrates that the expression of MAR in 345-2RifC increased its ability to survive the stresses of the slaughter and chilling processes. Therefore in E. coli, MAR can give a selective advantage, compared to non-MAR strains, for persistence on chilled carcasses thereby facilitating transit of these strains through the food chain. (C) 2010 Elsevier B.V. All rights reserved.

Colonisation of the chicken caecum by afimbriate and aflagellate derivatives of Salmonella enterica serotype Enteritidis

A semi-quantitative cloacal-swab method was used as an indirect measure of caecal colonisation of one-day old and five-day old chicks after oral dosing with wild-type Salmonella enterica serovar Enteritidis PT4 and,genetically defined isogenic derivatives lacking the ability to elaborate flagella or fimbriae. Birds of both ages were readily and persistently colonised by all strains although there war a decline in shedding by the older birds after about 21 days. There were no significant differences in shedding of wild-type or mutants in single-dose experiments. In competition experiments, in which five-day old birds were dosed orally with wild-type and mutants together, shedding of non-motile derivatives was significantly lower than wild-type, At 35 days post infection, birds were sacrificed and direct counts of mutants and wild-type from each caecum were determined. Whilst there appeared to be poor correlation between direct counts and the indirect swab method, the overall trends shown by these methods of assessment indicated that flagella and not fimbriae were important in caecal colonisation in these models. Crown Copyright (C) 1999 Published by Elsevier Science B.V.

A Gaussian-mixture ensemble transform filter

We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions. Copyright © 2011 Royal Meteorological Society

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Fast identification algorithms for Gaussian process model

A class identification algorithms is introduced for Gaussian process(GP)models.The fundamental approach is to propose a new kernel function which leads to a covariance matrix with low rank,a property that is consequently exploited for computational efficiency for both model parameter estimation and model predictions.The objective of either maximizing the marginal likelihood or the Kullback–Leibler (K–L) divergence between the estimated output probability density function(pdf)and the true pdf has been used as respective cost functions.For each cost function,an efficient coordinate descent algorithm is proposed to estimate the kernel parameters using a one dimensional derivative free search, and noise variance using a fast gradient descent algorithm. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

Commodity price dynamics and derivatives valuation: a review

This paper reviews extant research on commodity price dynamics and commodity derivatives pricing models. In the first half, we provide an overview of stylized facts of commodity price behavior that have been explored and documented in the theoretical and empirical literature. In the second half, we review existing derivatives pricing models and discuss how the peculiarities of commodity markets have been integrated in these models. We conclude the paper with a brief outlook on important research questions that need to be addressed in the future.

Observation impact in data assimilation: the effect of non-Gaussian observation error.

Data assimilation methods which avoid the assumption of Gaussian error statistics are being developed for geoscience applications. We investigate how the relaxation of the Gaussian assumption affects the impact observations have within the assimilation process. The effect of non-Gaussian observation error (described by the likelihood) is compared to previously published work studying the effect of a non-Gaussian prior. The observation impact is measured in three ways: the sensitivity of the analysis to the observations, the mutual information, and the relative entropy. These three measures have all been studied in the case of Gaussian data assimilation and, in this case, have a known analytical form. It is shown that the analysis sensitivity can also be derived analytically when at least one of the prior or likelihood is Gaussian. This derivation shows an interesting asymmetry in the relationship between analysis sensitivity and analysis error covariance when the two different sources of non-Gaussian structure are considered (likelihood vs. prior). This is illustrated for a simple scalar case and used to infer the effect of the non-Gaussian structure on mutual information and relative entropy, which are more natural choices of metric in non-Gaussian data assimilation. It is concluded that approximating non-Gaussian error distributions as Gaussian can give significantly erroneous estimates of observation impact. The degree of the error depends not only on the nature of the non-Gaussian structure, but also on the metric used to measure the observation impact and the source of the non-Gaussian structure.

Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach

The analysis step of the (ensemble) Kalman filter is optimal when (1) the distribution of the background is Gaussian, (2) state variables and observations are related via a linear operator, and (3) the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA) can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1)-(3) are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.

Liquidity effects and FFA returns in the international shipping derivatives market

The study examines the impact of liquidity risk on freight derivatives returns. The Amihud liquidity ratio and bid–ask spreads are utilized to assess the existence of liquidity risk in the freight derivatives market. Other macroeconomic variables are used to control for market risk. Results indicate that liquidity risk is priced and both liquidity measures have a significant role in determining freight derivatives returns. Consistent with expectations, both liquidity measures are found to have positive and significant effects on the returns of freight derivatives. The results have important implications for modeling freight derivatives, and consequently, for trading and risk management purposes.

Alternative generation of CNS neural stem cells and PNS derivatives from neural crest-derived peripheral stem cells

Neural crest-derived stem cells (NCSCs) from the embryonic peripheral nervous system (PNS) can be reprogrammed in neurosphere (NS) culture to rNCSCs that produce central nervous system (CNS) progeny, including myelinating oligodendrocytes. Using global gene expression analysis we now demonstrate that rNCSCs completely lose their previous PNS characteristics and acquire the identity of neural stem cells derived from embryonic spinal cord. Reprogramming proceeds rapidly and results in a homogenous population of Olig2-, Sox3-, and Lex-positive CNS stem cells. Low-level expression of pluripotency inducing genes Oct4, Nanog, and Klf4 argues against a transient pluripotent state during reprogramming. The acquisition of CNS properties is prevented in the presence of BMP4 (BMP NCSCs) as shown by marker gene expression and the potential to produce PNS neurons and glia. In addition, genes characteristic for mesenchymal and perivascular progenitors are expressed, which suggests that BMP NCSCs are directed toward a pericyte progenitor/mesenchymal stem cell (MSC) fate. Adult NCSCs from mouse palate, an easily accessible source of adult NCSCs, display strikingly similar properties. They do not generate cells with CNS characteristics but lose the neural crest markers Sox10 and p75 and produce MSC-like cells. These findings show that embryonic NCSCs acquire a full CNS identity in NS culture. In contrast, MSC-like cells are generated from BMP NCSCs and pNCSCs, which reveals that postmigratory NCSCs are a source for MSC-like cells up to the adult stage.

Estimation of Gaussian process regression model using probability distance measures

A new class of parameter estimation algorithms is introduced for Gaussian process regression (GPR) models. It is shown that the integration of the GPR model with probability distance measures of (i) the integrated square error and (ii) Kullback–Leibler (K–L) divergence are analytically tractable. An efficient coordinate descent algorithm is proposed to iteratively estimate the kernel width using golden section search which includes a fast gradient descent algorithm as an inner loop to estimate the noise variance. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

Gaussian processes autoencoder for dimensionality reduction

Learning low dimensional manifold from highly nonlinear data of high dimensionality has become increasingly important for discovering intrinsic representation that can be utilized for data visualization and preprocessing. The autoencoder is a powerful dimensionality reduction technique based on minimizing reconstruction error, and it has regained popularity because it has been efficiently used for greedy pretraining of deep neural networks. Compared to Neural Network (NN), the superiority of Gaussian Process (GP) has been shown in model inference, optimization and performance. GP has been successfully applied in nonlinear Dimensionality Reduction (DR) algorithms, such as Gaussian Process Latent Variable Model (GPLVM). In this paper we propose the Gaussian Processes Autoencoder Model (GPAM) for dimensionality reduction by extending the classic NN based autoencoder to GP based autoencoder. More interestingly, the novel model can also be viewed as back constrained GPLVM (BC-GPLVM) where the back constraint smooth function is represented by a GP. Experiments verify the performance of the newly proposed model.

On-line Gaussian mixture density estimator for adaptive minimum bit-error-rate beamforming receivers

We develop an on-line Gaussian mixture density estimator (OGMDE) in the complex-valued domain to facilitate adaptive minimum bit-error-rate (MBER) beamforming receiver for multiple antenna based space-division multiple access systems. Specifically, the novel OGMDE is proposed to adaptively model the probability density function of the beamformer’s output by tracking the incoming data sample by sample. With the aid of the proposed OGMDE, our adaptive beamformer is capable of updating the beamformer’s weights sample by sample to directly minimize the achievable bit error rate (BER). We show that this OGMDE based MBER beamformer outperforms the existing on-line MBER beamformer, known as the least BER beamformer, in terms of both the convergence speed and the achievable BER.

Exploring quercetin and luteolin derivatives as antiangiogenic agents

The formation of new blood vessels from the pre-existing vasculature (angiogenesis) is a crucial stage in cancer progression and, indeed, angiogenesis inhibitors are now used as anticancer agents, clinically. Here we have explored the potential of flavonoid derivatives as antiangiogenic agents. Specifically, we have synthesised methoxy and 4-thio derivatives of the natural flavones quercetin and luteolin, two of which (4-thio quercetin and 4-thio luteolin) had never been previously reported. Seven of these compounds showed significant (P<0.05) antiangiogenic activity in an in vitro scratch assay. Their activity ranged from an 86% inhibition of the vascular endothelium growth factor (VEGF)-stimulated migration (observed for methoxyquercetin at 10 µM and for luteolin at 1 µM) to a 36% inhibition (for thiomethoxy quercetin at 10 µM). Western blotting studies showed that most (4 out of 7) compounds inhibited phosphorylation of the VEGF receptor-2 (VEGFR2), suggesting that the antiangiogenic activity was due to an interference with the VEGF/VEGFR2 pathway. Molecular modelling studies looking at the affinity of our compounds towards VEGFR and/or VEGF confirmed this hypothesis, and indeed the compound with the highest antiangiogenic activity (methoxyquercetin) showed the highest affinity towards VEGFR and VEGF. As reports from others have suggested that structurally similar compounds can elicit biological responses via a non-specific, promiscuous membrane perturbation, potential interactions of the active compounds with a model lipid bilayer were assessed via DSC. Luteolin and its derivatives did not perturb the model membrane even at concentrations 10 times higher than the biologically active concentration and only subtle interactions were observed for quercetin and its derivatives. Finally, cytotoxicity assessment of these flavonoid derivatives against MCF-7 breast cancer cells demonstrated also a direct anticancer activity albeit at generally higher concentrations than those required for an antiangiogenic effect (10 fold higher for the methoxy analogues). Taken together these results show promise for flavonoid derivatives as antiangiogenic agents.