The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

On aposteriori error analysis of dG schemes approximating hyperbolic conservation laws

This contribution is concerned with aposteriori error analysis of discontinuous Galerkin (dG) schemes approximating hyperbolic conservation laws. In the scalar case the aposteriori analysis is based on the L1 contraction property and the doubling of variables technique. In the system case the appropriate stability framework is in L2, based on relative entropies. It is only applicable if one of the solutions, which are compared to each other, is Lipschitz. For dG schemes approximating hyperbolic conservation laws neither the entropy solution nor the numerical solution need to be Lipschitz. We explain how this obstacle can be overcome using a reconstruction approach which leads to an aposteriori error estimate.

Geoadditive models for regional count data: an application to industrial location

We propose a geoadditive negative binomial model (Geo-NB-GAM) for regional count data that allows us to address simultaneously some important methodological issues, such as spatial clustering, nonlinearities, and overdispersion. This model is applied to the study of location determinants of inward greenfield investments that occurred during 2003–2007 in 249 European regions. After presenting the data set and showing the presence of overdispersion and spatial clustering, we review the theoretical framework that motivates the choice of the location determinants included in the empirical model, and we highlight some reasons why the relationship between some of the covariates and the dependent variable might be nonlinear. The subsequent section first describes the solutions proposed by previous literature to tackle spatial clustering, nonlinearities, and overdispersion, and then presents the Geo-NB-GAM. The empirical analysis shows the good performance of Geo-NB-GAM. Notably, the inclusion of a geoadditive component (a smooth spatial trend surface) permits us to control for spatial unobserved heterogeneity that induces spatial clustering. Allowing for nonlinearities reveals, in keeping with theoretical predictions, that the positive effect of agglomeration economies fades as the density of economic activities reaches some threshold value. However, no matter how dense the economic activity becomes, our results suggest that congestion costs never overcome positive agglomeration externalities.

National boundaries and the location of multinational firms in Europe

Using data on 5,102 subsidiaries established in the period 1991–1999, we examine the location choice of multinational firms of different nationalities in 47 regions of five EU countries. In particular we estimate a nested logit model and find that European multinationals consider regions across different countries as relatively closer substitutes than regions within national borders. This is consistent with the hypothesis that European regions compete to attract foreign direct investments relatively more across than within countries. However, in line with previous studies, we also find that national boundaries still play some role in choices made by non-European multinationals.

Theoretical insight into diagnosing observation error correlations using observation-minus-background and observation-minus-analysis statistics

To improve the quantity and impact of observations used in data assimilation it is necessary to take into account the full, potentially correlated, observation error statistics. A number of methods for estimating correlated observation errors exist, but a popular method is a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. The accuracy of the results it yields is unknown as the diagnostic is sensitive to the difference between the exact background and exact observation error covariances and those that are chosen for use within the assimilation. It has often been stated in the literature that the results using this diagnostic are only valid when the background and observation error correlation length scales are well separated. Here we develop new theory relating to the diagnostic. For observations on a 1D periodic domain we are able to the show the effect of changes in the assumed error statistics used in the assimilation on the estimated observation error covariance matrix. We also provide bounds for the estimated observation error variance and eigenvalues of the estimated observation error correlation matrix. We demonstrate that it is still possible to obtain useful results from the diagnostic when the background and observation error length scales are similar. In general, our results suggest that when correlated observation errors are treated as uncorrelated in the assimilation, the diagnostic will underestimate the correlation length scale. We support our theoretical results with simple illustrative examples. These results have potential use for interpreting the derived covariances estimated using an operational system.

Location choices of multinational firms in Europe: the role of EU cohesion policy

Using data on 5509 foreign subsidiaries established in 50 regions of 8 EU countries over the period 1991–1999, we estimate a mixed logit model of the location choice of multinational firms in Europe. In particular, we focus on the role of EU Cohesion Policy in attracting foreign investors from both within and outside Europe. We find that, after controlling for the role of agglomeration economies as well as a number of other regional and country characteristics and allowing for a very flexible correlation pattern among choices, Structural and Cohesion funds allocated by the EU to laggard regions have indeed contributed to attracting multinationals. These policies as well as other determinants play a different role in the case of European investors as opposed to non-European ones.

Multinational companies and productivity spillovers: is there a specification error?

Recent empirical works on the within-sector impact of inward investments on domestic firms’ productivity have found rather robust evidence of no (or even negative) effects. We suggest that, among other reasons, a specification error might explain some of these results. A more general specification, which includes the usual one as a special case, is proposed. Using data on Italian manufacturing firms in 1992–2000, we find positive externalities only once we allow for the more flexible specification.

The multidimensional character of accounting numbers

This paper takes as its motivation debates surrounding the multiplicity of functions of accounting information. We are in particular interested in the existential function of accounting numbers and argue that numerical signs having discursive possibilities may acquire new meanings through reframing. Drawing on Goffman’s (1974) frame analysis and Vollmer’s (2007) work on three-dimensional character of numerical signs, we explore the ways in which numbers can go through instantaneous transformations and tell a new kind of story. In our analysis, we look at the main historical developments and current controversies surrounding accounting practice with a specific focus on scandals involving numerical signs as moments where our understandings and the discursive function of previously inoffensive signs shifts through a collective involvement. We map the purpose and usefulness of Vollmer’s three-dimensional framework in the analysis of selected financial accounting practices and scandals as examples of instances where numbers are reframed to suddenly perform a different existential function in context of their calculative and symptomatic dimensions.

Numbers in motion

We explore the debates surrounding the constructive and discursive capabilities of accounting information focusing in particular on the reception volatility of numbers once they are produced and ‘exposed’ to various communities of minds. Drawing on Goffman’s (1974) frame analysis and Vollmer’s (2007) work on the three-dimensional character of numerical signs, we explore how numbers can go through gradual or instantaneous transformations, get caught up in public debates and become ‘agents’ or ‘captives’ in creating social order and in some cases social drama. In our analysis we also relate to the work of Durkheim (1993, 2002) on the sociology of morality to illustrate how numbers can become indicators of moral transgression. The study explores both historical and contemporary examples of controversies and recent accounting scandals to demonstrate how preparers (of financial information) can lose control over numbers which then acquire new meanings through social context and collective (re)framing. The main contribution of the study is to illustrate how the narratives attached to numbers are malleable and fluid across both time and space.

A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems

We present and analyse a space–time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential equation to be discretised in each element of the (space–time) mesh. The method considered is a modification of the discontinuous Galerkin schemes of Kretzschmar et al. (2014) and of Monk & Richter (2005). For Maxwell’s equations in one space dimension, we prove stability of the method, quasi-optimality, best approximation estimates for polynomial Trefftz spaces and (fully explicit) error bounds with high order in the meshwidth and in the polynomial degree. The analysis framework also applies to scalar wave problems and Maxwell’s equations in higher space dimensions. Some numerical experiments demonstrate the theoretical results proved and the faster convergence compared to the non-Trefftz version of the scheme.

Evaluation of positioning error-induced pixel shifts on satellite linear push-broom imagery

Georeferencing is one of the major tasks of satellite-borne remote sensing. Compared to traditional indirect methods, direct georeferencing through a Global Positioning System/inertial navigation system requires fewer and simpler steps to obtain exterior orientation parameters of remotely sensed images. However, the pixel shift caused by geographic positioning error, which is generally derived from boresight angle as well as terrain topography variation, can have a great impact on the precision of georeferencing. The distribution of pixel shifts introduced by the positioning error on a satellite linear push-broom image is quantitatively analyzed. We use the variation of the object space coordinate to simulate different kinds of positioning errors and terrain topography. Then a total differential method was applied to establish a rigorous sensor model in order to mathematically obtain the relationship between pixel shift and positioning error. Finally, two simulation experiments are conducted using the imaging parameters of Chang’ E-1 satellite to evaluate two different kinds of positioning errors. The experimental results have shown that with the experimental parameters, the maximum pixel shift could reach 1.74 pixels. The proposed approach can be extended to a generic application for imaging error modeling in remote sensing with terrain variation.