An upper bound on the Bayesian error bars for generalized linear regression

In the Bayesian framework, predictions for a regression problem are expressed in terms of a distribution of output values. The mode of this distribution corresponds to the most probable output, while the uncertainty associated with the predictions can conveniently be expressed in terms of error bars. In this paper we consider the evaluation of error bars in the context of the class of generalized linear regression models. We provide insights into the dependence of the error bars on the location of the data points and we derive an upper bound on the true error bars in terms of the contributions from individual data points which are themselves easily evaluated.

On the relationship between Bayesian error bars and the input data density

We investigate the dependence of Bayesian error bars on the distribution of data in input space. For generalized linear regression models we derive an upper bound on the error bars which shows that, in the neighbourhood of the data points, the error bars are substantially reduced from their prior values. For regions of high data density we also show that the contribution to the output variance due to the uncertainty in the weights can exhibit an approximate inverse proportionality to the probability density. Empirical results support these conclusions.

Aluminium administered in drinking water but not in the diet influences biopterin metabolism in the rodent

To investigate the neurotoxic effects of aluminium (Al) Al was administered: 1) in the diet of the rat (30 mg Al/kg body weight for 6 weeks); 2) as a suspension of aluminium acetate in drinking water of the rat for 3 months and 3) in a long-term study in the mouse in which aluminosilicates were incorporated into a pelleted diet (1035 mg/kg of food over 23 months). In the latter treatment, increased Al was combined with a reduction in calcium and magnesium; a treatment designed to increase absorption of Al into the body. Administration of Al in the drinking water significantly reduced total brain biopterins and BH4 synthesis. However, no significant affect of Al in the diet on total biopterins or BH4 synthesis was found either in the rat or in the long-term study in the mouse. In addition, in the mouse no significant effects of the Al diet on levels of noradrenaline, serotonin, dopamine, 5-HIAA or CAT could be demonstrated. Hence, the occurrence of brain alterations may depend on the Al species present and the method of administration. Al salts in drinking water may increase brain tissue levels compared with the administration of a more insoluble species. Since alterations in biopterin metabolism are also a feature of Alzheimer's disease (AD) these results support the hypothesis that Al in the water supply may be a factor in AD.

Edges and bars: where do people see features in 1-D images?

There have been two main approaches to feature detection in human and computer vision - based either on the luminance distribution and its spatial derivatives, or on the spatial distribution of local contrast energy. Thus, bars and edges might arise from peaks of luminance and luminance gradient respectively, or bars and edges might be found at peaks of local energy, where local phases are aligned across spatial frequency. This basic issue of definition is important because it guides more detailed models and interpretations of early vision. Which approach better describes the perceived positions of features in images? We used the class of 1-D images defined by Morrone and Burr in which the amplitude spectrum is that of a (partially blurred) square-wave and all Fourier components have a common phase. Observers used a cursor to mark where bars and edges were seen for different test phases (Experiment 1) or judged the spatial alignment of contours that had different phases (e.g. 0 degrees and 45 degrees ; Experiment 2). The feature positions defined by both tasks shifted systematically to the left or right according to the sign of the phase offset, increasing with the degree of blur. These shifts were well predicted by the location of luminance peaks (bars) and gradient peaks (edges), but not by energy peaks which (by design) predicted no shift at all. These results encourage models based on a Gaussian-derivative framework, but do not support the idea that human vision uses points of phase alignment to find local, first-order features. Nevertheless, we argue that both approaches are presently incomplete and a better understanding of early vision may combine insights from both. (C)2004 Elsevier Ltd. All rights reserved.

Bars and edges: what makes a feature for human vision?

There have been two main approaches to feature detection in human and computer vision - luminance-based and energy-based. Bars and edges might arise from peaks of luminance and luminance gradient respectively, or bars and edges might be found at peaks of local energy, where local phases are aligned across spatial frequency. This basic issue of definition is important because it guides more detailed models and interpretations of early vision. Which approach better describes the perceived positions of elements in a 3-element contour-alignment task? We used the class of 1-D images defined by Morrone and Burr in which the amplitude spectrum is that of a (partially blurred) square wave and Fourier components in a given image have a common phase. Observers judged whether the centre element (eg ±458 phase) was to the left or right of the flanking pair (eg 0º phase). Lateral offset of the centre element was varied to find the point of subjective alignment from the fitted psychometric function. This point shifted systematically to the left or right according to the sign of the centre phase, increasing with the degree of blur. These shifts were well predicted by the location of luminance peaks and other derivative-based features, but not by energy peaks which (by design) predicted no shift at all. These results on contour alignment agree well with earlier ones from a more explicit feature-marking task, and strongly suggest that human vision does not use local energy peaks to locate basic first-order features. [Supported by the Wellcome Trust (ref: 056093)]

On the adoption decision and the intensity of use of complementary innovations: The intra firm diffusion of management practices across UK establishments

This paper contributes to the literature on the intra-firm diffusion of innovations by investigating the factors that affect the firm’s decision to adopt and use sets of complementary innovations. We define complementary innovations those innovations whose joint use generates super additive gains, i.e. the gain from the joint adoption is higher than the sum of the gains derived from the adoption of each innovation in isolation. From a theoretical perspective, we present a simple decision model, whereby the firm decides ‘whether’ and ‘how much’ to invest in each of the innovations under investigation based upon the expected profit gain from each possible combination of adoption and use. The model shows how the extent of complementarity among the innovations can affect the firm’s profit gains and therefore the likelihood that the firm will adopt these innovations jointly, rather than individually. From an empirical perspective, we focus on four sets of management practices, namely operating (OMP), monitoring (MMP), targets (TMP) and incentives (IMP) management practices. We show that these sets of practices, although to a different extent, are complementary to each other. Then, we construct a synthetic indicator of the depth of their use. The resulting intra-firm index is built to reflect not only the number of practices adopted but also the depth of their individual use and the extent of their complementarity. The empirical testing of the decision model is carried out using the evidence from the adoption behaviour of a sample of 1,238 UK establishments present in the 2004 Workplace Employment Relations Survey (WERS). Our empirical results show that the intra-firm profitability based model is a good model in that it can explain more of the variability of joint adoption than models based upon the variability of adoption and use of individual practices. We also investigate whether a number of firm specific and market characteristics by affecting the size of the gains (which the joint adoption of innovations can generate) may drive the intensity of use of the four innovations. We find that establishment size, whether foreign owned, whether exposed to an international market and the degree of homogeneity of the final product are important determinants of the intensity of the joint adoption of the four innovations. Most importantly, our results point out that the factors that the economics of innovation literature has been showing to affect the intensity of use of a technological innovation do also affect the intensity of use of sets of innovative management practices. However, they can explain only a small part of the diversity of their joint adoption use by the firms in the sample.

The intra-firm diffusion of complementary innovations: Evidence from the adoption of management practices by British establishments

This paper presents a simple profitability-based decision model to show how synergistic gains generated by the joint adoption of complementary innovations may influence the firm's adoption decision. For this purpose a weighted index of intra-firm diffusion is built to investigate empirically the drivers of the intensity of joint use of a set of complementary innovations. The findings indicate that establishment size, ownership structure and product market concentration are important determinants of the intensity of use. Interestingly, the factors that affect the extent of use of technological innovations do also affect that of clusters of management practices. However, they can explain only part of the heterogeneity of the benefits from joint use.

Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars

Perception of Mach bands may be explained by spatial filtering ('lateral inhibition') that can be approximated by 2nd derivative computation, and several alternative models have been proposed. To distinguish between them, we used a novel set of ‘generalised Gaussian’ images, in which the sharp ramp-plateau junction of the Mach ramp was replaced by smoother transitions. The images ranged from a slightly blurred Mach ramp to a Gaussian edge and beyond, and also included a sine-wave edge. The probability of seeing Mach Bands increased with the (relative) sharpness of the junction, but was largely independent of absolute spatial scale. These data did not fit the predictions of MIRAGE, nor 2nd derivative computation at a single fine scale. In experiment 2, observers used a cursor to mark features on the same set of images. Data on perceived position of Mach bands did not support the local energy model. Perceived width of Mach bands was poorly explained by a single-scale edge detection model, despite its previous success with Mach edges (Wallis & Georgeson, 2009, Vision Research, 49, 1886-1893). A more successful model used separate (odd and even) scale-space filtering for edges and bars, local peak detection to find candidate features, and the MAX operator to compare odd- and even-filter response maps (Georgeson, VSS 2006, Journal of Vision 6(6), 191a). Mach bands are seen when there is a local peak in the even-filter (bar) response map, AND that peak value exceeds corresponding responses in the odd-filter (edge) maps.

The influence of aluminium, administered in the diet and in drinking water, on biopterin metabolism

To investigate the neurotoxic effects of aluminium (Al) three studies were carried out in which Al was administered: 1) in the diet, 2) as a suspension of aluminium acetate in drinking water and 3) a long-term study in which aluminosilicates were incorporated into a pelleted diet. Admistration of Al in the drinking water significantly reduced total brain biopterin. However, no significant affect of Al in the diet on total bipterins or BH4 synthesis was found.

Bayesian error bars for regression

Regression problems are concerned with predicting the values of one or more continuous quantities, given the values of a number of input variables. For virtually every application of regression, however, it is also important to have an indication of the uncertainty in the predictions. Such uncertainties are expressed in terms of the error bars, which specify the standard deviation of the distribution of predictions about the mean. Accurate estimate of error bars is of practical importance especially when safety and reliability is an issue. The Bayesian view of regression leads naturally to two contributions to the error bars. The first arises from the intrinsic noise on the target data, while the second comes from the uncertainty in the values of the model parameters which manifests itself in the finite width of the posterior distribution over the space of these parameters. The Hessian matrix which involves the second derivatives of the error function with respect to the weights is needed for implementing the Bayesian formalism in general and estimating the error bars in particular. A study of different methods for evaluating this matrix is given with special emphasis on the outer product approximation method. The contribution of the uncertainty in model parameters to the error bars is a finite data size effect, which becomes negligible as the number of data points in the training set increases. A study of this contribution is given in relation to the distribution of data in input space. It is shown that the addition of data points to the training set can only reduce the local magnitude of the error bars or leave it unchanged. Using the asymptotic limit of an infinite data set, it is shown that the error bars have an approximate relation to the density of data in input space.

The role of government research establishments : a study of the concept of public patronage for applied research and development

This thesis follows the argument that, to fully understand the current position of national research laboratories in Great Britain one needs to study the historical development of the government research establishment as a specific social institution. A particular model is outlined in which it is argued that institutional characteristics evolve through the continual interplay between internal development and environmental factors within a changing political and economic context, and that the continuous development of an institution depends on its ability to adapt to changes in its operational environment. Within this framework important historical precedents for formal government institutional support for applied research are identified. and the transition from private to public patronage documented. The emergence and consolidation of government research laboratories in Britain is described in detail. The subsequent relative decline of public laboratories is interpreted in terms of the undermining of a traditional role resulting in legitimation crisis. It is concluded that it is no longer feasible to consider the public research laboratory as a coherent institutional form, and that the future of each individual laboratory can only be considered in relation to the institutional needs of its own sphere of operation. Nevertheless the laboratories have been forced into decline in an essentially unplanned way which may have serious consequences for the maintenance of the scientific and technical infrastructures, necessary for material progress in the national context.