Bayesian estimation of the spatial Durbin error model with an application to voter turnout in the 2004 presidential election

The potential for spatial dependence in models of voter turnout, although plausible from a theoretical perspective, has not been adequately addressed in the literature. Using recent advances in Bayesian computation, we formulate and estimate the previously unutilized spatial Durbin error model and apply this model to the question of whether spillovers and unobserved spatial dependence in voter turnout matters from an empirical perspective. Formal Bayesian model comparison techniques are employed to compare the normal linear model, the spatially lagged X model (SLX), the spatial Durbin model, and the spatial Durbin error model. The results overwhelmingly support the spatial Durbin error model as the appropriate empirical model.

Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

On the approximation of local and linear radiative damping in the middle atmosphere

The validity of approximating radiative heating rates in the middle atmosphere by a local linear relaxation to a reference temperature state (i.e., ‘‘Newtonian cooling’’) is investigated. Using radiative heating rate and temperature output from a chemistry–climate model with realistic spatiotemporal variability and realistic chemical and radiative parameterizations, it is found that a linear regressionmodel can capture more than 80% of the variance in longwave heating rates throughout most of the stratosphere and mesosphere, provided that the damping rate is allowed to vary with height, latitude, and season. The linear model describes departures from the climatological mean, not from radiative equilibrium. Photochemical damping rates in the upper stratosphere are similarly diagnosed. Threeimportant exceptions, however, are found.The approximation of linearity breaks down near the edges of the polar vortices in both hemispheres. This nonlinearity can be well captured by including a quadratic term. The use of a scale-independentdamping rate is not well justified in the lower tropical stratosphere because of the presence of a broad spectrum of vertical scales. The local assumption fails entirely during the breakup of the Antarctic vortex, where large fluctuations in temperature near the top of the vortex influence longwave heating rates within the quiescent region below. These results are relevant for mechanistic modeling studies of the middle atmosphere, particularly those investigating the final Antarctic warming.

Forecasting US output growth with non-linear models in the presence of data uncertainty

We consider the impact of data revisions on the forecast performance of a SETAR regime-switching model of U.S. output growth. The impact of data uncertainty in real-time forecasting will affect a model's forecast performance via the effect on the model parameter estimates as well as via the forecast being conditioned on data measured with error. We find that benchmark revisions do affect the performance of the non-linear model of the growth rate, and that the performance relative to a linear comparator deteriorates in real-time compared to a pseudo out-of-sample forecasting exercise.

Nonlinearity of ocean heat uptake during warming and cooling in the FAMOUS climate model

Atmospheric CO2 concentration is expected to continue rising in the coming decades, but natural or artificial processes may eventually reduce it. We show that, in the FAMOUS atmosphere-ocean general circulation model, the reduction of ocean heat content as radiative forcing decreases is greater than would be expected from a linear model simulation of the response to the applied forcings. We relate this effect to the behavior of the Atlantic meridional overturning circulation (AMOC): the ocean cools more efficiently with a strong AMOC. The AMOC weakens as CO2 rises, then strengthens as CO2 declines, but temporarily overshoots its original strength. This nonlinearity comes mainly from the accumulated advection of salt into the North Atlantic, which gives the system a longer memory. This implies that changes observed in response to different CO2 scenarios or from different initial states, such as from past changes, may not be a reliable basis for making projections.

Exploring the spatial relations between soil physical properties and apparent electrical conductivity

Relations between the apparent electrical conductivity of the soil (ECa) and top- and sub-soil physical properties were examined for two arable fields in southern England (Crowmarsh Battle Farms and the Yattendon Estate). The spatial variation of ECa and the soil properties was explored geostatistically. The variogram ranges showed that ECa varied on a similar spatial scale to many of the soil physical properties in both fields. Several features in the map of kriged predictions of ECa were also evident in maps of the soil properties. In addition, the correlation coefficients showed a strong relation between ECa and several soil properties. A moving correlation analysis enabled differences in the relations between ECa and the soil properties to be examined within the fields. The results indicated that relations were inconsistent; they were stronger in some areas than others. A regression of ECa on the principal component scores of the leading components for both fields showed that the first two components accounted for a large proportion of the variance in ECa, whereas the others accounted for little or none. For Crowmarsh topsoil sand and clay, loss on ignition and volumetric water measured in the autumn had large correlations on the first component, and for Yattendon they were large for topsoil sand and clay, and autumn and spring volumetric water. The cross-variograms suggested strong coregionalization between ECa and several soil physical properties; in particular subsoil sand and silt at Crowmarsh, and subsoil sand and clay at Yattendon. The structural correlations from the linear model of coregionalization confirmed the strength of the relations between ECa and the subsoil properties. Nevertheless, no one property was consistently important for both fields. Although a map of ECa can indicate the general patterns of spatial variation in the soil, it is not a substitute for information on soil properties obtained by sampling and analysing the soil. Nevertheless, it could be used to guide further sampling. (c) 2005 Elsevier B.V. All rights reserved.

Orographic precipitation in the tropics: large-eddy simulations and theory

Recent radar and rain-gauge observations from the island of Dominica, which lies in the eastern Caribbean sea at 15 N, show a strong orographic enhancement of trade-wind precipitation. The mechanisms behind this enhancement are investigated using idealized large-eddy simulations with a realistic representation of the shallow trade-wind cumuli over the open ocean upstream of the island. The dominant mechanism is found to be the rapid growth of convection by the bulk lifting of the inhomogenous impinging flow. When rapidly lifted by the terrain, existing clouds and other moist parcels gain buoyancy relative to rising dry air because of their different adiabatic lapse rates. The resulting energetic, closely-packed convection forms precipitation readily and brings frequent heavy showers to the high terrain. Despite this strong precipitation enhancement, only a small fraction (1%) of the impinging moisture flux is lost over the island. However, an extensive rain shadow forms to the lee of Dominica due to the convective stabilization, forced descent, and wave breaking. A linear model is developed to explain the convective enhancement over the steep terrain.

The spacing of orographic rainbands triggered by small-scale topography

A combination of idealized numerical simulations and analytical theory is used to investigate the spacing between convective orographic rainbands over the Coastal Range of western Oregon. The simulations, which are idealized from an observed banded precipitation event over the Coastal Range, indicate that the atmospheric response to conditionally unstable flow over the mountain ridge depends strongly on the subridge-scale topographic forcing on the windward side of the ridge. When this small-scale terrain contains only a single scale (l) of terrain variability, the band spacing is identical to l, but when a spectrum of terrain scales are simultaneously present, the band spacing ranges between 5 and 10 km, a value that is consistent with observations. Based on the simulations, an inviscid linear model is developed to provide a physical basis for understanding the scale selection of the rainbands. This analytical model, which captures the transition from lee waves upstream of the orographic cloud to moist convection within it, reveals that the spacing of orographic rainbands depends on both the projection of lee-wave energy onto the unstable cap cloud and the growth rate of unstable perturbations within the cloud. The linear model is used in tandem with numerical simulations to determine the sensitivity of the band spacing to a number of environmental and terrain-related parameters.

Singular vector ensemble forecasting systems and the prediction of flow dependent uncertainty

The ECMWF ensemble weather forecasts are generated by perturbing the initial conditions of the forecast using a subset of the singular vectors of the linearised propagator. Previous results show that when creating probabilistic forecasts from this ensemble better forecasts are obtained if the mean of the spread and the variability of the spread are calibrated separately. We show results from a simple linear model that suggest that this may be a generic property for all singular vector based ensemble forecasting systems based on only a subset of the full set of singular vectors.

Some factors affecting variation in milk yield in crossbred dairy cows on smallholder farms in north-east Tanzania

A 2-year longitudinal survey was carried out to investigate factors affecting milk yield in crossbred cows on smallholder farms in and around an urban centre. Sixty farms were visited at approximately 2-week intervals and details of milk yield, body condition score (BCS) and heart girth measurements were collected. Fifteen farms were within the town (U), 23 farms were approximately 5 km from town (SU), and 22 farms approximately 10 km from town (PU). Sources of variation in milk yield were investigated using a general linear model by a stepwise forward selection and backward elimination approach to judge important independent variables. Factors considered for the first step of formulation of the model included location (PU, SU and U), calving season, BCS at calving, at 3 months postpartum and at 6 months postpartum, calving year, herd size category, source of labour (hired and family labour), calf rearing method (bucket and partial suckling) and parity number of the cow. Daily milk yield (including milk sucked by calves) was determined by calving year (p < 0.0001), calf rearing method (p = 0.044) and BCS at calving (p < 0.0001). Only BCS at calving contributed to variation in volume of milk sucked by the calf, lactation length and lactation milk yield. BCS at 3 months after calving was improved on farms where labour was hired (p = 0.041) and BCS change from calving to 6 months was more than twice as likely to be negative on U than SU and PU farms. It was concluded that milk production was predominantly associated with BCS at calving, lactation milk yield increasing quadratically from score 1 to 3. BCS at calving may provide a simple, single indicator of the nutritional status of a cow population.

Some factors affecting reproductive success in crossbred dairy cows on smallholder farms in coastal north-east Tanzania

A 2-year longitudinal survey was carried out to investigate factors affecting reproduction in crossbred cows on smallholder farms in and around an urban centre. Sixty farms were visited at approximately 2-week intervals and details of reproductive traits and body condition score (BCS) were collected. Fifteen farms were within the town (U), 23 farms were approximately 5 km from town (SU), and 22 farms approximately 10 km from town (PU). Sources of variation in reproductive traits were investigated using a general linear model (GLM) by a stepwise forward selection and backward elimination approach to judge important independent variables. Factors considered for the first step of formulation of the model included location (PU, SU and U), type of insemination, calving season, BCS at calving, at 3 months postpartum and at 6 months postpartum, calving year, herd size category, source of labour (hired and family labour), calf rearing method (bucket and partial suckling) and parity number of the cow. The effects of the independent variables identified were then investigated using a non-parametric survival technique. The number of days to first oestrus was increased on the U site (p = 0.045) and when family labour was used (p = 0.02). The non-parametric test confirmed the effect of site (p = 0.059), but effect of labour was not significant. The number of days from calving to conception was reduced by hiring labour (p = 0.003) and using natural service (p = 0.028). The non-parametric test confirmed the effects of type of insemination (p = 0.0001) while also identifying extended calving intervals on U and SU sites (p = 0.014). Labour source was again non-significant. Calving interval was prolonged on U and SU sites (p = 0.021), by the use of AI (p = 0.031) and by the use of family labour (p = 0.001). The non-parametric test confirmed the effect of site (p = 0.008) and insemination type (p > 0.0001) but not of labour source. It was concluded that under favourable conditions (PU site, hired labour and natural service) calving intervals of around 440 days could be achieved.

Statistical design and analysis of pharmacogenetic trials

Pharmacogenetic trials investigate the effect of genotype on treatment response. When there are two or more treatment groups and two or more genetic groups, investigation of gene-treatment interactions is of key interest. However, calculation of the power to detect such interactions is complicated because this depends not only on the treatment effect size within each genetic group, but also on the number of genetic groups, the size of each genetic group, and the type of genetic effect that is both present and tested for. The scale chosen to measure the magnitude of an interaction can also be problematic, especially for the binary case. Elston et al. proposed a test for detecting the presence of gene-treatment interactions for binary responses, and gave appropriate power calculations. This paper shows how the same approach can also be used for normally distributed responses. We also propose a method for analysing and performing sample size calculations based on a generalized linear model (GLM) approach. The power of the Elston et al. and GLM approaches are compared for the binary and normal case using several illustrative examples. While more sensitive to errors in model specification than the Elston et al. approach, the GLM approach is much more flexible and in many cases more powerful. Copyright © 2005 John Wiley & Sons, Ltd.

A Bayesian approach for dose-escalation in a phase I clinical trial incorporating pharmacodynamic endpoints

Bayesian decision procedures have already been proposed for and implemented in Phase I dose-escalation studies in healthy volunteers. The procedures have been based on pharmacokinetic responses reflecting the concentration of the drug in blood plasma and are conducted to learn about the dose-response relationship while avoiding excessive concentrations. However, in many dose-escalation studies, pharmacodynamic endpoints such as heart rate or blood pressure are observed, and it is these that should be used to control dose-escalation. These endpoints introduce additional complexity into the modeling of the problem relative to pharmacokinetic responses. Firstly, there are responses available following placebo administrations. Secondly, the pharmacodynamic responses are related directly to measurable plasma concentrations, which in turn are related to dose. Motivated by experience of data from a real study conducted in a conventional manner, this paper presents and evaluates a Bayesian procedure devised for the simultaneous monitoring of pharmacodynamic and pharmacokinetic responses. Account is also taken of the incidence of adverse events. Following logarithmic transformations, a linear model is used to relate dose to the pharmacokinetic endpoint and a quadratic model to relate the latter to the pharmacodynamic endpoint. A logistic model is used to relate the pharmacokinetic endpoint to the risk of an adverse event.

Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so. that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.

Imagery rescripting as a brief stand-alone treatment for depressed patients with intrusive memories

Many depressed patients report intrusive and distressing memories of specific events in their lives. Where present, these memories are believed to act as a maintaining factor. A series of ten patients with major depressive disorder and intrusive memories, many of them reporting severe, chronic, or recurrent episodes of depression, were given an average of 8.1 sessions of imagery rescripting as a stand-alone treatment. Hierarchical linear modelling demonstrated large treatment effects that were well maintained at one year follow-up. Seven patients showed reliable improvement, and six patients clinically significant improvement. These gains were achieved entirely by working through patients' visual imagination and without verbal challenging of negative beliefs. Spontaneous changes in beliefs, rumination, and behaviour were nevertheless observed. (C) 2009 Elsevier Ltd. All rights reserved.