Early warning with calibrated and sharper probabilistic forecasts

Given a nonlinear model, a probabilistic forecast may be obtained by Monte Carlo simulations. At a given forecast horizon, Monte Carlo simulations yield sets of discrete forecasts, which can be converted to density forecasts. The resulting density forecasts will inevitably be downgraded by model mis-specification. In order to enhance the quality of the density forecasts, one can mix them with the unconditional density. This paper examines the value of combining conditional density forecasts with the unconditional density. The findings have positive implications for issuing early warnings in different disciplines including economics and meteorology, but UK inflation forecasts are considered as an example.

Spatial disaggregation and intensity correction of TRMM-based rainfall time series for hydrological applications in dryland catchments

A novel approach is presented for combining spatial and temporal detail from newly available TRMM-based data sets to derive hourly rainfall intensities at 1-km spatial resolution for hydrological modelling applications. Time series of rainfall intensities derived from 3-hourly 0.25° TRMM 3B42 data are merged with a 1-km gridded rainfall climatology based on TRMM 2B31 data to account for the sub-grid spatial distribution of rainfall intensities within coarse-scale 0.25° grid cells. The method is implemented for two dryland catchments in Tunisia and Senegal, and validated against gauge data. The outcomes of the validation show that the spatially disaggregated and intensity corrected TRMM time series more closely approximate ground-based measurements than non-corrected data. The method introduced here enables the generation of rainfall intensity time series with realistic temporal and spatial detail for dynamic modelling of runoff and infiltration processes that are especially important to water resource management in arid regions.

Calibration and bias correction of climate projections for crop modelling: an idealised case study over Europe

Producing projections of future crop yields requires careful thought about the appropriate use of atmosphere-ocean global climate model (AOGCM) simulations. Here we describe and demonstrate multiple methods for ‘calibrating’ climate projections using an ensemble of AOGCM simulations in a ‘perfect sibling’ framework. Crucially, this type of analysis assesses the ability of each calibration methodology to produce reliable estimates of future climate, which is not possible just using historical observations. This type of approach could be more widely adopted for assessing calibration methodologies for crop modelling. The calibration methods assessed include the commonly used ‘delta’ (change factor) and ‘nudging’ (bias correction) approaches. We focus on daily maximum temperature in summer over Europe for this idealised case study, but the methods can be generalised to other variables and other regions. The calibration methods, which are relatively easy to implement given appropriate observations, produce more robust projections of future daily maximum temperatures and heat stress than using raw model output. The choice over which calibration method to use will likely depend on the situation, but change factor approaches tend to perform best in our examples. Finally, we demonstrate that the uncertainty due to the choice of calibration methodology is a significant contributor to the total uncertainty in future climate projections for impact studies. We conclude that utilising a variety of calibration methods on output from a wide range of AOGCMs is essential to produce climate data that will ensure robust and reliable crop yield projections.

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

Individual differences in brain structure underpin empathizing–systemizing cognitive styles in male adults

Individual differences in cognitive style can be characterized along two dimensions: ‘systemizing’ (S, the drive to analyze or build ‘rule-based’ systems) and ‘empathizing’ (E, the drive to identify another's mental state and respond to this with an appropriate emotion). Discrepancies between these two dimensions in one direction (S > E) or the other (E > S) are associated with sex differences in cognition: on average more males show an S > E cognitive style, while on average more females show an E > S profile. The neurobiological basis of these different profiles remains unknown. Since individuals may be typical or atypical for their sex, it is important to move away from the study of sex differences and towards the study of differences in cognitive style. Using structural magnetic resonance imaging we examined how neuroanatomy varies as a function of the discrepancy between E and S in 88 adult males from the general population. Selecting just males allows us to study discrepant E-S profiles in a pure way, unconfounded by other factors related to sex and gender. An increasing S > E profile was associated with increased gray matter volume in cingulate and dorsal medial prefrontal areas which have been implicated in processes related to cognitive control, monitoring, error detection, and probabilistic inference. An increasing E > S profile was associated with larger hypothalamic and ventral basal ganglia regions which have been implicated in neuroendocrine control, motivation and reward. These results suggest an underlying neuroanatomical basis linked to the discrepancy between these two important dimensions of individual differences in cognitive style.

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.

Regularized logistic models for probabilistic forecasting and diagnostics

Logistic models are studied as a tool to convert dynamical forecast information (deterministic and ensemble) into probability forecasts. A logistic model is obtained by setting the logarithmic odds ratio equal to a linear combination of the inputs. As with any statistical model, logistic models will suffer from overfitting if the number of inputs is comparable to the number of forecast instances. Computational approaches to avoid overfitting by regularization are discussed, and efficient techniques for model assessment and selection are presented. A logit version of the lasso (originally a linear regression technique), is discussed. In lasso models, less important inputs are identified and the corresponding coefficient is set to zero, providing an efficient and automatic model reduction procedure. For the same reason, lasso models are particularly appealing for diagnostic purposes.

Probabilistic evaluation of time series models : a comparison of several approaches

Several methods are examined which allow to produce forecasts for time series in the form of probability assignments. The necessary concepts are presented, addressing questions such as how to assess the performance of a probabilistic forecast. A particular class of models, cluster weighted models (CWMs), is given particular attention. CWMs, originally proposed for deterministic forecasts, can be employed for probabilistic forecasting with little modification. Two examples are presented. The first involves estimating the state of (numerically simulated) dynamical systems from noise corrupted measurements, a problem also known as filtering. There is an optimal solution to this problem, called the optimal filter, to which the considered time series models are compared. (The optimal filter requires the dynamical equations to be known.) In the second example, we aim at forecasting the chaotic oscillations of an experimental bronze spring system. Both examples demonstrate that the considered time series models, and especially the CWMs, provide useful probabilistic information about the underlying dynamical relations. In particular, they provide more than just an approximation to the conditional mean.