Efficient modeling and inference for event-related fMRI data

Event-related functional magnetic resonance imaging (efMRI) has emerged as a powerful technique for detecting brains' responses to presented stimuli. A primary goal in efMRI data analysis is to estimate the Hemodynamic Response Function (HRF) and to locate activated regions in human brains when specific tasks are performed. This paper develops new methodologies that are important improvements not only to parametric but also to nonparametric estimation and hypothesis testing of the HRF. First, an effective and computationally fast scheme for estimating the error covariance matrix for efMRI is proposed. Second, methodologies for estimation and hypothesis testing of the HRF are developed. Simulations support the effectiveness of our proposed methods. When applied to an efMRI dataset from an emotional control study, our method reveals more meaningful findings than the popular methods offered by AFNI and FSL. (C) 2008 Elsevier B.V. All rights reserved.

Ranald Macdonald and statistical inference

Ranald Roderick Macdonald (1945-2007) was an important contributor to mathematical psychology in the UK, as a referee and action editor for British Journal of Mathematical and Statistical Psychology and as a participant and organizer at the British Psychological Society's Mathematics, statistics and computing section meetings. This appreciation argues that his most important contribution was to the foundations of significance testing, where his concern about what information was relevant in interpreting the results of significance tests led him to be a persuasive advocate for the 'Weak Fisherian' form of hypothesis testing.

Robustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems

In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices. Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both - systematic and probability error are presented. It is shown that the values of both errors can be controlled independently by different algorithmic parameters. The results present how the systematic error depends on the matrix spectrum. The analysis of the probability error is presented. It shows that the close (in some sense) the matrix under consideration is to the stochastic matrix the smaller is this error. Sufficient conditions for constructing robust and interpolation Monte Carlo algorithms are obtained. For stochastic matrices an interpolation Monte Carlo algorithm is constructed. A number of numerical tests for large symmetric dense matrices are performed in order to study experimentally the dependence of the systematic error from the structure of matrix spectrum. We also study how the probability error depends on the balancing of the matrix. (c) 2007 Elsevier Inc. All rights reserved.

Tracking and mean structure of easterly waves over the Intra-Americas Sea

Easterly waves (EWs) are prominent features of the intertropical convergence zone (ITCZ), found in both the Atlantic and Pacific during the Northern Hemisphere summer and fall, where they commonly serve as precursors to hurricanes over both basins.Alarge proportion of Atlantic EWs are known to form over Africa, but the origin of EWs over the Caribbean and east Pacific in particular has not been established in detail. In this study reanalyses are used to examine the coherence of the large-scale wave signatures and to obtain track statistics and energy conversion terms for EWs across this region. Regression analysis demonstrates that some EW kinematic structures readily propagate between the Atlantic and east Pacific, with the highest correlations observed across Costa Rica and Panama. Track statistics are consistent with this analysis and suggest that some individual waves are maintained as they pass from the Atlantic into the east Pacific, whereas others are generated locally in the Caribbean and east Pacific. Vortex anomalies associated with the waves are observed on the leeward side of the Sierra Madre, propagating northwestward along the coast, consistent with previous modeling studies of the interactions between zonal flow and EWs with model topography similar to the Sierra Madre. An energetics analysis additionally indicates that the Caribbean low-level jet and its extension into the east Pacific—known as the Papagayo jet—are a source of energy for EWs in the region. Two case studies support these statistics, as well as demonstrate the modulation of EW track and storm development location by the MJO.

The evaluation of CloudSat and CALIPSO ice microphysical products using ground-based cloud radar and lidar observations

In this paper, the statistical properties of tropical ice clouds (ice water content, visible extinction, effective radius, and total number concentration) derived from 3 yr of ground-based radar–lidar retrievals from the U.S. Department of Energy Atmospheric Radiation Measurement Climate Research Facility in Darwin, Australia, are compared with the same properties derived using the official CloudSat microphysical retrieval methods and from a simpler statistical method using radar reflectivity and air temperature. It is shown that the two official CloudSat microphysical products (2B-CWC-RO and 2B-CWC-RVOD) are statistically virtually identical. The comparison with the ground-based radar–lidar retrievals shows that all satellite methods produce ice water contents and extinctions in a much narrower range than the ground-based method and overestimate the mean vertical profiles of microphysical parameters below 10-km height by over a factor of 2. Better agreements are obtained above 10-km height. Ways to improve these estimates are suggested in this study. Effective radii retrievals from the standard CloudSat algorithms are characterized by a large positive bias of 8–12 μm. A sensitivity test shows that in response to such a bias the cloud longwave forcing is increased from 44.6 to 46.9 W m−2 (implying an error of about 5%), whereas the negative cloud shortwave forcing is increased from −81.6 to −82.8 W m−2. Further analysis reveals that these modest effects (although not insignificant) can be much larger for optically thick clouds. The statistical method using CloudSat reflectivities and air temperature was found to produce inaccurate mean vertical profiles and probability distribution functions of effective radius. This study also shows that the retrieval of the total number concentration needs to be improved in the official CloudSat microphysical methods prior to a quantitative use for the characterization of tropical ice clouds. Finally, the statistical relationship used to produce ice water content from extinction and air temperature obtained by the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite is evaluated for tropical ice clouds. It is suggested that the CALIPSO ice water content retrieval is robust for tropical ice clouds, but that the temperature dependence of the statistical relationship used should be slightly refined to better reproduce the radar–lidar retrievals.

A technique for delivering individualised formative problems and examples

Active learning plays a strong role in mathematics and statistics, and formative problems are vital for developing key problem-solving skills. To keep students engaged and help them master the fundamentals before challenging themselves further, we have developed a system for delivering problems tailored to a student‟s current level of understanding. Specifically, by adapting simple methodology from clinical trials, a framework for delivering existing problems and other illustrative material has been developed, making use of macros in Excel. The problems are assigned a level of difficulty (a „dose‟), and problems are presented to the student in an order depending on their ability, i.e. based on their performance so far on other problems. We demonstrate and discuss the application of the approach with formative examples developed for a first year course on plane coordinate geometry, and also for problems centred on the topic of chi-square tests.

Solar influence on global and regional climates

The literature relevant to how solar variability influences climate is vast—but much has been based on inadequate statistics and non-robust procedures. The common pitfalls are outlined in this review. The best estimates of the solar influence on the global mean air surface temperature show relatively small effects, compared with the response to anthropogenic changes (and broadly in line with their respective radiative forcings). However, the situation is more interesting when one looks at regional and season variations around the global means. In particular, recent research indicates that winters in Eurasia may have some dependence on the Sun, with more cold winters occurring when the solar activity is low. Advances in modelling ‘‘top-down’’ mechanisms, whereby stratospheric changes influence the underlying troposphere, offer promising explanations of the observed phenomena. In contrast, the suggested modulation of low-altitude clouds by galactic cosmic rays provides an increasingly inadequate explanation of observations.

Law and the power of feminism: how marriage lost its power to oppress women

In Feminism and the Power of Law Carol Smart argued that feminists should use non-legal strategies rather than looking to law to bring about women’s liberation. This article seeks to demonstrate that, as far as marriage is concerned, she was right. Statistics and contemporary commentary show how marriage, once the ultimate and only acceptable status for women, has declined in social significance to such an extent that today it is a mere lifestyle choice. This is due to many factors, including the ‘sexual revolution’ of the 1960s, improved education and job opportunities for women, and divorce law reform, but the catalyst for change was the feminist critique that called for the abandonment (rather than the reform) of the institution and made the unmarried state possible for women. I conclude that this loss of significance has been more beneficial to British women in terms of the possibility of ‘liberation’ than appeals for legal change and recognition, and that we should continue to be wary of looking to law to solve women’s problems.

Probability of survival in a random exchange economy with dependent agents

In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy.

Integrating science into humanitarian and development planning and practice to enhance community resilience

There has been an increased emphasis upon the application of science for humanitarian and development planning, decision-making and practice; particularly in the context of understanding, assessing and anticipating risk (e.g. HERR, 2011). However, there remains very little guidance for practitioners on how to integrate sciences they may have had little contact with in the past (e.g. climate). This has led to confusion as to which ‘science’ might be of use and how it would be best utilised. Furthermore, since this integration has stemmed from a need to be more predictive, agencies are struggling with the problems associated with uncertainty and probability. Whilst a range of expertise is required to build resilience, these guidelines focus solely upon the relevant data, information, knowledge, methods, principles and perspective which scientists can provide, that typically lie outside of current humanitarian and development approaches. Using checklists, real-life case studies and scenarios the full guidelines take practitioners through a five step approach to finding, understanding and applying science. This document provides a short summary of the five steps and some key lessons for integrating science.

Real-time factor model forecasting and the effects of instability

Factor forecasting models are shown to deliver real-time gains over autoregressive models for US real activity variables during the recent period, but are less successful for nominal variables. The gains are largely due to the Financial Crisis period, and are primarily at the shortest (one quarter ahead) horizon. Excluding the pre-Great Moderation years from the factor forecasting model estimation period (but not from the data used to extract factors) results in a marked fillip in factor model forecast accuracy, but does the same for the AR model forecasts. The relative performance of the factor models compared to the AR models is largely unaffected by whether the exercise is in real time or is pseudo out-of-sample.

Turbulent structure and scaling of the inertial subrange in a stratocumulus-topped boundary layer observed by a Doppler lidar

The turbulent structure of a stratocumulus-topped marine boundary layer over a 2-day period is observed with a Doppler lidar at Mace Head in Ireland. Using profiles of vertical velocity statistics, the bulk of the mixing is identified as cloud driven. This is supported by the pertinent feature of negative vertical velocity skewness in the sub-cloud layer which extends, on occasion, almost to the surface. Both coupled and decoupled turbulence characteristics are observed. The length and timescales related to the cloud-driven mixing are investigated and shown to provide additional information about the structure and the source of the mixing inside the boundary layer. They are also shown to place constraints on the length of the sampling periods used to derive products, such as the turbulent dissipation rate, from lidar measurements. For this, the maximum wavelengths that belong to the inertial subrange are studied through spectral analysis of the vertical velocity. The maximum wavelength of the inertial subrange in the cloud-driven layer scales relatively well with the corresponding layer depth during pronounced decoupled structure identified from the vertical velocity skewness. However, on many occasions, combining the analysis of the inertial subrange and vertical velocity statistics suggests higher decoupling height than expected from the skewness profiles. Our results show that investigation of the length scales related to the inertial subrange significantly complements the analysis of the vertical velocity statistics and enables a more confident interpretation of complex boundary layer structures using measurements from a Doppler lidar.

Uniform factorial decay estimate for the remainder of rough Taylor expansion

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.

University teaching: recognition and reward

Teaching in universities has increased in importance in recent years which, in part, is a consequence of the change in funding of universities from block grants to student tuition fees. Various initiatives have been made which serve to raise the profile of teaching and give it greater recognition. It is also important that teaching is recognised even more fully and widely, and crucially that it is rewarded accordingly. We propose a mechanism for recognising and rewarding university teaching that is based on a review process that is supported by documented evidence whose outcomes can be fed into performance and development reviews, and used to inform decisions about reward and promotion, as well as the review of probationary status where appropriate.