Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation

Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for such models. It replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values, and comparing summary statistics of the simulated data with summary statistics of the observed data. Here we show how to construct appropriate summary statistics for ABC in a semi-automatic manner. We aim for summary statistics which will enable inference about certain parameters of interest to be as accurate as possible. Theoretical results show that optimal summary statistics are the posterior means of the parameters. Although these cannot be calculated analytically, we use an extra stage of simulation to estimate how the posterior means vary as a function of the data; and we then use these estimates of our summary statistics within ABC. Empirical results show that our approach is a robust method for choosing summary statistics that can result in substantially more accurate ABC analyses than the ad hoc choices of summary statistics that have been proposed in the literature. We also demonstrate advantages over two alternative methods of simulation-based inference.

A Summary of the NATO ASI on Polar Cap Boundary Phenomena

The polar cap boundary is a subject of central importance to current magnetosphere-ionosphere research and its applications in “space weather” activities. The problems are that it has a number of definitions, and that the most physically meaningful definition (namely the open-closed field line boundary) is very difficult to identify in observations. New understanding of the importance of the structure and dynamics of the boundary region made the time right for a meeting reviewing our knowledge in this area. The Advanced Study Institute (ASI) on Svalbard in June 1997 discussed the boundary on both the dayside and the nightside, mapping magnetically to the dayside magnetopause and to tail plasma sheet/lobe interface, respectively. We held a “brainstorming” session, in which different ideas which arose from the presented papers were discussed and developed, and a summary session, in which session convenors gave a personal view of progress that has been made and problems which still need solving. Both were designed as ways of promoting further discussion. This paper attempts to distil some of the themes that emerged from these discussions.

Vertical structure and physical processes of the Madden-Julian oscillation: synthesis and summary

The "Vertical structure and physical processes of the Madden-Julian oscillation (MJO)" project comprises three experiments, designed to evaluate comprehensively the heating, moistening and momentum associated with tropical convection in general circulation models (GCMs). We consider here only those GCMs that performed all experiments. Some models display relatively higher or lower MJO fidelity in both initialized hindcasts and climate simulations, while others show considerable variations in fidelity between experiments. Fidelity in hindcasts and climate simulations are not meaningfully correlated. The analysis of each experiment led to the development of process-oriented diagnostics, some of which distinguished between GCMs with higher or lower fidelity in that experiment. We select the most discriminating diagnostics and apply them to data from all experiments, where possible, to determine if correlations with MJO fidelity hold across scales and GCM states. While normalized gross moist stability had a small but statistically significant correlation with MJO fidelity in climate simulations, we find no link with fidelity in medium-range hindcasts. Similarly, there is no association between timestep-to-timestep rainfall variability, identified from short hindcasts, and fidelity in medium-range hindcasts or climate simulations. Two metrics that relate precipitation to free-tropospheric moisture--the relative humidity for extreme daily precipitation, and variations in the height and amplitude of moistening with rain rate--successfully distinguish between higher- and lower-fidelity GCMs in hindcasts and climate simulations. To improve the MJO, developers should focus on relationships between convection and both total moisture and its rate of change. We conclude by offering recommendations for further experiments.

Recognition, assessment and treatment of social anxiety disorder: summary of NICE guidance

Social anxiety disorder is one of the most persistent and common of the anxiety disorders, with lifetime prevalence rates in Europe of 6.7% (range 3.9-13.7%).1 It often coexists with depression, substance use disorder, generalised anxiety disorder, panic disorder, and post-traumatic stress disorder.2 It can severely impair a person’s daily functioning by impeding the formation of relationships, reducing quality of life, and negatively affecting performance at work or school. Despite this, and the fact that effective treatments exist, only about half of people with this condition seek treatment, many after waiting 10-15 years.3 Although about 40% of those who develop the condition in childhood or adolescence recover before adulthood,4 for many the disorder persists into adulthood, with the chance of spontaneous recovery then limited compared with other mental health problems. This article summarises the most recent recommendations from the National Institute for Health and Care Excellence (NICE) on recognising, assessing, and treating social anxiety disorder in children, young people, and adults.5