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.

Performance analysis of AF cooperative systems with HPA nonlinearity in semi-blind relays

In this paper, dual-hop amplify-and-forward (AF) cooperative systems in the presence of high-power amplifier (HPA) nonlinearity at semi-blind relays, are investigated. Based on the modified AF cooperative system model taking into account the HPA nonlinearity, the expression for the output signal-to-noise ratio (SNR) at the destination node is derived, where the interference due to both the AF relaying mechanism and the HPA nonlinearity is characterized. The performance of the AF cooperative system under study is evaluated in terms of average symbol error probability (SEP), which is derived using the moment-generating function (MGF) approach, considering transmissions over Nakagami-m fading channels. Numerical results are provided and show the effects of some system parameters, such as the HPA parameters, numbers of relays, quadrature amplitude modulation (QAM) order, Nakagami parameters, on performance.

Natural ventilation assessment in typical open an semi-open urban environments under various wind directions

Semi-open street roofs protect pedestrians from intense sunshine and rains. Their effects on natural ventilation of urban canopy layers (UCL) are less understood. This paper investigates two idealized urban models consisting of 4(2×2) or 16(4×4) buildings under a neutral atmospheric condition with parallel (0°) or non-parallel (15°,30°,45°) approaching wind. The aspect ratio (building height (H) / street width (W)) is 1 and building width is B=3H. Computational fluid dynamic (CFD) simulations were first validated by experimental data, confirming that standard k-ε model predicted airflow velocity better than RNG k-ε model, realizable k–ε model and Reynolds stress model. Three ventilation indices were numerically analyzed for ventilation assessment, including flow rates across street roofs and openings to show the mechanisms of air exchange, age of air to display how long external air reaches a place after entering UCL, and purging flow rate to quantify the net UCL ventilation capacity induced by mean flows and turbulence. Five semi-open roof types are studied: Walls being hung above street roofs (coverage ratio λa=100%) at z=1.5H, 1.2H, 1.1H ('Hung1.5H', 'Hung1.2H', 'Hung1.1H' types); Walls partly covering street roofs (λa=80%) at z=H ('Partly-covered' type); Walls fully covering street roofs (λa=100%) at z=H ('Fully-covered' type).They basically obtain worse UCL ventilation than open street roof type due to the decreased roof ventilation. 'Hung1.1H', 'Hung1.2H', 'Hung1.5H' types are better designs than 'Fully-covered' and 'Partly-covered' types. Greater urban size contains larger UCL volume and requires longer time to ventilate. The methodologies and ventilation indices are confirmed effective to quantify UCL ventilation.

Livelihoods and Vulnerability in the Arid and Semi-Arid Lands of Southern Africa: Exploring the links between ecosystem services and poverty alleviation

This book sets out the findings of research conducted into the links between ecosystem services and poverty alleviation in Southern Africa. It follows from extensive primary research conducted in the region, as well as intensive engagement with researchers, policy-makers and relevant institutions in several countries in southern Africa, as part of the Ecosystem Services and Poverty Alleviation Programme led by DFI, NERC and ESRC.

A semi-distributed ntegrated itrogen model for multiple source assessment in tchments (INCA): Part I — model structure and process equations

A new model has been developed for assessing multiple sources of nitrogen in catchments. The model (INCA) is process based and uses reaction kinetic equations to simulate the principal mechanisms operating. The model allows for plant uptake, surface and sub-surface pathways and can simulate up to six land uses simultaneously. The model can be applied to catchment as a semi-distributed simulation and has an inbuilt multi-reach structure for river systems. Sources of nitrogen can be from atmospheric deposition, from the terrestrial environment (e.g. agriculture, leakage from forest systems etc.), from urban areas or from direct discharges via sewage or intensive farm units. The model is a daily simulation model and can provide information in the form of time series at key sites, or as profiles down river systems or as statistical distributions. The process model is described and in a companion paper the model is applied to the River Tywi catchment in South Wales and the Great Ouse in Bedfordshire.

Solutions of the fully compressible semi-geostrophic system

The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.

Landscape evolution and ice-sheet behaviour in a semi-arid polar environment: James Ross Island, NE Antarctic Peninsula

This study of landscape evolution presents both new modern and palaeo process-landform data, and analyses the behaviour of the Antarctic Peninsula Ice Sheet through the Last Glacial Maximum (LGM), the Holocene and to the present day. Six sediment-landform assemblages are described and interpreted for Ulu Peninsula, James Ross Island, NE Antarctic Peninsula: (1) the Glacier Ice and Snow Assemblage; (2) the Glacigenic Assemblage, which relates to LGM sediments and comprises both erratic-poor and erratic-rich drift, deposited by cold-based and wet-based ice and ice streams respectively; (3) the Boulder Train Assemblage, deposited during a Mid-Holocene glacier readvance; (4) the Ice-cored Moraine Assemblage, found in front of small cirque glaciers; (5) the Paraglacial Assemblage including scree, pebble-boulder lags, and littoral and fluvial processes; and (6) the Periglacial Assemblage including rock glaciers, protalus ramparts, blockfields, solifluction lobes and extensive patterned ground. The interplay between glacial, paraglacial and periglacial processes in this semi-arid polar environment is important in understanding polygenetic landforms. Crucially, cold-based ice was capable of sediment and landform genesis and modification. This landsystem model can aid the interpretation of past environments, but also provides new data to aid the reconstruction of the last ice sheet to overrun James Ross Island.

The composite-tendency RAW filter in semi-implicit integrations

The time discretization in weather and climate models introduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leapfrog integrations from first-order to fifth-order. This improvement is achieved by replacing the Robert--Asselin filter with the RAW filter and using a linear combination of the unfiltered and filtered states to compute the tendency term. The purpose of the present paper is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model, and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leapfrog scheme is suitable for use in semi-implicit integrations.

Land use and climate change impacts on soil organic carbon stocks in semi-arid Spain

Purpose The sensitivity of soil organic carbon to global change drivers, according to the depth profile, is receiving increasing attention because of its importance in the global carbon cycle and its potential feedback to climate change. A better knowledge of the vertical distribution of SOC and its controlling factors—the aim of this study—will help scientists predict the consequences of global change. Materials and methods The study area was the Murcia Province (S.E. Spain) under semiarid Mediterranean conditions. The database used consists of 312 soil profiles collected in a systematic grid, each 12 km2 covering a total area of 11,004 km2. Statistical analysis to study the relationships between SOC concentration and control factors in different soil use scenarios was conducted at fixed depths of 0–20, 20–40, 40–60, and 60–100 cm. Results and discussion SOC concentration in the top 40 cm ranged between 6.1 and 31.5 g kg−1, with significant differences according to land use, soil type and lithology, while below this depth, no differences were observed (SOC concentration 2.1–6.8 g kg−1). The ANOVA showed that land use was the most important factor controlling SOC concentration in the 0–40 cm depth. Significant differences were found in the relative importance of environmental and textural factors according to land use and soil depth. In forestland, mean annual precipitation and texture were the main predictors of SOC, while in cropland and shrubland, the main predictors were mean annual temperature and lithology. Total SOC stored in the top 1 m in the region was about 79 Tg with a low mean density of 7.18 kg Cm−3. The vertical distribution of SOC was shallower in forestland and deeper in cropland. A reduction in rainfall would lead to SOC decrease in forestland and shrubland, and an increase of mean annual temperature would adversely affect SOC in croplands and shrubland. With increasing depth, the relative importance of climatic factors decreases and texture becomes more important in controlling SOC in all land uses. Conclusions Due to climate change, impacts will be much greater in surface SOC, the strategies for C sequestration should be focused on subsoil sequestration, which was hindered in forestland due to bedrock limitations to soil depth. In these conditions, sequestration in cropland through appropriate management practices is recommended.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Interactive effect of floral abundance and semi-natural habitats on pollinators in field beans (Vicia faba)

Pollination services are economically important component of agricultural biodiversity which enhance the yield and quality of many crops. An understanding of the suitability of extant habitats for pollinating species is crucial for planning management actions to protect and manage these service providers. In a highly modified agricultural ecosystem, we tested the effect of different pollination treatments (open, autonomous self- and wind-pollination) on pod set, seed set, and seed weight in field beans (Vicia faba). We also investigated the effect of semi-natural habitats and flower abundance on pollinators of field beans. Pollinator sampling was undertaken in ten field bean fields along a gradient of habitat complexity; CORINE land cover classification was used to analyse the land use patterns between 500–3000 m around the sites. Total yield from open-pollination increased by 185% compared to autonomous self-pollination. There was positive interactive effect of local flower abundance and cover of semi-natural habitats on overall abundance of pollinators at 1500 and 2000 m, and abundance of bumblebees (Bombus spp.) at 1000–2000 m. In contrast, species richness of pollinators was only correlated with flower abundance and not with semi-natural habitats. We did not find a link between pod set from open-pollination and pollinator abundance, possibly due to variations in the growing conditions and pollinator communities between sites. We conclude that insect pollination is essential for optimal bean yields and therefore the maintenance of semi-natural habitats in agriculture-dominated landscapes should ensure stable and more efficient pollination services in field beans.

A model analysis of climate and CO2 controls on tree growth in a semi-arid woodland

We used a light-use efficiency model of photosynthesis coupled with a dynamic carbon allocation and tree-growth model to simulate annual growth of the gymnosperm Callitris columellaris in the semi-arid Great Western Woodlands, Western Australia, over the past 100 years. Parameter values were derived from independent observations except for sapwood specific respiration rate, fine-root turnover time, fine-root specific respiration rate and the ratio of fine-root mass to foliage area, which were estimated by Bayesian optimization. The model reproduced the general pattern of interannual variability in radial growth (tree-ring width), including the response to the shift in precipitation regimes that occurred in the 1960s. Simulated and observed responses to climate were consistent. Both showed a significant positive response of tree-ring width to total photosynthetically active radiation received and to the ratio of modeled actual to equilibrium evapotranspiration, and a significant negative response to vapour pressure deficit. However, the simulations showed an enhancement of radial growth in response to increasing atmospheric CO2 concentration (ppm) ([CO2]) during recent decades that is not present in the observations. The discrepancy disappeared when the model was recalibrated on successive 30-year windows. Then the ratio of fine-root mass to foliage area increases by 14% (from 0.127 to 0.144 kg C m-2) as [CO2] increased while the other three estimated parameters remained constant. The absence of a signal of increasing [CO2] has been noted in many tree-ring records, despite the enhancement of photosynthetic rates and water-use efficiency resulting from increasing [CO2]. Our simulations suggest that this behaviour could be explained as a consequence of a shift towards below-ground carbon allocation.

The composite-tendency Robert-Asselin-Williams (RAW) filter in semi-implicit integrations

Timediscretization in weatherandclimate modelsintroduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leap-frog integrations from first-order to fifth-order.This improvement is achieved by replacing the Robert–Asselin filter with the Robert–Asselin–Williams (RAW) filter and using a linear combination of unfiltered and filtered states to compute the tendency term. The purpose of the present article is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leap-frog scheme is suitable for use in semi-implicit integrations.

Just add water and salt: the optimisation of petrogenic hydrocarbon biodegradation in soils from semi-arid Barrow Island, Western Australia

We investigated the potential of soil moisture and nutrient amendments to enhance the biodegradation of oil in the soils from an ecologically unique semi-arid island. This was achieved using a series of controlled laboratory incubations where moisture or nutrient levels were experimentally manipulated. Respired CO2 increased sharply with moisture amendment reflecting the severe moisture limitation of these porous and semi-arid soils. The greatest levels of CO2 respiration were generally obtained with a soil pore water saturation of 50–70%. Biodegradation in these nutrient poor soils was also promoted by the moderate addition of a nitrogen fertiliser. Increased biodegradation was greater at the lowest amendment rate (100 mg N kg−1 soil) than the higher levels (500 or 1,000 mg N kg−1 soil), suggesting the higher application rates may introduce N toxicity. Addition of phosphorous alone had little effect, but a combined 500 mg N and 200 mg P kg−1 soil amendment led to a synergistic increase in CO2 respiration (3.0×), suggesting P can limit the biodegradation of hydrocarbons following exogenous N amendment.

Dietary copper absorption and excretion in three semi-terrestrial grapsoid crabs with different levels of terrestrial adaptation

Three species of phylogenetically related semi-terrestrial crabs (Superfamily Grapsoidea - Sesarma rectum, Goniopsis cruentata and Neohelice granulata (formerly: Chasmagnathus granulatus) with different degrees of terrestriality were studied to quantify the accumulation of copper (Cu) in hemolymph, gills, hepatopancreas and antennal gland, and its excretion through the faeces. These crabs were fed for 15 days practical diets containing 0 (A), 0.5 (B), 1.0 (C), and 1.5% (D) of added CuCl2 (corresponding to 0, 0.2, 0.5 and 0.7% of Cu2+, respectively). The amount of food ingested was directly proportional to the degree of terrestriality: S. rectum, the most terrestrial species, ate around 2-3 times more than the other crabs, whereas G. cruentata ate 1.5-2 times more than N. granulata, the least terrestrial. The amount of Cu excreted in the feces was proportional to Cu ingestion, and was 76.8% and 64.2% higher for Sesarma fed diet D compared to G. cruentata and N. granulata, respectively. Sesarma also displayed higher Cu concentration in the haemolymph, gills and antennal glands, but not in the hepatopancreas. A detoxifying mechanism followed by elimination was probably present at this last organ, preventing Cu accumulation. More terrestrial crabs, such as Sesarma, may accumulate more Cu in hemolymph and tissues, showing a correlation between metal accumulation and increased terrestriality. In this aspect, contaminated feed sources with Cu may have more impact in conservation of terrestrial crabs. (C) 2008 Elsevier Inc. All rights reserved.