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Results for “Journal of Applied Probability”

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At least 37 records · Page 2Linked to original sources
USGS1995

Mark-resighting analysis of a California gull population

California gulls ( Larus californicus ) of known age and sex were censused on their breeding colony in 1979, 1980 and 1984 through 1993. Ages of 235 males and 196 females ranged from 4 to 27 years. Age classes used in the analysis were limited to 17, 4 through 19, and 20 or more as a final age category because data on gulls over 20 were sparse. Survival declined with age in a way that was parsimoniously modelled with a quadratic function. Other factors, sex and time, did not explain any variation in survival. Resighting depended on age, sex and time. Younger adults skipped breeding more frequently than did older adults, and females skipped breeding more frequently than did males. There was also good evidence for time dependence in resighting probability, but its inclusion in the model occurred at the expense of interpretability and precision. In a data set such as this, resighting probability may assume more importance than a mere 'nuisance parameter'. In this study, resighting history measured attendance at the breeding ground. In turn, attendance rates may be a manifestation of reproductive strategy, which can also have consequences for survival. In this situation, there may be heterogeneity in both survival and resighting probability that is unexplained by the model. While such complexity may well be a nuisance to deal with, it can also point to important biological questions.

Wyoming↗
USGS2018

Analysis of population change and movement using robust design removal data

In capture-mark-reencounter studies, Pollock’s robust design combines methods for open populations with methods for closed populations. Open population features of the robust design allow for estimation of rates of death or permanent emigration, and closed population features enhance estimation of population sizes. We describe a similar design, but for use with removal data. Data collection occurs on secondary sampling occasions clustered within primary sampling periods. Primary sampling periods are intervals of brief enough duration that it can be safely assumed that the population is unchanged by births, deaths, immigration or emigration during them; all population change and movement occurs between primary sampling periods. Our model provides a basis for inference about population size, changes in population size, and movement rates among sample locations between primary sampling periods. Movement rates are modeled as functions of distance and time. Capture probabilities are modeled as a function of effort. We apply the model to data obtained in attempting to eradicate an introduced population of veiled chameleons ( Chamaeleo calyptratus ) on the island of Maui in Hawaii.

Journal of Agricultural, Biological, and Environme↗
USGS1993

Concentrations, distribution, and sources of selenium from irrigated lands in western United States

Concentrations, distribution, and sources of selenium from irrigated lands were studied between 1986 and 1990 at 20 reconnaissance project areas in 17 western states under the Department of Interior's National Irrigation Water Quality Program. Samples of water, bottom sediment, whole‐body fish, and bird livers for analysis of selenium concentrations were collected before, during, and after irrigation season from streams, canals, lakes, and ground water in each project area. Selenium concentrations in water ranged from less than the detection limit of 1 μg/L in 42% of the 586 samples collected to 4,800 μg/L from a well in the Pine River Area, in southern Colorado. Selenium concentrations in 223 samples of bottom sediment ranged from less than the detection limit of 0.1 μg/g to 85 μg/g in a sample from the Middle Green River Basin, in Utah. Selenium concentrations in whole‐body fish (all species) ranged from 0.1 μg to 50 μg per gram dry weight, with the maximum concentration observed in a carp from the Gunnison River Basin, in western Colorado. Selenium concentrations in bird livers (all species) ranged from less than 0.32 μg to 170 μg per gram dry weight with the maximum concentration observed in the liver of an avocet from the Kendrick Reclamation Project, in Wyoming. Cretaceous‐age marine shales probably are the original sources for selenium in 16 of the 20 areas studied. In several areas, evaporative concentration of applied irrigation water and drainage of this water to wetlands, canals, streams, and lakes appears to be responsible for elevated concentrations of selenium.

Colorado, Utah, Wyoming↗
USGS2001

Effects of diquat, an aquatic herbicide, on the development of mallard embryos

Bipyridylium herbicides produce embryotoxic and teratogenic effects in dipteran, amphibian, avian, and mammalian organisms. Diquat dibromide, a bipyridylium compound, is commonly used as an aquatic herbicide. Mallard (Anas platyrhynchos) eggs were exposed to diquat by immersing the eggs for 10s in solutions of 0.88, 3.5, 7, 14, or 56 g/L on either the fourth or twenty-first day of incubation. Application of diquat on day 4 yielded an estimated LC50 of 19.5 g/L through 18 days of incubation, and 9.6 g/L through hatching. Body and organ weights, and bone lengths of hatchlings did not differ between control and treatment groups with the exception of a slight increase in brain weight in the 14 g/L group. Malformations in diquat-treated embryos included defects of the brain, eye, bill, limb, and pelvis; skeletal scoliosis; and incomplete ossification. Subcutaneous edema was also present. Significant manifestations of oxidative stress were apparent in hatchlings and included increased hepatic thiobarbituric acid reactive substances (TBARS) (lipid peroxidation) and decreased brain reduced glutathione (GSH). Brain protein-bound sulfhydryls (PBSH) increased. Diquat applied on day 21 of incubation yielded an estimated LC50 of 12.6 g/L through hatching. Exposure at this late stage of development did not produce deformities. Body and organ weights, and, bone lengths of hatchlings did not differ between control and treatment groups. Significant manifestations of oxidative stress in hatchlings included decreased brain GSH, increased oxidized glutathione (GSSG) and ratio of GSSG:GSH. This study suggests that concentrations of diquat commonly used for aquatic weed control, when based upon the expected dilution effect of average water depth of the application area, would probably have little impact on mallard embryos. However, concentrations applied above ground to weeds and cattails along the edge of waters and ditches could adversely affect the survival and development of mallard embryos, and presumably other avian species nesting in such habitats.

Journal of Toxicology and Environmental Health, Pa↗
USGS2009

A hierarchical model for estimating density in camera-trap studies

Estimating animal density using capture–recapture data from arrays of detection devices such as camera traps has been problematic due to the movement of individuals and heterogeneity in capture probability among them induced by differential exposure to trapping. We develop a spatial capture–recapture model for estimating density from camera-trapping data which contains explicit models for the spatial point process governing the distribution of individuals and their exposure to and detection by traps. We adopt a Bayesian approach to analysis of the hierarchical model using the technique of data augmentation. The model is applied to photographic capture–recapture data on tigers Panthera tigris in Nagarahole reserve, India. Using this model, we estimate the density of tigers to be 14·3 animals per 100 km 2 during 2004. Synthesis and applications. Our modelling framework largely overcomes several weaknesses in conventional approaches to the estimation of animal density from trap arrays. It effectively deals with key problems such as individual heterogeneity in capture probabilities, movement of traps, presence of potential ‘holes’ in the array and ad hoc estimation of sample area. The formulation, thus, greatly enhances flexibility in the conduct of field surveys as well as in the analysis of data, from studies that may involve physical, photographic or DNA-based ‘captures’ of individual animals.

Journal of Applied Ecology↗
USGS2010

Modelling detection probabilities to evaluate management and control tools for an invasive species

For most ecologists, detection probability (p) is a nuisance variable that must be modelled to estimate the state variable of interest (i.e. survival, abundance, or occupancy). However, in the realm of invasive species control, the rate of detection and removal is the rate-limiting step for management of this pervasive environmental problem. For strategic planning of an eradication (removal of every individual), one must identify the least likely individual to be removed, and determine the probability of removing it. To evaluate visual searching as a control tool for populations of the invasive brown treesnake Boiga irregularis, we designed a mark-recapture study to evaluate detection probability as a function of time, gender, size, body condition, recent detection history, residency status, searcher team and environmental covariates. We evaluated these factors using 654 captures resulting from visual detections of 117 snakes residing in a 5-ha semi-forested enclosure on Guam, fenced to prevent immigration and emigration of snakes but not their prey. Visual detection probability was low overall (= 0??07 per occasion) but reached 0??18 under optimal circumstances. Our results supported sex-specific differences in detectability that were a quadratic function of size, with both small and large females having lower detection probabilities than males of those sizes. There was strong evidence for individual periodic changes in detectability of a few days duration, roughly doubling detection probability (comparing peak to non-elevated detections). Snakes in poor body condition had estimated mean detection probabilities greater than snakes with high body condition. Search teams with high average detection rates exhibited detection probabilities about twice that of search teams with low average detection rates. Surveys conducted with bright moonlight and strong wind gusts exhibited moderately decreased probabilities of detecting snakes. Synthesis and applications. By emphasizing and modelling detection probabilities, we now know: (i) that eradication of this species by searching is possible, (ii) how much searching effort would be required, (iii) under what environmental conditions searching would be most efficient, and (iv) several factors that are likely to modulate this quantification when searching is applied to new areas. The same approach can be use for evaluation of any control technology or population monitoring programme. ?? 2009 The Authors. Journal compilation ?? 2009 British Ecological Society.

Journal of Applied Ecology↗
USGS2015

Maximum likelihood Bayesian model averaging and its predictive analysis for groundwater reactive transport models

While Bayesian model averaging (BMA) has been widely used in groundwater modeling, it is infrequently applied to groundwater reactive transport modeling because of multiple sources of uncertainty in the coupled hydrogeochemical processes and because of the long execution time of each model run. To resolve these problems, this study analyzed different levels of uncertainty in a hierarchical way, and used the maximum likelihood version of BMA, i.e., MLBMA, to improve the computational efficiency. This study demonstrates the applicability of MLBMA to groundwater reactive transport modeling in a synthetic case in which twenty-seven reactive transport models were designed to predict the reactive transport of hexavalent uranium (U(VI)) based on observations at a former uranium mill site near Naturita, CO. These reactive transport models contain three uncertain model components, i.e., parameterization of hydraulic conductivity, configuration of model boundary, and surface complexation reactions that simulate U(VI) adsorption. These uncertain model components were aggregated into the alternative models by integrating a hierarchical structure into MLBMA. The modeling results of the individual models and MLBMA were analyzed to investigate their predictive performance. The predictive logscore results show that MLBMA generally outperforms the best model, suggesting that using MLBMA is a sound strategy to achieve more robust model predictions relative to a single model. MLBMA works best when the alternative models are structurally distinct and have diverse model predictions. When correlation in model structure exists, two strategies were used to improve predictive performance by retaining structurally distinct models or assigning smaller prior model probabilities to correlated models. Since the synthetic models were designed using data from the Naturita site, the results of this study are expected to provide guidance for real-world modeling. Limitations of applying MLBMA to the synthetic study and future real-world modeling are discussed.

California↗
USGS2012

A robust method to forecast volcanic ash clouds

Ash clouds emanating from volcanic eruption columns often form trails of ash extending thousands of kilometers through the Earth's atmosphere, disrupting air traffic and posing a significant hazard to air travel. To mitigate such hazards, the community charged with reducing flight risk must accurately assess risk of ash ingestion for any flight path and provide robust forecasts of volcanic ash dispersal. In response to this need, a number of different transport models have been developed for this purpose and applied to recent eruptions, providing a means to assess uncertainty in forecasts. Here we provide a framework for optimal forecasts and their uncertainties given any model and any observational data. This involves random sampling of the probability distributions of input (source) parameters to a transport model and iteratively running the model with different inputs, each time assessing the predictions that the model makes about ash dispersal by direct comparison with satellite data. The results of these comparisons are embodied in a likelihood function whose maximum corresponds to the minimum misfit between model output and observations. Bayes theorem is then used to determine a normalized posterior probability distribution and from that a forecast of future uncertainty in ash dispersal. The nature of ash clouds in heterogeneous wind fields creates a strong maximum likelihood estimate in which most of the probability is localized to narrow ranges of model source parameters. This property is used here to accelerate probability assessment, producing a method to rapidly generate a prediction of future ash concentrations and their distribution based upon assimilation of satellite data as well as model and data uncertainties. Applying this method to the recent eruption of Eyjafjallajökull in Iceland, we show that the 3 and 6 h forecasts of ash cloud location probability encompassed the location of observed satellite-determined ash cloud loads, providing an efficient means to assess all of the hazards associated with these ash clouds.

Journal of Geophysical Research D: Atmospheres↗
USGS2009

Evaluation of trap capture in a geographically closed population of brown treesnakes on Guam

1. Open population mark-recapture analysis of unbounded populations accommodates some types of closure violations (e.g. emigration, immigration). In contrast, closed population analysis of such populations readily allows estimation of capture heterogeneity and behavioural response, but requires crucial assumptions about closure (e.g. no permanent emigration) that are suspect and rarely tested empirically. 2. In 2003, we erected a double-sided barrier to prevent movement of snakes in or out of a 5-ha semi-forested study site in northern Guam. This geographically closed population of >100 snakes was monitored using a series of transects for visual searches and a 13 ?? 13 trapping array, with the aim of marking all snakes within the site. Forty-five marked snakes were also supplemented into the resident population to quantify the efficacy of our sampling methods. We used the program mark to analyse trap captures (101 occasions), referenced to census data from visual surveys, and quantified heterogeneity, behavioural response, and size bias in trappability. Analytical inclusion of untrapped individuals greatly improved precision in the estimation of some covariate effects. 3. A novel discovery was that trap captures for individual snakes consisted of asynchronous bouts of high capture probability lasting about 7 days (ephemeral behavioural effect). There was modest behavioural response (trap happiness) and significant latent (unexplained) heterogeneity, with small influences on capture success of date, gender, residency status (translocated or not), and body condition. 4. Trapping was shown to be an effective tool for eradicating large brown treesnakes Boiga irregularis (>900 mm snout-vent length, SVL). 5. Synthesis and applications. Mark-recapture modelling is commonly used by ecological managers to estimate populations. However, existing models involve making assumptions about either closure violations or response to capture. Physical closure of our population on a landscape scale allowed us to determine the relative importance of covariates influencing capture probability (body size, trappability periods, and latent heterogeneity). This information was used to develop models in which different segments of the population could be assigned different probabilities of capture, and suggests that modelling of open populations should incorporate easily measured, but potentially overlooked, parameters such as body size or condition. ?? 2008 The Authors.

Journal of Applied Ecology↗
USGS2018

Determinants of Pseudogymnoascus destructans within bat hibernacula: Implications for surveillance and management of white-nose syndrome

Fungal diseases are an emerging global problem affecting human health, food security and biodiversity. Ability of many fungal pathogens to persist within environmental reservoirs can increase extinction risks for host species and presents challenges for disease control. Understanding factors that regulate pathogen spread and persistence in these reservoirs is critical for effective disease management. White-nose syndrome (WNS) is a disease of hibernating bats caused by Pseudogymnoascus destructans ( Pd ), a fungus that establishes persistent environmental reservoirs within bat hibernacula, which contribute to seasonal disease transmission dynamics in bats. However, host and environmental factors influencing distribution of Pd within these reservoirs are unknown. We used model selection on longitudinally collected field data to test multiple hypotheses describing presence–absence and abundance of Pd in environmental substrates and on bats within hibernacula at different stages of WNS. First detection of Pd in the environment lagged up to 1 year after first detection on bats within that hibernaculum. Once detected, the probability of detecting Pd within environmental samples from a hibernaculum increased over time and was higher in sediment compared to wall surfaces. Temperature had marginal effects on the distribution of Pd . For bats, prevalence and abundance of Pd were highest on Myotis lucifugus and on bats with visible signs of WNS. Synthesis and applications . Our results indicate that distribution of Pseudogymnoascus destructans ( Pd ) within a hibernaculum is driven primarily by bats with delayed establishment of environmental reservoirs. Thus, collection of samples from Myotis lucifugus , or from sediment if bats cannot be sampled, should be prioritized to improve detection probabilities for Pd surveillance. Long-term persistence of Pd in sediment suggests that disease management for white-nose syndrome should address risks of sustained transmission from environmental reservoirs.

Journal of Applied Ecology↗
USGS2012

Advances in the simulation and automated measurement of well-sorted granular material: 2. Direct measures of particle properties

1. In this, the second of a pair of papers on the structure of well-sorted natural granular material (sediment), new methods are described for automated measurements from images of sediment, of: 1) particle-size standard deviation (arithmetic sorting) with and without apparent void fraction; and 2) mean particle size in material with void fraction. A variety of simulations of granular material are used for testing purposes, in addition to images of natural sediment. Simulations are also used to establish that the effects on automated particle sizing of grains visible through the interstices of the grains at the very surface of a granular material continue to a depth of approximately 4 grain diameters and that this is independent of mean particle size. Ensemble root-mean squared error between observed and estimated arithmetic sorting coefficients for 262 images of natural silts, sands and gravels (drawn from 8 populations) is 31%, which reduces to 27% if adjusted for bias (slope correction between observed and estimated values). These methods allow non-intrusive and fully automated measurements of surfaces of unconsolidated granular material. With no tunable parameters or empirically derived coefficients, they should be broadly universal in appropriate applications. However, empirical corrections may need to be applied for the most accurate results. Finally, analytical formulas are derived for the one-step pore-particle transition probability matrix, estimated from the image's autocorrelogram, from which void fraction of a section of granular material can be estimated directly. This model gives excellent predictions of bulk void fraction yet imperfect predictions of pore-particle transitions.

Journal of Geophysical Research F: Earth Surface↗
USGS2001

Pesticides are involved with population declines of amphibians in the California Sierra Nevadas

Several species of frogs and toads are in serious decline in the Sierra Nevada Mountains of California. These species include the threatened red-legged frog ( Rana aurora ), foothill yellow-legged frog ( R. boylii ), mountain yellow-legged frog ( R. muscosa ), Cascades frog ( Rana cascadae ), western toad ( Bufo boreas ) and Yosemite toad ( B. canorus ). For many of these species current distributions are down to 10% of historical ranges. Several factors including introduced predators, habitat loss, and ultraviolet radiation have been suggested as causes of these declines. Another probable cause is air-borne pesticides from the Central Valley of California. The Central Valley, especially the San Joaquin Valley, is a major agricultural region where millions of pounds of active ingredient pesticides are applied each year (http://www.cdpr.ca.gov/dprdatabase.htm). Prevailing westerly winds from the Pacific Coast transport these pesticides into the into the Sierras.

Scientific World Journal↗
USGS2011

Use of recent and historical records to estimate status and trends of a rare and imperiled stream fish, Percina jenkinsi (Percidae)

Rarely encountered animals may be present but undetected, potentially leading to incorrect assumptions about the persistence of a local population or the conservation priority of a particular area. The federally endangered and narrowly endemic Conasauga logperch ( Percina jenkinsi ) is a good example of a rarely encountered fish species of conservation concern, for which basic population statistics are lacking. We evaluated the occurrence frequency for this species using surveys conducted with a repeat-observation sampling approach during the summer of 2008. We also analyzed museum records since the late 1980s to evaluate the trends in detected status through time. The results of these analyses provided support for a declining trend in this species over a portion of its historical range, despite low estimated detection probability. We used the results to identify the expected information return for a given level of monitoring where the sampling approach incorporates incomplete detection. The method applied here may be of value where historic occurrence records are available, provided that the assumption of constant capture efficiency is reasonable.

Canadian Journal of Fisheries and Aquatic Sciences↗
USGS2004

Nitrate and herbicide loading in two groundwater basins of Illinois' sinkhole plain

This investigation was designed to estimate the mass loading of nitrate (NO3-) and herbicides in spring water discharging from groundwater basins in an agriculturally dominated, mantled karst terrain. The loading was normalized to land use and NO3- and herbicide losses were compared to estimated losses in other agricultural areas of the Midwestern USA. Our study area consisted of two large karst springs that drain two adjoining groundwater basins (total area of 37.7 km2) in southwestern Illinois' sinkhole plain, USA. The springs and stream that they form were monitored for almost 2 years. Nitrate-nitrogen (NO3-N) concentrations at three monitoring sites were almost always above the background concentration (1.9 mg/l). NO3-N concentrations at the two springs ranged from 1.08 to 6.08 with a median concentration of 3.61 mg/l. Atrazine and alachlor concentrations ranged from <0.01 to 34 ??g/l and <0.01 to 0.98 ??g/l, respectively, with median concentrations of 0.48 and 0.12 ??g/l, respectively. Approximately 100,000 kg/yr of NO3-N, 39 kg/yr of atrazine, and 2.8 kg/yr of alachlor were discharged from the two springs. Slightly more than half of the discharged NO3- came from background sources and most of the remainder probably came from fertilizer. This represents a 21-31% loss of fertilizer N from the groundwater basins. The pesticide losses were 3.8-5.8% of the applied atrazine, and 0.05-0.08% of the applied alachlor. The loss of atrazine adsorbed to the suspended solid fraction was about 2 kg/yr, only about 5% of the total mass of atrazine discharged from the springs. ?? 2004 Elsevier B.V. All rights reserved.

Journal of Hydrology↗
USGS2010

Consumptive use and resulting leach-field water budget of a mountain residence

Consumptive use of water in a dispersed rural community has important implications for maximum housing density and its effects on sustainability of groundwater withdrawals. Recent rapid growth in Colorado, USA has stressed groundwater supplies in some areas, thereby increasing scrutiny of approximate methods developed there more than 30 years ago to estimate consumptive use that are still used today. A foothills residence was studied during a 2-year period to estimate direct and indirect water losses. Direct losses are those from evaporation inside the home, plus any outdoor use. Indirect loss is evapotranspiration ( ET ) from the residential leach-field in excess of ET from the immediately surrounding terrain. Direct losses were 18.7% of water supply to the home, substantially larger than estimated historically in Colorado. A new approach was developed to estimate indirect loss, using chamber methods together with the Penman&ndash;Monteith model. Indirect loss was only 0.9% of water supply, but this value probably was anomalously low due to a recurring leach-field malfunction. Resulting drainage beneath the leach-field was 80.4% of water supply. Guidelines are given to apply the same methodology at other sites and combine results with a survey of leach-fields in an area to obtain more realistic average values of ET losses.

Colorado↗
USGS1992

Mechanisms and function of school formation in subyearling American shad (Alosa sapidissima)

Summary The behavioural repertoire of subyearling American shad ( Alosa sapidissima ) was studied in the laboratory to examine pathways leading to Aggregation and School formation at various group sizes (3–100 fish per 500-liter tank). Three hypotheses were tested: (1) schooling is the dominant behavioural activity of subyearling American shad, (2) development and maintenance of cohesive social behaviour is affected b group size, and (3) survival is a function of group size. Seventeen discrete behaviour patterns were observed. In relation to group size, the amount of time spent Schooling varied directly whereas Following and Aggregating varied inversely. The number of bouts of Parallel orient, Parallel swim, and Pivot also varied inversely with group size. A conceptual model was developed and tested to show how normal schooling behaviour is achieved in small or fragmented groups through intermediary modal action patterns. Sequence analysis showed behavioural diversity to diminish with group size, thereby increasing group cohesion and uniformity of response to stimuli. Probability of survival, determined from weekly mortality in experimental tanks, increased significantly with group size (0.87–0.98 for 3–100 fish). It is hypothesized that survival improves with an increase in the proportion of time spent Schooling, which may increase feeding efficiency, reduce stress, or reduce metabolic expenditures.

Journal of Applied Ichthyology↗
USGS1969

Taxonomy of the common dolphins of the eastern Pacific Ocean

Delphinus bairdii Dall is a species of dolphin distinct from D. delphis Linnaeus, with which it has usually been synonymized. D. bairdii has a longer rostrum relative to the zygomatic width of the skull; the ratio of these measurements falls at 1.55 or above for bairdii and 1.53 and below for delphis. In the eastern Pacific Ocean, D. bairdii is found in the Gulf of California and along the west coast of Baja California, Mexico; D. delphis is presently found in the waters off California. Until approximately the beginning of the present century, bairdii occurred farther north in the eastern Pacific Ocean, at least to the Monterey Bay area of California. Restriction of bairdii to more southerly waters, probably as an indirect result of a change in water temperature, may have permitted delphis to move into inshore Californian waters. The Pacific population of D. delphis has a somewhat shorter rostrum than the Atlantic population, and is perhaps subspecifically different. A thorough analysis of the entire genus Delphinus is needed before the relationship of all the populations can be understood and names properly applied.

Baja, California, Gulf of California↗
USGS2008

Hierarchical Bayesian Markov switching models with application to predicting spawning success of shovelnose sturgeon

The timing of spawning in fish is tightly linked to environmental factors; however, these factors are not very well understood for many species. Specifically, little information is available to guide recruitment efforts for endangered species such as the sturgeon. Therefore, we propose a Bayesian hierarchical model for predicting the success of spawning of the shovelnose sturgeon which uses both biological and behavioural (longitudinal) data. In particular, we use data that were produced from a tracking study that was conducted in the Lower Missouri River. The data that were produced from this study consist of biological variables associated with readiness to spawn along with longitudinal behavioural data collected by using telemetry and archival data storage tags. These high frequency data are complex both biologically and in the underlying behavioural process. To accommodate such complexity we developed a hierarchical linear regression model that uses an eigenvalue predictor, derived from the transition probability matrix of a two-state Markov switching model with generalized auto-regressive conditional heteroscedastic dynamics. Finally, to minimize the computational burden that is associated with estimation of this model, a parallel computing approach is proposed. ?? Journal compilation 2009 Royal Statistical Society.

Journal of the Royal Statistical Society. Series C↗