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In a series of aerial photographic surveys of bowhead whales migrating past Barrow in Alaska in the spring, 40 individuals were captured in more than one year. To study individual-specific persistency in migratory pattern, the relative ranks of the captures of these whales among all captures that year were analysed. Controlling for body length and the presence of calves, the correlation of relative ranks in individuals captured multiple times was found not to be significantly different from zero (p-value=0.78).

In the period November 1963 to July 1983, 118 patients received a kidney transplant at Ullevål Hospital. All future kidney transplants were subsequently performed at Oslo University Hospital, Rikshospitalet. The purpose of our study is to present demographic data and show patient and graft survival from the first patient cohort of kidney transplant recipients in Norway.The patients were identified in surgical protocols from Ullevål Hospital and the Norwegian Renal Registry using follow-up data up to December 2016. We recorded the patients' age and sex, cause of renal failure, donor characteristics, patient and graft survival, number of retransplants and cause of death.118 patients: 38 women and 80 men, aged 14-67 years, received a transplant during the reference period. The most common indicators for transplantation were chronic glomerulonephritis (n = 61), chronic pyelonephritis (n = 20) and polycystic kidney disease (n = 14). Seventy-two patients (61 %) received a kidney from a deceased donor. After one year, 94 of the patients were still living (80 %), after five years, 66 of the patients (56 %) were still living, and after twenty years, the figure was 34 (29 %). Cardiovascular disease was the most common cause of death. The median graft survival was 3.8 years (quartile range 14.4 years). Thirty-two patients underwent retransplantation.Even in this pioneering era, patient survival rates and the functional life of donated kidneys were acceptable.

This is the guest editors’ general introduction to a Special Issue of the Journal of Statistical Planning and Inference, dedicated to confidence distributions and related themes. Confidence distributions (CDs) are distributions for parameters of interest, constructed via a statistical model after analysing the data. As such they serve the same purpose for the frequentist statisticians as the posterior distributions for the Bayesians. There have been several attempts in the literature to put up a clear theory for such confidence distributions, from Fisher’s fiducial inference and onwards. There are certain obstacles and difficulties involved in these attempts, both conceptually and operationally, which have contributed to the CDs being slow in entering statistical mainstream. Recently there is a renewed surge of interest in CDs and various related themes, however, reflected in both series of new methodological research, advanced applications to substantive sciences, and dissemination and communication via workshops and conferences. The present special issue of the JSPI is a collection of papers emanating from the Inference With Confidence workshop in Oslo, May 2015. Several of the papers appearing here were first presented at that workshop. The present collection includes however also new research papers from other scholars in the field.

There are strong propositions in the literature that abiotic factors override biotic drivers of diversity on time scales of the fossil record. In order to study the interaction of biotic and abiotic forces on long term changes, we devise a spatio-temporal discrete-time Markov process model of macroevolution featuring population formation, speciation, migration and extinction, where populations are free to migrate. In our model, the extinction probability of these populations is controlled by latitudinally and temporally varying environment (temperature) and competition. Although our model is general enough to be applicable to disparate taxa, we explicitly address planktic organisms, which are assumed to disperse freely without barriers over the Earth’s oceans. While rapid and drastic environmental changes tend to eliminate many species, generalists preferentially survive and hence leave generalist descendants. In other words, environmental fluctuations result in generalist descendants which are resilient to future environmental changes. Periods of stable or slow environmental changes lead to more specialist species and higher population numbers. Simulating Cenozoic diversity dynamics with both competition and the environmental component of our model produces diversity curves that reflect current empirical knowledge, which cannot be obtained with just one component. Our model predicts that the average temperature optimum at which planktic species thrive best has declined over the Neogene, following the trend of global average temperatures.

In this study, we developed a method of fractional parentage analysis using microsatellite markers. We propose a method for calculating parentage probability, which considers missing data and genotyping errors due to null alleles and other causes, by regarding observed alleles as realizations of random variables which take values in the set of alleles at the locus and developing a method for simultaneously estimating the true and null allele frequencies of all alleles at each locus. We then applied our proposed method to a large sample collected from a wild population of brown trout (Salmo trutta). On analyzing the data using our method, we found that the reproductive success of brown trout obeyed a power law, indicating that when the parent-offspring relationship is regarded as a link, the reproductive system of brown trout is a scale-free network. Characteristics of the reproductive network of brown trout include individuals with large bodies as hubs in the network and different power exponents of degree distributions between males and females.

We construct a detailed bioeconomic model of the Norwegian coastal cod fishery. This fishery has been open access up to the policy change during the "cod crisis" of 1989/1990. To answer to what extent the subsequent increase in biomass and profits was due to improved management, we isolate the effect of environmental variability. Projecting stock and harvest forward in the counterfactual scenario of no intervention, we show that the policy had a small positive impact on biomass, but a pronounced positive effect on profit. The main drivers of profit gains are increases in productivity and savings in fuel and labor costs. (JEL D23, Q22)

In its orthodoxy standard frequentist statistics deals only with aleatory probability, suppressing the intuitive epistemic probability representing inferential uncertainty. Confidence distributions, which are posterior distributions not based on any Bayesian priors, are discussed in nontechnical terms, with emphasis on the confidence curve. The correspondence between confidence curves and likelihoods allows independent confidence curves and confidence intervals to be integrated. Confidence and (serious) p -values are interpreted as epistemic probabilities, which do not fully follow ordinary probability calculus. Dimension reduction and other operations might be done on the likelihood related to the confidence curve. Confidence distributions and objective Bayes have much in common.

Previous chapters have developed concepts and methodology pertaining to confidence distributions and related inference procedures. Some of these methods take the form of generally applicable recipes, via log-likelihood profiles, deviances and first-order large-sample approximations to the distribution of estimators of the focus estimands in question. Sometimes these recipes are too coarse and are in need of modification and perfection, however, which is the topic of the present chapter. We discuss methods based on mean and bias corrected deviance curves, t-bootstrapping, a certain acceleration and bias correction method, approximations via expansions, prepivoting and modified likelihood profiles. The extent to which these methods lead to improvements is also briefly illustrated and discussed. Introduction Uniformly most powerful exact inference is in the presence of nuisance parameters available only in regular exponential models for continuous data and other models with Neyman structure, as discussed and exemplified in Chapter 5. Exact confidence distributions exist in a wider class of models, but need not be canonical. The estimate of location based on the Wilcoxon statistic, for example, has an exact known distribution in the location model where only symmetry is assumed; see Section 11.4. In more complex models, the statistic on which to base the confidence distribution might be chosen on various grounds: the structure of the likelihood function, perceived robustness, asymptotic properties, computational feasibility, perspective and tradition of the study. In the given model, with finite data, it might be difficult to obtain an exact confidence distribution based on the chosen statistic. As we shall see there are various techniques available for obtaining approximate confidence distributions and confidence likelihoods, however, improving on the first-order ones worked with in Chapters 3–4. Bootstrapping, simulation and asymptotics are useful tools in calculating approximate confidence distributions and in characterising their power properties. When an estimator, often the maximum likelihood estimator of the interest parameter, is used as the statistic on which the confidence distribution is based, bootstrapping provides an estimate of the sampling distribution of the statistic. This empirical sampling distribution can be turned into an approximate confidence distribution in several ways, which we address in the text that follows.

To obtain a distribution representing the inferred uncertain knowledge about the parameter directly from the data without access to any prior distribution was the glorious goal that Fisher succeeded in reaching with his fiducial distribution for a scalar parameter, but for vector parameters he got into trouble. He regarded the fiducial distribution as an ordinary probability distribution subject to the usual Kolmogorovian laws for sigma-additive probability measures. Fisher did not develop any mathematical theory of fiducial probability, but chose to illustrate his thoughts by examples. It was soon found that even in Fisher's examples with more than one parameter, there were no unique fiducial distributions, and inconsistencies and paradoxes were identified. After re-visiting Fisher's ideas over 1930–1935, which underlie our confidence distributions, we summarise and discuss the big debate over the fiducial argument, which died out only after Fisher's death in 1962, leaving the statistical community to regard it as badly flawed and Fisher's biggest blunder. The chapter ends with three attempts at saving the fiducial argument. Despite the potential problems with multivariate fiducial distributions, their marginals are often exact or approximate confidence distributions. The initial argument Fisher introduced the fiducial argument in 1930. In the introduction to Fisher (1930) he indicates that he had solved a very important problem that had escaped “the most eminent men of their time” since Bayes introduced his theorem and the method of inverse probability was established by Laplace. Later he stated that he really had a solution to “more than 150 years of disputation between the pros and cons of inverse probability [that] had left the subject only more befogged by doubt and frustration” (Fisher discussing Neyman in Neyman [1934, p. 617]). This was a view he held throughout his life. Fisher saw the fiducial probability as a probability measure over the parameter inherited from the probability model of the sampling experiment and the observed data. His early interpretation of fiducial probability was very similar to Neyman's coverage probability for intervals. Later he thought of fiducial distributions as a representation of the information in the data as seen on the background of the statistical model. It would then serve as an epistemic probability distribution for rational people. This is close to the Bayesian understanding of a posterior distribution, at least for people agreeing on the prior distribution.

This chapter is an invitation to the central themes of the book: confidence, likelihood, probability and confidence distributions. We sketch the historical backgrounds and trace various sources of influence leading to the present and somewhat bewildering state of ‘modern statistics’, which perhaps to the confusion of many researchers working in the applied sciences is still filled with controversies and partly conflicting paradigms regarding even basic concepts. Introduction The aim of this book is to prepare for a synthesis of the two main traditions of statistical inference: those of the Bayesians and of the frequentists. Sir Ronald Aylmer Fisher worked out the theory of frequentist statistical inference from around 1920. From 1930 onward he developed his fiducial argument, which was intended to yield Bayesian-type results without the often ill-founded prior distributions needed in Bayesian analyses. Unfortunately, Fisher went wrong on the fiducial argument. We think, nevertheless, that it is a key to obtaining a synthesis of the two, partly competing statistical traditions. Confidence, likelihood and probability are words used to characterise uncertainty in most everyday talk, and also in more formal contexts. The Intergovernmental Panel on Climate Change (IPCC), for example, concluded in 2007, “Most of the observed increase in global average temperature since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations” (Summary for Policymakers, IPCC, 2007). They codify ‘very likely’ as having probability between 0.90 and 0.95 according to expert judgment. In its 2013 report IPCC is firmer and more precise in its conclusion. The Summary for Policymakers states, “It is extremely likely that more than half of the observed increase in global surface temperature from 1951 to 2010 was caused by the anthropogenic increase in greenhouse gas concentrations and other anthropogenic forcings together” (IPCC, 2013, p. 17). By extremely likely they mean more than 95% certainty. We would have used ‘confidence’ rather than ‘likelihood’ to quantify degree of belief based on available data. We will use the term ‘likelihood’ in the technical sense usual in statistics. Confidence, likelihood and probability are pivotal words in the science of statistics. Mathematical probability models are used to build likelihood functions that lead to confidence intervals. Why do we need three words, and actually additional words such as credibility and propensity, to measure uncertainty and frequency of chance events?

This lively book lays out a methodology of confidence distributions and puts them through their paces. Among other merits, they lead to optimal combinations of confidence from different sources of information, and they can make complex models amenable to objective and indeed prior-free analysis for less subjectively inclined statisticians. The generous mixture of theory, illustrations, applications and exercises is suitable for statisticians at all levels of experience, as well as for data-oriented scientists. Some confidence distributions are less dispersed than their competitors. This concept leads to a theory of risk functions and comparisons for distributions of confidence. Neyman–Pearson type theorems leading to optimal confidence are developed and richly illustrated. Exact and optimal confidence distribution is the gold standard for inferred epistemic distributions. Confidence distributions and likelihood functions are intertwined, allowing prior distributions to be made part of the likelihood. Meta-analysis in likelihood terms is developed and taken beyond traditional methods, suiting it in particular to combining information across diverse data sources.

The build up of information in a continued capture-recapture experiment of simple random sampling of an open population is studied by predicting the conditional approximate Fisher information for abundance in data from one survey given the previous data. By neglecting the stochasticity in survival, a simple approximate likelihood is obtained. Optimal temporal allocation of a given total effort is found by numerical optimization for various objective functions based on the approximate Fisher information. For aerial photographic surveys of bowhead whales, the performance of estimates of abundance and of demographic parameters is compared between constant yearly survey effort and nominally optimal sampling by simulating a realistic model over 50 years. Copyright 2012, Oxford University Press.

Harvesting regulations for crustacean decapods generally focus on total catch and minimum legal size of individuals. However, there are trade-offs between total catch and minimum size, and possibly also for max- imum size. The outcome of various harvesting restrictions was assessed by model iterations for one lake based on a long time series (29 years) of crayfish population size and annual harvesting. The paper explores how this decline might have been avoided by alternative harvest regulations based on a strong decline in the surveyed population and use of a deterministic model with two stable equilibria. The results of the model simulations suggested that the decline may have been avoided by reducing the annual catches by 15% without changing the minimum size regulation of 95 mm. The decline may also have been avoided by protecting the largest (and most fecund) individuals, e.g. by allowing harvesting of crayfish between 50 and 98 mm without reducing the total catches. The latter strategy might also have counteracted a long-term evolution towards smaller crayfish caused by selective harvesting of the largest individuals.

Abundance, mortality, and population growth of bowhead whales (Balaenamysticetus) are estimated from captures of 4,894 putatively different individuals obtained from 10 years of systematic photographic surveys conducted during the spring migration when most of the Bering–Chukchi–Beaufort population of bowheads migrates past Point Barrow, Alaska. A stringent matching protocol designed to prevent false positive matches of the naturally, but variably marked individuals, led to 42 resightings between years. The flip side of this stringency is a presence of false negatives, i.e., some true recaptures are not recognized as such. The problem of false negatives is addressed by modeling the capture process and the matching process. The captures of an individual are assumed to follow a Poisson process with intensity depending stochastically on the individual whale and on the year. The probability of successfully matching a capture to a previous capture is estimated by logistic regression on the degree of marking and image quality. Individuals are recruited by the Pella–Tomlinson population model, and their mortality rate is assumed to be constant. The point estimate of yearly growth rate is 3.2%, and bowhead abundance in 2001 is estimated to be 8,250, similar to previous estimates.

Species arise and establish themselves over the geologic time scale. This process is manifested as a change in the relative frequency of occurrences of a given species in the global pool of species. Our main goal here is to model this rise and the eventual decline of microfossil species using a mixed-effects model where groups each have a characteristic occurrence trajectory (main effects) and each species belonging to those groups is allowed to deviate from the given group trajectory (random effects). Our model can be described as a “hat” with logistic forms in the periods of increase and decline. Using the estimated timings of rises and falls, we find that the lengths of the periods of rise are about as long as the lengths of the periods when species are above 50% of their estimated maximal occurrences. These latter periods are here termed periods of dominance, which are in turn about the same length as the species' periods of fall. The peak rates of the rises of microfossils are in general faster than their peak rates of falls. These quantified observations may have broad macroevolutionary and macroecological implications. Further, we hypothesize that species that have experienced and survived high levels of environmental volatility (specifically, periods of greater than average variation in temperature and productivity) during their formative periods should have longer periods of dominance. This is because subsequent environmental variations should not drive them to decline with ease. We find that higher estimated environmental volatility early in the life of a species positively correlates with lengths of periods of dominance, given that a species survives the initial stress of the environmental fluctuations. However, we find no evidence that the steepness of the rise of a species is affected by environmental volatility in the early phases of its life.

By the modified directed likelihood, higher order accurate confidence limits for a scalar parameter are obtained from the likelihood. They are conveniently described in terms of a confidence distribution, that is a sample dependent distribution function on the parameter space. In this paper we explore a different route to accurate confidence limits via tail-symmetric confidence curves, that is curves that describe equal tailed intervals at any level. Instead of modifying the directed likelihood, we consider inversion of the log-likelihood ratio when evaluated at the median of the maximum likelihood estimator. This is shown to provide equal tailed intervals, and thus an exact confidence distribution, to the third-order of approximation in regular one-dimensional models. Median bias correction also provides an alternative approximation to the modified directed likelihood which holds up to the second order in exponential families., Comment: 19 pages, 3 figures

We develop a general framework for analysing and testing genetic structure within a migratory assemblage that is based on measures of genetic differences between individuals. We demonstrate this method using microsatellite DNA data from the Bering-Chukchi-Beaufort stock of bowhead whales (Balaena mysticetus), sampled via Inuit hunting during the spring and autumn migration off Barrow, Alaska. This study includes a number of covariates such as whale ages and the time separation between captures. Applying the method to a sample of 117 bowhead whales, we use permutation methods to test for temporal trends in genetic differences that can be ascribed to age-related effects or to timing of catches during the seasons. The results reveal a pattern with elevated genetic differences among whales caught about a week apart, and are statistically significant for the autumn migration. In contrast, we find no effects of time of birth or age-difference on genetic differences. We discuss possible explanations for the results, including population substructuring, demographic consequences of historical overexploitation, and social structuring during migration.

An approach to estimating the statistical uncertainty in age-specific abundance of Norwegian spring-spawning herring is presented. The method is applied to data from a survey on the overwintering stock in the Vestfjord system of northern Norway in December 1996. It is based on building separate statistical models for acoustic and biological data. The acoustic data are modelled as a gamma-transformed spatial random field and fitted to echo readings from the survey. The biological data are fitted to a two-stage model using multinomial sampling from Dirichlet-distributed age proportions. Uncertainty in the abundance by age distribution is obtained by bootstrapping. Previous assessments have a priori taken the abundance by age from a skewed distribution, such as gamma or log-normal families. In contrast, this analysis results in an estimated abundance by age that seems symmetric and does not display heavy tails.

Confidence intervals for a single parameter are spanned by quantiles of a confidence distribution, and one-sided p-values are cumulative confidences. Confidence distributions are thus a unifying format for representing frequentist inference for a single parameter. The confidence distribution, which depends on data, is exact (unbiased) when its cumulative distribution function evaluated at the true parameter is uniformly distributed over the unit interval. A new version of the Neyman-Pearson lemma is given, showing that the confidence distribution based on the natural statistic in exponential models with continuous data is less dispersed than all other confidence distributions, regardless of how dispersion is measured. Approximations are necessary for discrete data, and also in many models with nuisance parameters. Approximate pivots might then be useful. A pivot based on a scalar statistic determines a likelihood in the parameter of interest along with a confidence distribution. This proper likelihood is reduced of all nuisance parameters, and is appropriate for meta-analysis and updating of information. The reduced likelihood is generally different from the confidence density. Confidence distributions and reduced likelihoods are rooted in Fisher-Neyman statistics. This frequentist methodology has many of the Bayesian attractions, and the two approaches are briefly compared. Concepts, methods and techniques of this brand of Fisher-Neyman statistics are presented. Asymptotics and bootstrapping are used to find pivots and their distributions, and hence reduced likelihoods and confidence distributions. A simple form of inverting bootstrap distributions to approximate pivots of the abc type is proposed. Our material is illustrated in a number of examples and in an application to multiple capture data for bowhead whales.

The aim of the present study is to compare suicide rates between 1960 and 1989 for Norwegian physicians with corresponding rates for other Norwegians with and without university education, by age, gender, and five-year period, based on death certificates for all Norwegians who died in the period 1960-1989. There were 82 registered physician suicides, of which 9 were female, 265 suicides by persons with other university education, and 11,165 by persons with no university education. Suicide rate is measured in number of deaths per 100,000 person years. Crude suicide rates were 47.7 (95% CI 37.7-60.4) for male physicians, 20.1 (17.7-22.9) for other male university graduates, and 22.7 (22.2-23.2) for men with no university education. The corresponding figures for females were 32.3 (15.8-63.7), 13.0 (8.4-19.8) and 7.7 (7.5-8.0). Both for males and females, suicide rates, controlled for age and period, were significantly higher for physicians than for persons with other or no university education. Poisson modelling showed that the risk of suicide for male physicians has the same age pattern as for other males with higher education. In 1985-89 the suicide rate for male physicians increased nearly linearly from about 35 at the age 35-40 to about 100 at the age 75-79, which was almost three times higher than for the other male university graduates. For the age group 50-54 the estimated rate increases from about 50 in 1960-64 to about 90 in 1985-89. For the female physicians, the low number of cases prevents reliable estimation of trends. For male physicians, the trend from 1960 to 1989 is increasing. The estimated risk for a single physician to commit suicide was almost 5 times that of a married or co-habitant colleague. For 52% of the male and 85% of the female physicians the suicide method was poisoning. This is about twice the rates in the general population.

In the 1950s, the majority of scientists in the International Whaling Commission (IWC) argued that the fin whale was overexploited in the Southern Hemisphere. However, several other scientists throughout the period persistently objected to this view. The scientific controversy attendant to this issue engendered great uncertainty. This uncertainty contributed towards extending the period of excessive whaling, and nearly destroyed the IWC. This paper reviews the fin whale debate in detail, puts the debate in a political perspective, and argues that the intentional injection of controversy for non‐scientific reasons in decision‐making forums, which the author terms “distortion of uncertainty,” constitutes an act of scientific misconduct.

The conventional line transect approach of estimating effective search width from the perpendicular distance distribution is inappropriate in certain types of surveys, e.g., when an unknown fraction of the animals on the track line is detected, the animals can be observed only at discrete points in time, there are errors in positional measurements, and covariate heterogeneity exists in detectability. For such situations a hazard probability framework for independent observer surveys is developed. The likelihood of the data, including observed positions of both initial and subsequent observations of animals, is established under the assumption of no measurement errors. To account for measurement errors and possibly other complexities, this likelihood is modified by a function estimated from extensive simulations. This general method of simulated likelihood is explained and the methodology applied to data from a double-platform survey of minke whales in the northeastern Atlantic in 1995.

Summary. The likelihood function for data from independent observer line transect surveys is derived, and a hazard model is proposed for the situation where animals are available for detection only at discrete time points. Under the assumption that the time points of availability follow a Poisson point process, we obtain an analytical expression for the detection function. We discuss different criteria for choosing the hazard function and consider in particular two different parametric families of hazard functions. Discrete and continuous hazard models are compared and the robustness of the discrete model is investigated. Finally, the methodology is applied to data from a survey for minke whales in the northeastern Atlantic.

Fisheries management has generally suffered from lack of explicitly stated management objectives. This may have contributed to overexploitation by putting more emphasis on short-term losses rather than longterm gains from reducing ®shing effort. Uncertainties are often not properly measured and usually not explicitly accounted for in yield predictions, resulting in management strategies with substantial risk of stock depletion. Uncertainties related to ®shermen's behaviour (investments, over®shing, discards) are also important from a management point of view, but seldom taken properly into account. On behalf of its research programme Marine Resource Management, the Research Council of Norway sponsored and arranged a symposium in Bergen 3±5 June 1997 on ` Objectives and uncertainties in ®sheries management with emphasis on three North Atlantic ecosystems''. The organising and program committee of the symposium consisted of eyvind Ulltang (chair), Ola Flaaten, Tore Schweder and Anne G.V. Salvanes (co-ordinator). The symposium concentrated on ®sheries management in the Barents Sea, the waters around Iceland and the waters east of Canada. Although focused on the North Atlantic, contributions referring to other areas were also presented. The main aim of the symposium was to initiate a multidisciplinary discussion of potential gains from being more explicit about ®sheries management objectives, and in acknowledging more properly the uncertainties surrounding both the ecosystem and the industry. The goal was further to present research and identify research potentials of importance to improve management in the North Atlantic and elsewhere. Of the titles submitted, 43 were selected for oral presentation and 13 for display at poster sessions at the symposium. During the symposium, seminars were arranged for having in-depth discussions of some key problems identi®ed by speakers under the theme sessions. Of a total of 44 manuscripts submitted for publication, 24 were accepted after peer review and included in this volume.

In a model with four species – cod, capelin, herring and minke whales – the fish populations are age and length distributed, while the minke whale is age and sex distributed. The time step is one month, and there are two areas (The Barents Sea and parts of the Norwegian Sea). There is a food-web with minke whales as top predators, consuming herring, capelin and cod according to a non-linear consumption function in available prey abundance. The consumption function for minke whales is roughly estimated. The opportunistic minke whale may forage on plankton and other fish than cod, capelin or herring, and is thus, modelled as having carrying capacity and demographic parameters independent of the status of the fish stocks in the model. The fish-fisheries are managed by fixed VPA-based fishing mortalities (cod and herring) and Captool (capelin), while minke whaling is managed according to the RMP of the IWC. The model is stochastic in fish recruitment and in survey indices for minke whales. The model is simulated over 100-year periods in a number of scenarios spanned by nine experimental factors. The core of the experimental design is an orthogonal array with 27 points. The primary study variable is the tuning of the RMP, and the response variables are catches and stock sizes of cod, herring and minke whale. The responses are taken as yearly means over the last 90 years of the period. When the tuning of the RMP is changed from the current level of targeting the final stock at 72% of carrying capacity to 60%, the annual catch of whales increases with some 300 animals, while the annual catch of cod increases with some 0.1 million ton on the average. For herring, no clear main effect was found on catch or mortality rate. The catch of cod is estimated to increase in annual mean with some 6 ton with a mean reduction in the whale stock of one animal. The results concerning the effects on the cod and herring fisheries must be taken as tentative since the ecosystem model used could be improved, and so could the strategies for managing the fisheries. The study exemplifies how scenario experimentation can be used as a tool for investigating the properties of fishery management regimes.

Directly observed data are in many cases combined with diverse indirect information to draw inference on parameters of interest to the fishery scientist. The indirect information might be based on previous data, analogous data or the researcher's expert judgement. The Bayesian prior distribution is the most common concept for representing such indirect information, and the Bayesian paradigm is gaining popularity. An alternative methodology based on the likelihood principle is presented and compared to the Bayesian. In the tradition of R.A. Fisher, the method concentrates on the likelihood function, without bringing in prior distributions that are not based on data. To provide for the integration of relevant indirect statistical information into the likelihood function, the concept of indirect likelihood is proposed. The indirect likelihood is treated as an ordinary independent component of the likelihood. If the indirect likelihood of a parameter is based on previous data, the inclusion of the indirect likelihood in the new study amounts to combining the old and the new data. The two methods are explained and compared, and it is argued that the likelihood method often is advantageous in the scientific context.

An extensive research program has been undertaken in Norway on physician health, sickness, working conditions and quality of life. Data are collected from cross-sectional and longitudinal prospective and retrospective surveys, qualitative studies, and vital statistics. This paper presents findings on subjectively experienced health problems, emotional distress, experienced job stress and job satisfaction, based on an extensive cross-sectional postal questionnaire study in 1993. An overlapping questionnaire design was used to allow many relationships to be estimated without exhausting the recipients. 9266 active physicians were included, which comprises close to the total Norwegian physician work-force minus a representative sample of 2100, used for other studies. The primary questionnaire was returned by 6652 (71.8%), the great majority of which also returned three secondary questionnaires. The results indicate that health complaints were significantly more frequent in female physicians and decreased with age. Low job satisfaction, high job stress, and emotional distress were all found to be significant predictors of subjective health complaints, as measured by the Ursin Health Inventory.

We consider the problem of estimating the parameters of a two-dimensional Neyman-Scott process, from data collected through a line transect survey. Cowling (1998, Biometrics 54, 828-839) suggested an estimation method based on a one-dimensional K-function along the transect line. However, her expression for the theoretical K-function is wrong. In this article, we correct her K-function.

Time series of cell size evolution in unicellular marine algae (division Haptophyta; Coccolithus lineage), covering 57 million years, are studied by a system of linear stochastic differential equations of hierarchical structure. The data consists of size measurements of fossilized calcite platelets (coccoliths) that cover the living cell, found in deep-sea sediment cores from six sites in the world oceans and dated to irregular points in time. To accommodate biological theory of populations tracking their fitness optima, and to allow potentially interpretable correlations in time and space, the model framework allows for an upper layer of partially observed site-specific population means, a layer of site-specific theoretical fitness optima and a bottom layer representing environmental and ecological processes. While the modeled process has many components, it is Gaussian and analytically tractable. A total of 710 model specifications within this framework are compared and inference is drawn with respect to model structure, evolutionary speed and the effect of global temperature., Comment: Published in at http://dx.doi.org/10.1214/12-AOAS559 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

The first session of invited papers at the 18th Nordic Conference on Mathematical Statistics held from 5 to 8 June 2000 in Grimstad, Norway, ran under the title "Large structured models in applied sciences; challenges for statistics". The economist Jansen, the meteorologist Gustafsson and the fishery scientists Gavaris and lanelli gave papers that were discussed by statisticians. These papers and the discussions are presented in this issue of SJS. The programme committee, which I chaired, wanted to expose Nordic statisticians to current use of large structured models. By working together with the applied scientists, statisticians can surely help to solve problems and to improve practices. This is done in many branches of science today, but the scope for co-operation is wide and the demand for skilled statisticians that are willing to dive into applied fields is increasing. Statisticians can also contribute as go-betweens. Much of the advance in the field of statistics results from applied work, either by innovations within the field as such, or by co-operation involving statisticians. These advances are often useful in other applied areas as well. The statistician can help to spread new ideas by formulating the specific innovations in the general language of statistics. To be successful go-betweens, statisticians must thus keep a sufficient foothold in their mother field of statistics. Large structured models are used in many sciences and for various purposes. In addition to economics, fisheries and meteorology, one could mention epidemiology, physiology, ecology, oceanography, and climatology. Large structured models describe complex processes. In order to represent the multivariate nature of the process, the model must be sufficiently rich in variables and parameters, and thus is large. Linear or non-linear difference or differential equations, definitional equations, and other structural restrictions are imposed on variables and parameters to represent the dynamics in time and space of the system as postulated by the substantive theory in question. Take the climatic system of the earth as an example. In order to represent the climate in its spatial and temporal diversity, the model needs to be large. Geophysics, assisted with other relevant branches of the natural sciences, provides physical laws and other regularities that give structure to the overarching model. Although smaller partial models are useful to study separate aspects of the system, large structured models are needed to describe and measure the system as a whole, with its interactions, simultaneity, delayed reaction, non-linearity, chock propagation and other complexities. The non-linearities might be severe, even bifurcations (e.g. epochs of rapid cooling or heating of the north Atlantic region, as inferred from glacial cores from Greenland). Large structured models are used for forecasting and prediction. They might be useful in making sense of data (e.g. Greenland ice-core data), and to assess the current state of the system. Policy analyses are carried out in many fields, and to account for indirect effects, delays, and non-linearities, large structured models are often required. Addressing statisticians, Gustafsson, Jansen and Gavaris & lanelli use their space primarily on statistical issues associated with large structured models in their fields of meteorology, economics, and fisheries rather than on the many issues associated with the use and utility of such models. Current and potential use should, however, be kept in mind when reading their papers.