Statistical Methods and the Meaning of Probabilities. A Philosopher Looks at Statistics

The talk starts out with a short introduction to the philosophy of probability. I highlight the need to interpret probabilities in the sciences and motivate objectivist accounts of probabilities. Very roughly, according to such accounts, ascriptions of probabilities have truth-conditions that are independent of personal interests and needs. But objectivist accounts are pointless if they do not provide an objectivist epistemology, i.e., if they do not determine well-defined methods to support or falsify claims about probabilities. In the rest of the talk I examine recent philosophical proposals for an objectivist methodology. Most of them take up ideas well-known from statistics. I nevertheless find some proposals incompatible with objectivist aspirations.

Representation via Probabilities: Models of Probabilistic Modeling

How do probabilistic models represent their targets and how do they allow us to learn about them? The answer to this question depends on a number of details, in particular on the meaning of the probabilities involved. To classify the options, a minimalist conception of representation (Su\'arez 2004) is adopted: Modelers devise substitutes (``sources'') of their targets and investigate them to infer something about the target. Probabilistic models allow us to infer probabilities about the target from probabilities about the source. This leads to a framework in which we can systematically distinguish between different models of probabilistic modeling. I develop a fully Bayesian view of probabilistic modeling, but I argue that, as an alternative, Bayesian degrees of belief about the target may be derived from ontic probabilities about the source. Remarkably, some accounts of ontic probabilities can avoid problems if they are supposed to apply to sources only.

Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.

Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t,x→∞t,x→∞, where t>0t>0 is the time horizon and x>0x>0 is the starting point of the risk process, with y=t/xy=t/x held constant and assumed either below or above a certain constant.

Conservation of threatened habitat types under future climate change – Lessons from plant-distribution models and current extinction trends in southern Germany

A higher risk of future range losses as a result of climate change is expected to be one of the main drivers of extinction trends in vascular plants occurring in habitat types of high conservation value. Nevertheless, the impact of the climate changes of the last 60 years on the current distribution and extinction patterns of plants is still largely unclear. We applied species distribution models to study the impact of environmental variables (climate, soil conditions, land cover, topography), on the current distribution of 18 vascular plant species characteristic of three threatened habitat types in southern Germany: (i) xero-thermophilous vegetation, (ii) mesophilous mountain grasslands (mountain hay meadows and matgrass communities), and (iii) wetland habitats (bogs, fens, and wet meadows). Climate and soil variables were the most important variables affecting plant distributions at a spatial level of 10 × 10 km. Extinction trends in our study area revealed that plant species which occur in wetland habitats faced higher extinction risks than those in xero-thermophilous vegetation, with the risk for species in mesophilous mountain grasslands being intermediary. For three plant species characteristic either of mesophilous mountain grasslands or wetland habitats we showed exemplarily that extinctions from 1950 to the present day have occurred at the edge of the species’ current climatic niche, indicating that climate change has likely been the main driver of extinction. This is largely consistent with current extinction trends reported in other studies. Our study indicates that the analysis of past extinctions is an appropriate means to assess the impact of climate change on species and that vulnerability to climate change is both species- and habitat-specific.

Bounding Standard Gaussian Tail Probabilities

We review various inequalities for Mills' ratio (1 - Φ)= Ø, where Ø and Φ denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving finite continued fractions lead to a general approximation scheme which implies and refines several known bounds.

Transient Earth system responses to cumulative carbon dioxide emissions: linearities, uncertainties, and probabilities in an observation-constrained model ensemble

Information on the relationship between cumulative fossil CO2 emissions and multiple climate targets is essential to design emission mitigation and climate adaptation strategies. In this study, the transient response of a climate or environmental variable per trillion tonnes of CO2 emissions, termed TRE, is quantified for a set of impact-relevant climate variables and from a large set of multi-forcing scenarios extended to year 2300 towards stabilization. An  ∼ 1000-member ensemble of the Bern3D-LPJ carbon–climate model is applied and model outcomes are constrained by 26 physical and biogeochemical observational data sets in a Bayesian, Monte Carlo-type framework. Uncertainties in TRE estimates include both scenario uncertainty and model response uncertainty. Cumulative fossil emissions of 1000 Gt C result in a global mean surface air temperature change of 1.9 °C (68 % confidence interval (c.i.): 1.3 to 2.7 °C), a decrease in surface ocean pH of 0.19 (0.18 to 0.22), and a steric sea level rise of 20 cm (13 to 27 cm until 2300). Linearity between cumulative emissions and transient response is high for pH and reasonably high for surface air and sea surface temperatures, but less pronounced for changes in Atlantic meridional overturning, Southern Ocean and tropical surface water saturation with respect to biogenic structures of calcium carbonate, and carbon stocks in soils. The constrained model ensemble is also applied to determine the response to a pulse-like emission and in idealized CO2-only simulations. The transient climate response is constrained, primarily by long-term ocean heat observations, to 1.7 °C (68 % c.i.: 1.3 to 2.2 °C) and the equilibrium climate sensitivity to 2.9 °C (2.0 to 4.2 °C). This is consistent with results by CMIP5 models but inconsistent with recent studies that relied on short-term air temperature data affected by natural climate variability.

A pharyngeal jaw evolutionary innovation facilitated extinction in Lake Victoria cichlids

Evolutionary innovations, traits that give species access to previously unoccupied niches, may promote speciation and adaptive radiation. Here, we show that such innovations can also result in competitive inferiority and extinction. We present evidence that the modified pharyngeal jaws of cichlid fishes and several marine fish lineages, a classic example of evolutionary innovation, are not universally beneficial. A large-scale analysis of dietary evolution across marine fish lineages reveals that the innovation compromises access to energy-rich predator niches. We show that this competitive inferiority shaped the adaptive radiation of cichlids in Lake Tanganyika and played a pivotal and previously unrecognized role in the mass extinction of cichlid fishes in Lake Victoria after Nile perch invasion.

Occurrence and Range-through database of functional diversity of marine ecosystems after the Late Permian mass extinction event

The Late Permian mass extinction event about 252 million years ago was the most severe biotic crisis of the past 500 million years and occurred during an episode of global warming. The loss of around two-thirds of marine genera is thought to have had substantial ecological effects, but the overall impacts on the functioning of marine ecosystems and the pattern of marine recovery are uncertain. Here we analyse the fossil occurrences of all known benthic marine invertebrate genera from the Permian and Triassic periods, and assign each to a functional group based on their inferred lifestyle. We show that despite the selective extinction of 62-74% of these genera, all but one functional group persisted through the crisis, indicating that there was no significant loss of functional diversity at the global scale. In addition, only one new mode of life originated in the extinction aftermath. We suggest that Early Triassic marine ecosystems were not as ecologically depauperate as widely assumed. Functional diversity was, however, reduced in particular regions and habitats, such as tropical reefs; at these smaller scales, recovery varied spatially and temporally, probably driven by migration of surviving groups. We find that marine ecosystems did not return to their pre-extinction state, and by the Middle Triassic greater functional evenness is recorded, resulting from the radiation of previously subordinate groups such as motile, epifaunal grazers.

Avian occupancy probabilities, vegetation structure, and presence of Northern Bobwhite (Colinus virginianus) in eastern and central Oklahoma (2009-2011)

Changes in land use and land cover throughout the eastern half of North America have caused substantial declines in populations of birds that rely on grassland and shrubland vegetation types, including socially and economically important game birds such as the Northern Bobwhite (Colinus virginianus; hereafter bobwhites). As much attention is focused on habitat management and restoration for bobwhites, they may act as an umbrella species for other bird species with similar habitat requirements. We quantified the relationship of bobwhites to the overall bird community and evaluated the potential for bobwhites to act as an umbrella species for grassland and shrubland birds. We monitored bobwhite presence and bird community composition within 31 sample units on selected private lands in the south-central United States from 2009 to 2011. Bobwhites were strongly associated with other grassland and shrubland birds and were a significant positive predictor for 9 species. Seven of these, including Bell's Vireo (Vireo bellii), Dicksissel (Spiza americana), and Grasshopper Sparrow (Ammodramus savannarum), are listed as species of conservation concern. Species richness and occupancy probability of grassland and shrubland birds were higher relative to the overall bird community in sample units occupied by bobwhites. Our results show that bobwhites can act as an umbrella species for grassland and shrubland birds, although the specific species in any given situation will depend on region and management objectives. These results suggest that efficiency in conservation funding can be increased by using public interest in popular game species to leverage resources to meet multiple conservation objectives.

Benthic foraminifera extinction at the base of the Brunhes Chronozone at ODP Holes 108-658A and 108-659A

A faunal boundary found at the base of the Brunhes Chronozone at Sites 658 and 659 confirms previous observations from several locations in the Atlantic Ocean and may be classified as a supraregional "extinction event". Several benthic foraminifer species typical of the Pliocene disappear near the Brunhes/Matuyama boundary, thus marking the upper limit of a faunal zone (faunal unit). Improved chronological dating indicates that the disappearance of these species occurs over a period of about 100,000 yr.

Abrupt vegetation change after the Late Quaternary megafaunal extinction in southeastern Australia

A substantial extinction of megafauna occurred in Australia between 50 and 45 kyr ago, a period that coincides with human colonization of Australia. Large shifts in vegetation also occurred around this time, but it is unclear whether the vegetation changes were driven by the human use of fire-and thus contributed to the extinction event-or were a consequence of the loss of megafaunal grazers. Here we reconstruct past vegetation changes in southeastern Australia using the stable carbon isotopic composition of higher plant wax n-alkanes and levels of biomass burning from the accumulation rates of the biomarker levoglucosan from a well-dated sediment core offshore from the Murray-Darling Basin. We find that from 58 to 44 kyr ago, the abundance of plants with the C-4 carbon fixation pathway was generally high-between 60 and 70%. By 43 kyr ago, the abundance of C-4 plants dropped to 30% and biomass burning increased. This transient shift lasted for about 3,000 years and came after the period of human arrival and directly followed megafauna extinction at 48.9-43.6 kyr ago. We conclude that the vegetation shift was not the cause of the megafaunal extinction in this region. Instead, our data are consistent with the hypothesis that vegetation change was the consequence of the extinction of large browsers and led to the build-up of fire-prone vegetation in the Australian landscape.