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.

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.

Probability inundation map for a scenario combining storm surge and sea-level rise

Coastal managers require reliable spatial data on the extent and timing of potential coastal inundation, particularly in a changing climate. Most sea level rise (SLR) vulnerability assessments are undertaken using the easily implemented bathtub approach, where areas adjacent to the sea and below a given elevation are mapped using a deterministic line dividing potentially inundated from dry areas. This method only requires elevation data usually in the form of a digital elevation model (DEM). However, inherent errors in the DEM and spatial analysis of the bathtub model propagate into the inundation mapping. The aim of this study was to assess the impacts of spatially variable and spatially correlated elevation errors in high-spatial resolution DEMs for mapping coastal inundation. Elevation errors were best modelled using regression-kriging. This geostatistical model takes the spatial correlation in elevation errors into account, which has a significant impact on analyses that include spatial interactions, such as inundation modelling. The spatial variability of elevation errors was partially explained by land cover and terrain variables. Elevation errors were simulated using sequential Gaussian simulation, a Monte Carlo probabilistic approach. 1,000 error simulations were added to the original DEM and reclassified using a hydrologically correct bathtub method. The probability of inundation to a scenario combining a 1 in 100 year storm event over a 1 m SLR was calculated by counting the proportion of times from the 1,000 simulations that a location was inundated. This probabilistic approach can be used in a risk-aversive decision making process by planning for scenarios with different probabilities of occurrence. For example, results showed that when considering a 1% probability exceedance, the inundated area was approximately 11% larger than mapped using the deterministic bathtub approach. The probabilistic approach provides visually intuitive maps that convey uncertainties inherent to spatial data and analysis.

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.

Theoretical Transition Probabilities, Oscillator Strengths and Radiative Lifetimes Of Levels In Pb IV

Transitionprobabilities and oscillatorstrengths of 176 spectral lines with astrophysical interest arising from 5d10ns (n = 7,8), 5d10np (n = 6,7), 5d10nd (n = 6,7), 5d105f, 5d105g, 5d10nh (n = 6,7,8), 5d96s2, and 5d96s6p configurations, and radiativelifetimes for 43 levels of PbIV, have been calculated. These values were obtained in intermediate coupling (IC) and using relativistic Hartree–Fock calculations including core-polarization effects. For the IC calculations, we use the standard method of least-square fitting from experimental energy levels by means of the Cowan computer code. The inclusion in these calculations of the 5d107p and 5d105f configurations has facilitated a complete assignment of the energy levels in the PbIV. Transitionprobabilities, oscillatorstrengths, and radiativelifetimes obtained are generally in good agreement with the experimental data.

Ab initio calculations of Ca III Stark broadening parameters,transition probabilities and radiative lifetimes

We have determined matrix elements for all experimental configurations of Ca III, including the 3s3p63d configuration. These values have been obtained using intermediate coupling (IC). For these IC calculations, we have used the standard method of least-squares fitting from the experimental energy levels, using the computer code developed by Robert Cowan. In this paper, using these matrix elements, we report the calculated values of the Ca III Stark widths and shifts for 148 spectral lines, of 56 Ca III spectral line transition probabilities and of eight radiative lifetimes of Ca III levels. The Stark widths and shifts, calculated using the Griem semi-empirical approach, correspond to the spectral lines of Ca III and are presented for an electron density of 1017 cm?3 and temperatures T = 1.0?10.0 (×104 K). The theoretical trends of the Stark broadening parameter versus the temperature are presented for transitions that are of astrophysical interest. There is good agreement between our calculations, for transition probabilities and radiative lifetimes, and the experimental values presented in the literature. We have not been able to find any values for the Stark parameters in the references.

Application of laser-induced plasma spectroscopy to the measurement of transition probabilities of Ca I

We present improved experimental transition probabilities for the optical Ca I 4s4p-4s4d and 4s4p-4p2multiplets. The values were determined with an absolute uncertainty of 10%. Transition probabilities have been determined by the branching ratios from the measurement of relative line intensities emitted by laser-induced plasma (LIP). The line intensities were obtained with the target (leadcalcium) placed in argon atmosphere at 6 Torr, recorded at a 2.5 µs delay from the laser pulse, which provides appropriate measurement conditions, and analysed between 350.0 and 550.0 nm. They are measured when the plasma reaches local thermodynamic equilibrium (LTE). The plasma is characterized by electron temperature (T) of 11400 K and an electron number density (Ne) of 1.1 x 1016 cm-3. The influence self-absorption has been estimated for every line, and plasma homogeneity has been checked. The values obtained were compared with previous experimental values in the literature. The method for measurement of transition probabilities using laser-induced plasma as spectroscopic source has been checked.

Corticosterone levels predict survival probabilities of Galápagos marine iguanas during El Niño events

Plasma levels of corticosterone are often used as a measure of “stress” in wild animal populations. However, we lack conclusive evidence that different stress levels reflect different survival probabilities between populations. Galápagos marine iguanas offer an ideal test case because island populations are affected differently by recurring El Niño famine events, and population-level survival can be quantified by counting iguanas locally. We surveyed corticosterone levels in six populations during the 1998 El Niño famine and the 1999 La Niña feast period. Iguanas had higher baseline and handling stress-induced corticosterone concentrations during famine than feast conditions. Corticosterone levels differed between islands and predicted survival through an El Niño period. However, among individuals, baseline corticosterone was only elevated when body condition dropped below a critical threshold. Thus, the population-level corticosterone response was variable but nevertheless predicted overall population health. Our results lend support to the use of corticosterone as a rapid quantitative predictor of survival in wild animal populations.

DNA profile match probabilities in a subdivided population: when can subdivision be ignored?

Li and Chakravarti [Li, C.C. & Chakravarti, A. (1994) Hum. Hered. 44, 100-109] compared the probability (MO) of a random match between the two DNA profiles of a pair of individuals drawn from a random-mating population to the probability (MF) of the match between a pair of random individuals drawn from a subdivided population. The level of heterogeneity in this subdivided population is measured by the parameter F, where there is no subdivision when F = 0 and increasing values of F indicate increasing subdivisions. Li and Chakravarti concluded that it is conservative to use the match probability MO, which is derived under the assumption that the two individuals are drawn from a homogeneous random-mating population without subdivision. However, MO may not be always greater than MF, even for biologically reasonable values of F. We explore here those mathematical conditions under which MO is less than MF, and we find that MO is not conservative mainly when there is an allele with a much higher frequency than all the other alleles. When empirical data for both variable number of tandem repeat (VNTR) and short tandem repeat (STR) systems are evaluated, we find that in the majority of cases MO represents a conservative probability of a match, and so the subdivision of human populations may usually be ignored for a random match, although not, of course, for relatives. Loci for which MO is not conservative should be avoided for forensic inference.

Drinking driver and traffic safety project, final report: vol. II, probabilities for drinking drivers.

National Highway Traffic Safety Administration, Washington, D.C.

Shock-tube measurements of transition probabilities for oxygen and nitric oxide,

Mode of access: Internet.

Atomic transition probabilities; a critical data compilation

Mode of access: Internet.

An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities.

Mode of access: Internet.