Comment on ``Conditional Exceedance Probabilities''

In a recent paper, Mason et al. propose a reliability test of ensemble forecasts for a continuous, scalar verification. As noted in the paper, the test relies on a very specific interpretation of ensembles, namely, that the ensemble members represent quantiles of some underlying distribution. This quantile interpretation is not the only interpretation of ensembles, another popular one being the Monte Carlo interpretation. Mason et al. suggest estimating the quantiles in this situation; however, this approach is fundamentally flawed. Errors in the quantile estimates are not independent of the exceedance events, and consequently the conditional exceedance probabilities (CEP) curves are not constant, which is a fundamental assumption of the test. The test would reject reliable forecasts with probability much higher than the test size.

Methods for Estimating Annual Exceedance-Probability Discharges for Streams in Iowa, Based on Data through Water Year 2010, TR-519, 2013

A statewide study was performed to develop regional regression equations for estimating selected annual exceedance- probability statistics for ungaged stream sites in Iowa. The study area comprises streamgages located within Iowa and 50 miles beyond the State’s borders. Annual exceedanceprobability estimates were computed for 518 streamgages by using the expected moments algorithm to fit a Pearson Type III distribution to the logarithms of annual peak discharges for each streamgage using annual peak-discharge data through 2010. The estimation of the selected statistics included a Bayesian weighted least-squares/generalized least-squares regression analysis to update regional skew coefficients for the 518 streamgages. Low-outlier and historic information were incorporated into the annual exceedance-probability analyses, and a generalized Grubbs-Beck test was used to detect multiple potentially influential low flows. Also, geographic information system software was used to measure 59 selected basin characteristics for each streamgage. Regional regression analysis, using generalized leastsquares regression, was used to develop a set of equations for each flood region in Iowa for estimating discharges for ungaged stream sites with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities, which are equivalent to annual flood-frequency recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively. A total of 394 streamgages were included in the development of regional regression equations for three flood regions (regions 1, 2, and 3) that were defined for Iowa based on landform regions and soil regions. Average standard errors of prediction range from 31.8 to 45.2 percent for flood region 1, 19.4 to 46.8 percent for flood region 2, and 26.5 to 43.1 percent for flood region 3. The pseudo coefficients of determination for the generalized leastsquares equations range from 90.8 to 96.2 percent for flood region 1, 91.5 to 97.9 percent for flood region 2, and 92.4 to 96.0 percent for flood region 3. The regression equations are applicable only to stream sites in Iowa with flows not significantly affected by regulation, diversion, channelization, backwater, or urbanization and with basin characteristics within the range of those used to develop the equations. These regression equations will be implemented within the U.S. Geological Survey StreamStats Web-based geographic information system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the eight selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided by the Web-based tool. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these eight selected statistics are provided for the streamgage.

SEMIPARAMETRIC METHODS IN THE ESTIMATION OF TAIL PROBABILITIES AND EXTREME QUANTILES

In quantitative risk analysis, the problem of estimating small threshold exceedance probabilities and extreme quantiles arise ubiquitously in bio-surveillance, economics, natural disaster insurance actuary, quality control schemes, etc. A useful way to make an assessment of extreme events is to estimate the probabilities of exceeding large threshold values and extreme quantiles judged by interested authorities. Such information regarding extremes serves as essential guidance to interested authorities in decision making processes. However, in such a context, data are usually skewed in nature, and the rarity of exceedance of large threshold implies large fluctuations in the distribution's upper tail, precisely where the accuracy is desired mostly. Extreme Value Theory (EVT) is a branch of statistics that characterizes the behavior of upper or lower tails of probability distributions. However, existing methods in EVT for the estimation of small threshold exceedance probabilities and extreme quantiles often lead to poor predictive performance in cases where the underlying sample is not large enough or does not contain values in the distribution's tail. In this dissertation, we shall be concerned with an out of sample semiparametric (SP) method for the estimation of small threshold probabilities and extreme quantiles. The proposed SP method for interval estimation calls for the fusion or integration of a given data sample with external computer generated independent samples. Since more data are used, real as well as artificial, under certain conditions the method produces relatively short yet reliable confidence intervals for small exceedance probabilities and extreme quantiles.

Quantifying uncertainty in critical loads: (B) acidity mass balance critical loads on a sensitive site

This paper reports an uncertainty analysis of critical loads for acid deposition for a site in southern England, using the Steady State Mass Balance Model. The uncertainty bounds, distribution type and correlation structure for each of the 18 input parameters was considered explicitly, and overall uncertainty estimated by Monte Carlo methods. Estimates of deposition uncertainty were made from measured data and an atmospheric dispersion model, and hence the uncertainty in exceedance could also be calculated. The uncertainties of the calculated critical loads were generally much lower than those of the input parameters due to a "compensation of errors" mechanism - coefficients of variation ranged from 13% for CLmaxN to 37% for CL(A). With 1990 deposition, the probability that the critical load was exceeded was > 0.99; to reduce this probability to 0.50, a 63% reduction in deposition is required; to 0.05, an 82% reduction. With 1997 deposition, which was lower than that in 1990, exceedance probabilities declined and uncertainties in exceedance narrowed as deposition uncertainty had less effect. The parameters contributing most to the uncertainty in critical loads were weathering rates, base cation uptake rates, and choice of critical chemical value, indicating possible research priorities. However, the different critical load parameters were to some extent sensitive to different input parameters. The application of such probabilistic results to environmental regulation is discussed.

Earthquake forecasting and seismic hazard analysis: some insights on the testing phase and the modeling

This thesis is divided in three chapters. In the first chapter we analyse the results of the world forecasting experiment run by the Collaboratory for the Study of Earthquake Predictability (CSEP). We take the opportunity of this experiment to contribute to the definition of a more robust and reliable statistical procedure to evaluate earthquake forecasting models. We first present the models and the target earthquakes to be forecast. Then we explain the consistency and comparison tests that are used in CSEP experiments to evaluate the performance of the models. Introducing a methodology to create ensemble forecasting models, we show that models, when properly combined, are almost always better performing that any single model. In the second chapter we discuss in depth one of the basic features of PSHA: the declustering of the seismicity rates. We first introduce the Cornell-McGuire method for PSHA and we present the different motivations that stand behind the need of declustering seismic catalogs. Using a theorem of the modern probability (Le Cam's theorem) we show that the declustering is not necessary to obtain a Poissonian behaviour of the exceedances that is usually considered fundamental to transform exceedance rates in exceedance probabilities in the PSHA framework. We present a method to correct PSHA for declustering, building a more realistic PSHA. In the last chapter we explore the methods that are commonly used to take into account the epistemic uncertainty in PSHA. The most widely used method is the logic tree that stands at the basis of the most advanced seismic hazard maps. We illustrate the probabilistic structure of the logic tree, and then we show that this structure is not adequate to describe the epistemic uncertainty. We then propose a new probabilistic framework based on the ensemble modelling that properly accounts for epistemic uncertainties in PSHA.

Daily temperature trends in Trentino Alto Adige over the last century

Numerosi lavori apparsi sulla letteratura scientifica negli ultimi decenni hanno evidenziato come, dall’inizio del XX secolo, la temperatura media globale sia aumentata. Tale fenomeno si è fatto più evidente dagli anni ’80, infatti ognuno degli ultimi tre decenni risulta più caldo dei precedenti. L’Europa e l’area mediterranea sono fra le regioni in cui il riscaldamento risulta più marcato, soprattutto per le temperature massime (dal 1951 sono cresciute di +0.39 °C per decennio) che hanno mostrato trend maggiori delle minime. Questo comportamento è stato osservato anche a scala nazionale (+0.25°C/dec per le massime e +0.20°C/dec per le minime). Accanto all’aumento dei valori medi è stato osservato un aumento (diminuzione) degli eventi di caldo (freddo) estremo, studiati attraverso la definizione di alcuni indici basati sui percentili delle distribuzioni. Resta aperto il dibattito su quali siano le cause delle variazioni negli eventi estremi: se le variazioni siano da attribuire unicamente ad un cambiamento nei valori medi, quindi ad uno shift rigido della distribuzione, o se parte del segnale sia dovuto ad una variazione nella forma della stessa, con un conseguente cambiamento nella variabilità. In questo contesto si inserisce la presente tesi con l’obiettivo di studiare l’andamento delle temperature giornaliere sul Trentino-Alto-Adige a partire dal 1926, ricercando cambiamenti nella media e negli eventi estremi in due fasce altimetriche. I valori medi delle temperature massime e minime hanno mostrato un evidente riscaldamento sull’intero periodo specialmente per le massime a bassa quota (`0.13 ̆ 0.03 °C/dec), con valori più alti per la primavera (`0.22 ̆ 0.05 °C/dec) e l’estate (`0.17 ̆ 0.05 °C/dec). Questi trends sono maggiori dopo il 1980 e non significativi in precedenza. L’andamento del numero di giorni con temperature al di sopra e al di sotto delle soglie dei percentili più estremi (stimate sull’intero periodo) indica un chiaro aumento degli estremi caldi, con valori più alti per le massime ad alta quota ( fino a +26.8% per il 99-esimo percentile) e una diminuzione degli estremi freddi (fino a -8.5% per il primo percentile delle minime a bassa quota). Inoltre, stimando anno per anno le soglie di un set di percentili e confrontando i loro trend con quelli della mediana, si è osservato, unicamente per le massime, un trend non uniforme verso temperature più alte, con i percentili più bassi (alti) caratterizzati da trend inferiori (superiori) rispetto a quello della mediana, suggerendo un allargamento della PDF.

Kinematic parameters and membership probabilities of open clusters in the Bordeaux PM2000 catalogue

Aims. We derive lists of proper-motions and kinematic membership probabilities for 49 open clusters and possible open clusters in the zone of the Bordeaux PM2000 proper motion catalogue (+ 11 degrees <= delta <= + 18 degrees). We test different parametrisations of the proper motion and position distribution functions and select the most successful one. In the light of those results, we analyse some objects individually. Methods. We differenciate between cluster and field member stars, and assign membership probabilities, by applying a new and fully automated method based on both parametrisations of the proper motion and position distribution functions, and genetic algorithm optimization heuristics associated with a derivative-based hill climbing algorithm for the likelihood optimization. Results. We present a catalogue comprising kinematic parameters and associated membership probability lists for 49 open clusters and possible open clusters in the Bordeaux PM2000 catalogue region. We note that this is the first determination of proper motions for five open clusters. We confirm the non-existence of two kinematic populations in the region of 15 previously suspected non-existent objects.

Jensen inequalities for tunneling probabilities in complex systems

The Jensen theorem is used to derive inequalities for semiclassical tunneling probabilities for systems involving several degrees of freedom. These Jensen inequalities are used to discuss several aspects of sub-barrier heavy-ion fusion reactions. The inequality hinges on general convexity properties of the tunneling coefficient calculated with the classical action in the classically forbidden region.

Collision probabilities in the rarefaction fan of asymmetric exclusion processes

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p is an element of (1/2, 1.] and to the left at rate 1 - p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and I, and holes to the right of site I. We show that the probability that the two second-class particles eventually collide is (1 + p)/(3p), where a collision occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes. started from appropriate initial states and coupled using the so-called ""basic coupling,"" eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p = 1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.

Efficient time-independent wave packet scattering calculations within a Lanczos subspace: H+O-2 (J=0) state-to-state reaction probabilities

An efficient Lanczos subspace method has been devised for calculating state-to-state reaction probabilities. The method recasts the time-independent wave packet Lippmann-Schwinger equation [Kouri , Chem. Phys. Lett. 203, 166 (1993)] inside a tridiagonal (Lanczos) representation in which action of the causal Green's operator is affected easily with a QR algorithm. The method is designed to yield all state-to-state reaction probabilities from a given reactant-channel wave packet using a single Lanczos subspace; the spectral properties of the tridiagonal Hamiltonian allow calculations to be undertaken at arbitrary energies within the spectral range of the initial wave packet. The method is applied to a H+O-2 system (J=0), and the results indicate the approach is accurate and stable. (C) 2002 American Institute of Physics.

Cross sectional default probabilities in european corporate bonds

This study attempts to identify basis-trading opportunities in the European banking sector by comparing two different measures for the market’s assessment of risk: market-observed CDS spreads and model-implied Z-spreads. Using a sample of 10 banks, over a period of 3 years following the European banking crisis, it can be concluded that there were arbitrage opportunities in the sector, as evidenced by the derived negative bases.

Application of detection probabilities to the design of amphibian monitoring programs in temporary ponds

Failure to detect a species in an area where it is present is a major source of error in biological surveys. We assessed whether it is possible to optimize single-visit biological monitoring surveys of highly dynamic freshwater ecosystems by framing them a priori within a particular period of time. Alternatively, we also searched for the optimal number of visits and when they should be conducted. We developed single-species occupancy models to estimate the monthly probability of detection of pond-breeding amphibians during a four-year monitoring program. Our results revealed that detection probability was species-specific and changed among sampling visits within a breeding season and also among breeding seasons. Thereby, the optimization of biological surveys with minimal survey effort (a single visit) is not feasible as it proves impossible to select a priori an adequate sampling period that remains robust across years. Alternatively, a two-survey combination at the beginning of the sampling season yielded optimal results and constituted an acceptable compromise between sampling efficacy and survey effort. Our study provides evidence of the variability and uncertainty that likely affects the efficacy of monitoring surveys, highlighting the need of repeated sampling in both ecological studies and conservation management.

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table