Probability Of Entrance Research Articles

A variant of importance splitting for rare event estimation

Importance splitting is a simulation technique to estimate very small entrance probabilities for Markov processes by splitting sample paths at various stages before reaching the set of interest. This can be done in many ways, yielding different variants of the method. In this context, we propose a new one, called fixed number of successes. We prove unbiasedness for the new and some known variants, because in many papers, the proof is based on an incorrect argument. Further, we analyze its behavior in a simplified setting in terms of efficiency and asymptotics in comparison to the standard variant. The main difference is that it controls the imprecision of the estimator rather than the computational effort. Our analysis and simulation examples show that it is rather robust in terms of parameter choice and we present a two-stage procedure which also yields confidence intervals.

Estimating population characteristics of two saproxylic beetles: a mark-recapture approach

Using a mark-release-recapture technique we describe adult sex ratios, recapture rates and other sample characteristics of two saproxylic species: the nationally threatened longhorn beetle Leptura (Rutpela) maculata (Coleoptera: Cerambycidae) and the common L. quadrifasciata in southeastern Finland over two summers. Over 350 individuals of L. maculata and 150 individuals of L. quadrifasciata were captured on floral resource or in flight, and marked each summer. For L. maculata, the sex ratio was male-biased (2:1), whereas for L. quadrifasciata the bias was less clear. For both species, the male-bias may reflect behavioral differences between sexes, rather than true population differences. The proportion of recaptured individuals was low and varied between 7 and 33% depending on the species and year, which allowed us to estimate population parameters only for L. maculata in 2006. A model which assumed constant survival, but time-dependent catchability and entrance probability from a larger superpopulation, fit the data best. The precision of the total population size estimates were reasonable for all the models tested (coefficient of variation = 7–14%). Based on the estimated local adult population size (mean ± 95% confidence interval = 865 ± 131), and the current distribution area of L. maculata, we infer that the species is not in immediate risk of extinction in Finland. Our analysis shows that mark-recapture technique can provide precise estimates of adult population size of saproxylic beetles which have different adult and larval habitats, and thus be useful in assessing extinction risk and monitoring population trends.

Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities

In the present paper, the reward paths in non homogeneous semi-Markov systems in discrete time are examined with stochastic selection of the transition probabilities. The mean entrance probabilities and the mean rewards in the course of time are evaluated. Then the rate of the total reward for the homogeneous case is examined and the mean total reward is evaluated by means of p.g.f’s.

동해의 장구형 통발에 대한 빨간횟대 (Alcichthys alcicornis)의 망목선택성

동해안의 연안성 어족인 빨간횟대에 대해 망목크기 등을 달리한 8종류의 장구형 통발을 사용하여, 2003년 6월부터 12월까지 총 6차례에 걸쳐 어선 2척을 용선하여 조업한 어획실험으로부터 망목선택성 곡선을 구하여 합리적인 자원관리에 대한 기초 자료를 구하고자 하였다. 망목 크기가 20mm와 35mm인 두 통발의 빨간횟대 어획물로부터 체장에 따른 어획비율의 차이에 대해 특별한 경향을 발견할 수 없었다. 망목 크기가 20mm와 55mm인 두 통발의 경우에 대해 SELECT방법을 이용하여 equal split model 과 estimated split model을 적용한 결과, AIC 값이 적은 전자가 더 적절한 모델이므로, 빨간횟대의 경우는 이들 두 통발에 대한 입망률의 차이는 없는 것으로 나타났다. 망목 55mm의 통발에서 SELECT 모델로 구한 50% 어획될 빨간횟대의 전장은 22.0cm였다. 망목 크기가 20mm, 35mm, 55mm인 통발의 어획 자료에 Kitahara의 방법으로 logistic식을 적용하여 추정된 선택성 곡선식은 <TEX>$s(R)\;=\;\frac{1}{1+exp(-0.3545R+2.141)$</TEX>와 같았고, 현재 규정 망목 크기인 35mm 장구형 통발에 대해 50% 어획될 빨간횟대의 전장은 21.4cm이었다. The mesh selectivity of the drum net fish trap for elkhorn sculpin(Alcichthys alcicornis) in the estern sea of Korea was described. The selection curve for the elkhorn sculpin caught from the experiments between June 2003 and December 2003 was by SELECT(Share Each Length Class's Catch Total)model and by Kitahaa's method to a polynomial equation and two parameter logistic selection curve. The selection curve by SELECT model showed to be equal probability of entrance of the elkhorn sculpin in the large(55mm) and small(20mm) mesh traps by minimum AIC (Akaike Information Criteria). The equation of selectivity curve obtained by Kitahara's method using a logistic function with least square method was <TEX>$s(R)\;=\;\frac{1}{1+exp(-0.3545R+2.141)$</TEX>, where R=1/m, and/and m are total length and mesh size, respectively. The mesh selectivity curve showed that the current regulated mesh size(35mm) for the trap was corresponded to 21.4cm in the <TEX>$L_{50}$</TEX>of the selection curve for the elkhorn sculpin.

A first passage time distribution for a discrete version of the Ornstein–Uhlenbeck process

The probability of the first entrance to the negative semi-axis for a one-dimensional discrete Ornstein–Uhlenbeck (O-U) process is studied in this work. The discrete O-U process is a simple generalization of the random walk and many of its statistics may be calculated using essentially the same formalism. In particular, the case in which Sparre-Andersen's theorem applies for normal random walks is considered, and it is shown that the universal features of the first passage probability do not extend to the discrete O-U process. Finally, an explicit expression for the generating function of the probability of first entrance to the negative real axis at step n is calculated and analysed for a particular choice of the step distribution.

Gender versus Ethnic Wage Differentials among Professionals: Evidence from Israel

The purpose of this paper is to investigate wage structures of professional workers in the Israeli labor market using data from the 1983 Israeli census and correcting for selectivity at the state of entrance into the occupation. The sample of professionals is decomposed into several sub- samples: Jewish men and Jewish women; within the Jewish sample a dis- tinction is made between Westerners and Easterners. The core of this study is the investigation of wage differentials between the various groups, taking into account differences in entrance probabilities. The standard OAXACA decomposition does not take into account different probabilities of entering the professional occupations (i.e., occupational segregation). In order to incorporate this type of segregation into the wage differential decomposi- tions, two statistical methodologies are merged: the OAXACA methodology and the HECKMAN selectivity bias correction procedure. The decomposition procedure is then modified in order to take into account the contribution of segregation to the characteristics and the discrimination components. We propose four alternative decompositions of the selectivity corrected wage equations and present the results based on these decompositions.

Counting transitions—entrance probabilities in non-homogeneous semi-Markov systems

In the present paper, the concept of the number of transitions in a non-homogeneous semi-Markov system is introduced. Then the problem of finding the equations that describe the expected population structure, in relation with the number of transitions, is studied. Also, the entrance probabilities of the system are defined and their limit is provided, under certain conditions. © 1998 John Wiley & sons, Ltd.

Counting transitions—entrance probabilities in non‐homogeneous semi-Markov systems

Counting transitions—entrance probabilities in non‐homogeneous semi-Markov systems

Gender, age and the marriage market: Evidence on marriage in late adulthood in Russia

In this paper I explore one specific type of informal support, marital unions, and the ways in which patterns suggest differential access to this support mechanism based on age and sex. Through an examination of marriage patterns in the Russian Federation I show that women may be disadvantaged by low levels of access to marital unions past the age of 50 due to high differential mortality and age differentials at marriage. For both sexes, the probability of marital entrance is negatively related to age, but the negative influence of age follows different paths for men and women. In spite of high sex differentials in mortality, findings indicate that men, over 50 and outside of marital unions, are far more likely to marry than their female counterparts regardless of residence or age.

Trends along the debt-income axis: implications for medical students' selections of family practice careers.

To examine whether medical students' levels of debt have an influence on selection of family practice careers, independent of other factors. Data from the Jefferson Longitudinal Study were analyzed for 1,350 graduates from the classes of 1987-1993 at Jefferson Medical College of Thomas Jefferson University; a focused analysis for 326 graduates from the classes of 1992 and 1993 was specifically performed to identify recent trends. A binary logistic regression equation was used to predict the probability of a graduate's entrance into a family practice residency based on first-year preference for family practice, income expectation, debt level, age, and gender. A high level of indebtedness (at least $75,000) was a significant independent predictor of specialty choice (away from family practice); first-year preference for family practice and income expectation were also significant independent predictors. Combining these three factors (debt, specialty preference, and income expectation) led to a greater than 12-fold difference in specialty selection of family practice. Notably, 36% of the students graduating in 1992-1993 had debts of at least $75,000, more than three times the percentage in the classes graduating in 1987-1989. High levels of debt had a significant negative effect on family practice specialty, choice among recent Jefferson graduates. An increase in the number of students with such debt carries strong implications for the selection of careers in family practice.

Study on the active centers of methane coupling catalysts by means of fluorescence emission of Eu 3+

Eu 3+ ion was adopted as a probe to detect the probability of entrance of alkali elements into the crystal lattice of MgO, CaO and La 2O 3 by means of its characteristic emission. Based on the experimental data it is concluded that Li + and Na + ions can substitute Mg 2+ and Ca 2+ ions and only a small amount of K + ion can enter into the lattice of CaO. Whilst Li + ion can not enter into the lattice of lanthana. The conclusion of this investigation is in good agreement with that obtained by Lunsford by ESR studies.

Hot-electron transport properties of rare-gas solids derived from low-energy electron transmission experiments

The results of the analysis of available experimental low-energy electron transmission (LEET) data on thin solid rare-gas films deposited on a metal substrate are presented. The analysis is carried out on the basis of a most recent semiclassical electron transport model. Transport parameters inferred from the experiments are: (i) the entrance probability of the incident electrons at the vacuum-film interface; (ii) the total (elastic and inelastic) electron scattering mean free path (MFP); and (iii) the probability of inelastic scattering in the bulk of the studied materials (namely solid argon, krypton, and xenon). Comparisons made with recent energy band-structure calculations reveal that both the entrance probability and the inverse of the total MFP (or the total scattering frequency per unit pathlength) are highly correlated with the conduction-band density of states of these materials. A comparison of two sets of experimental data obtained for solid argon under different conditions of preparation of the metallic surface illustrates the reliability of our analysis to infer electron transport parameters from LEET experiments.

Analysis of low-energy (1–10 ev) electron transmission spectra of thin solid krypton films

We present and analyse the results of low-energy electron transmission experiments performed with solid krypton films deposited on a platinum substrate at 20 K. The film thicknesses range from about 0.3 to 10 nm. The analysis of the variation of the transmitted electron current with film thickness is done with the help of a probabilistic model of particle transport in the energy region (1–10 eV) where the electron scatterings are quasi-elastic. This analysis allows the determination of the entrance probability of electrons and their mean free path in the films. The entrance probability is found to reflect the electronic conduction-band structure of solid krypton. The electron mean free path values that we obtain are large for low electron energies (about 20 nm at 1 eV) and decrease rapidly to about 2 nm for energies larger than 3.5 eV.

Probabilistic description of particle transport. II. Analysis of low-energy electron transmission through thin solid Xe and N2 films.

The probabilistic description of quasielastic particle transport given in a previous paper is used to analyze the results of low-energy electron transmission experiments on thin solid xenon and molecular nitrogen films deposited on a metal substrate. Values of the entrance probabilities of the incident electrons at the vacuum-film interface and of the electron scattering mean free paths in the films are extracted in the electron energy range 1.6--7.9 eV for xenon, and 2.4--7.4 eV for molecular nitrogen. The effects of anisotropy in the surface scattering and in the reflections at the two interfaces of the films are also discussed.

The entrance probability and range of helium in W(100) for energies 8eV to 5000 eV as measured by thermal desorption spectrometry

Abstract Measurements have been made using thermal desorption spectrometry of the entrance probability η of He+ ions incident on a W(100) surface at energies 8 eV to 5000 eV. For energies above 250 eV, η for normal incidence, ηn, is within 20 of unity, while for “random” incidence ηn = 0.6 ± 0.1. Below 250 eV, both decrease and become equal for E ≤ 25 eV. At 25 eV, η = 0.2 and at 8 eV, η ≈ 0.01. The measured values of η were used to obtain values for the average penetration d of the helium ions from previously measured values of the product ηd for the same two directions of incidence. Above ∼ 150 eV. the range for random incidence. was found to be 0.12 E0.9 A (E in eV) while for normal incidence, the range is larger by a factor of about 3. Below 150 eV. both decrease rapidly and become equal (≈ 1 A) at 25 eV. The fraction of the normally incident ions channeled fc was derived from the measured η r and η n . It was found to be > 0.8 for E ≥ 1000 eV, and <0.5 for E < 200 eV.