Bounds for the probability generating functional of a Gibbs point process

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics such as the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity, and higher-order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Diffusion-weighted magnetic resonance imaging detects significant prostate cancer with high probability

PURPOSE We prospectively assessed the diagnostic accuracy of diffusion-weighted magnetic resonance imaging for detecting significant prostate cancer. MATERIALS AND METHODS We performed a prospective study of 111 consecutive men with prostate and/or bladder cancer who underwent 3 Tesla diffusion-weighted magnetic resonance imaging of the pelvis without an endorectal coil before radical prostatectomy (78) or cystoprostatectomy (33). Three independent readers blinded to clinical and pathological data assigned a prostate cancer suspicion grade based on qualitative imaging analysis. Final pathology results of prostates with and without cancer served as the reference standard. Primary outcomes were the sensitivity and specificity of diffusion-weighted magnetic resonance imaging for detecting significant prostate cancer with significance defined as a largest diameter of the index lesion of 1 cm or greater, extraprostatic extension, or Gleason score 7 or greater on final pathology assessment. Secondary outcomes were interreader agreement assessed by the Fleiss κ coefficient and image reading time. RESULTS Of the 111 patients 93 had prostate cancer, which was significant in 80 and insignificant in 13, and 18 had no prostate cancer on final pathology results. The sensitivity and specificity of diffusion-weighted magnetic resonance imaging for detecting significant PCa was 89% to 91% and 77% to 81%, respectively, for the 3 readers. Interreader agreement was good (Fleiss κ 0.65 to 0.74). Median reading time was between 13 and 18 minutes. CONCLUSIONS Diffusion-weighted magnetic resonance imaging (3 Tesla) is a noninvasive technique that allows for the detection of significant prostate cancer with high probability without contrast medium or an endorectal coil, and with good interreader agreement and a short reading time. This technique should be further evaluated as a tool to stratify patients with prostate cancer for individualized treatment options.

Voting Power and Probability

Voting power is commonly measured using a probability. But what kind of probability is this? Is it a degree of belief or an objective chance or some other sort of probability? The aim of this paper is to answer this question. The answer depends on the use to which a measure of voting power is put. Some objectivist interpretations of probabilities are appropriate when we employ such a measure for descriptive purposes. By contrast, when voting power is used to normatively assess voting rules, the probabilities are best understood as classical probabilities, which count possibilities. This is so because, from a normative stance, voting power is most plausibly taken to concern rights and thus possibilities. The classical interpretation also underwrites the use of the Bernoulli model upon which the Penrose/Banzhaf measure is based.

A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes

This article provides an importance sampling algorithm for computing the probability of ruin with recuperation of a spectrally negative Lévy risk process with light-tailed downwards jumps. Ruin with recuperation corresponds to the following double passage event: for some t∈(0,∞)t∈(0,∞), the risk process starting at level x∈[0,∞)x∈[0,∞) falls below the null level during the period [0,t][0,t] and returns above the null level at the end of the period tt. The proposed Monte Carlo estimator is logarithmic efficient, as t,x→∞t,x→∞, when y=t/xy=t/x is constant and below a certain bound.

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.

RRREG: Stata module to estimate linear probability model for randomized response data

rrreg fits a linear probability model for randomized response data