On An Intriguing Distributional Identity

For a continuous random variable X with support equal to (a, b), with c.d.f. F, and g: Ω₁ → Ω₂ a continuous, strictly increasing function, such that Ω₁∩Ω₂?(a, b), but otherwise arbitrary, we establish that the random variables F(X) ? F(g(X)) and F(g^{? 1}(X)) ? F(X) have the same distribution. Further developments, accompanied by illustrations and observations, address as well the equidistribution identity U ? ψ(U) = ^dψ^{? 1}(U) ? U for U ～ U(0, 1), where ψ is a continuous, strictly increasing and onto function, but otherwise arbitrary. Finally, we expand on applications with connections to variance reduction techniques, the discrepancy between distributions, and a risk identity in predictive density estimation.     

Evaluating the causal economic impacts of transport investments: evidence from the Madrid–Barcelona high speed rail corridor

This paper evaluates economic impacts arising from the introduction of high-speed rail (HSR) between Madrid and Barcelona. Using difference-in-differences estimation we estimate an average treatment effect for provinces with stops on the HSR line of 2.4% for economic output, 3.3% for numbers of firms, and 1.1% for labour productivity. We complement our DID results with a synthetic control analysis for Lleida and Tarragona, two provinces that we argue were assigned HSR stations largely due to their incidental location. We find that both the number of firms and labour productivity are substantially higher in these provinces than in their synthetic counterparts.     

Probabilistic linear solvers: a unifying view

Statistics and Computing - Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian...     

Climate regime shift detection with a trans‐dimensional,sequential Monte Carlo,variational Bayes method

We present an application study which exemplifies a cutting edge statistical approach for detecting climate regime shifts. The algorithm uses Bayesian computational techniques that make time‐efficient analysis of large volumes of climate data possible. Output includes probabilistic estimates of the number and duration of regimes, the number and probability distribution of hidden states, and the probability of a regime shift in any year of the time series. Analysis of the Pacific Decadal Oscillation (PDO) index is provided as an example. Two states are detected: one is associated with positive values of the PDO and presents lower interannual variability, while the other corresponds to negative values of the PDO and greater variability. We compare this approach with existing alternatives from the literature and highlight the potential for ours to unlock features hidden in climate data.     

The Representation of Hypergeometric Random Variables using Independent Bernoulli Random Variables

In this paper, we show that a hypergeometric random variable can be represented as a sum of independent Bernoulli random variables that are, except in degenerate cases, not identically distributed. In the proof, we use the factorial moment generating function. An asymptotic result on the probabilities of the Bernoulli random variables in the sum is also presented. Numerical examples are used to illustrate the results.     

A method for choosing the smoothing parameter in a semi-parametric model for detecting change-points in blood flow

In a smoothing spline model with unknown change-points, the choice of the smoothing parameter strongly influences the estimation of the change-point locations and the function at the change-points. In a tumor biology example, where change-points in blood flow in response to treatment were of interest, choosing the smoothing parameter based on minimizing generalized cross-validation (GCV) gave unsatisfactory estimates of the change-points. We propose a new method, aGCV, that re-weights the residual sum of squares and generalized degrees of freedom terms from GCV. The weight is chosen to maximize the decrease in the generalized degrees of freedom as a function of the weight value, while simultaneously minimizing aGCV as a function of the smoothing parameter and the change-points. Compared with GCV, simulation studies suggest that the aGCV method yields improved estimates of the change-point and the value of the function at the change-point.     

A general class of test statistics for Van Valen's Red Queen hypothesis

Van Valen's Red Queen hypothesis states that within a homogeneous taxonomic group the age is statistically independent of the rate of extinction. The case of the Red Queen hypothesis being addressed here is when the homogeneous taxonomic group is a group of similar species. Since Van Valen's work, various statistical approaches have been used to address the relationship between taxon age and the rate of extinction. We propose a general class of test statistics that can be used to test for the effect of age on the rate of extinction. These test statistics allow for a varying background rate of extinction and attempt to remove the effects of other covariates when assessing the effect of age on extinction. No model is assumed for the covariate effects. Instead we control for covariate effects by pairing or grouping together similar species. Simulations are used to compare the power of the statistics. We apply the test statistics to data on Foram extinctions and find that age has a positive effect on the rate of extinction. A derivation of the null distribution of one of the test statistics is provided in the supplementary material.     

A review of image-warping methods

SUMMARY Image warping is a transformation which maps all positions in one image plane to positions in a second plane. It arises in many image analysis problems, whether in order to remove optical distortions introduced by a camera or a particular viewing perspective, to register an image with a map or template, or to align two or more images. The choice of warp is a compromise between a smooth distortion and one which achieves a good match. Smoothness can be ensured by assuming a parametric form for the warp or by constraining it using differential equations. Matching can be specified by points to be brought into alignment, by local measures of correlation between images, or by the coincidence of edges. Parametric and non-parametric approaches to warping, and matching criteria, are reviewed.