Sampling with probabilities proportional to the variable of interest

To estimate the mean sojourn time, a sample of Tilburg fair visitors was asked for the duration of their stay on the fair grounds. The longer a visitor's sojourn, the larger his/her probability of being interviewed will be; therefore, longer sojourn times will be overrepresented in the sample. As a consequence, the arithmetic sample mean is not a suitable estimator. The paper places this problem against a theoretical background. As a better estimator the harmonic mean of the observed sojourn times is presented. In addition, a variance estimator is given. The properties of these estimators are difficult to derive analytically. Instead, their behaviour is studied in a number of examples.Probability;Estimation;Sampling;statistics

Does size matter?

For isolated objects in complete darkness, retinal image size contributes to distance judgments even if the true object size is unknown. Here we show that the same is true under more natural conditions. On a wide beach we positioned a red cube at 10–20 m distance and then asked subjects to walk to it while blindfolded. Subjects never had a close view of the cube and were unaware that on separate trials cubes with sides of 15 cm and 20 cm were positioned at the same locations. On average, subjects walked 1 m further after seeing the 15 cm cube than after seeing the 20 cm cube

Hotspot Zuidplaspolder: Climate adaptation in the Zuidplaspolder

Building at the lowest point in the Netherlands, in the Zuidplaspolder, is viewed as a challenge and not something that is impossible. The Xplorelab approach in the Hotspot Zuidplaspolder project is a combination of research, implementation of ideas into inspiring examples and evaluation

Estimate of halo ellipticity as a function of radius with flexions

The cold dark matter theory predicts triaxial dark matter haloes. The radial distribution of halo ellipticity depends on baryonic processes and the nature of dark matter particles (collisionless or collisional). Here we show that we can use lensing flexion ratios to measure the halo ellipticity as a function of radius. We introduce a weight function and study the relationship between the first and second order statistics of flexion ratios, both of which can be used to reduce the bias in the estimate of ellipticity. we perform numerical tests for our method, and demonstrate that it can reduce the bias and determine the halo ellipticity as a function of radius. We also point out that the minimum mean flexion ratio can be used to trace the centres of galaxy clusters.Comment: 9 pages,9 figures, MNRAS accepte

Are people adapted to their own glasses?

Negative lenses, either in the form of glasses or contact lenses, can correct nearsightedness. Unlike contact lenses, glasses do not only correct, but also induce optic distortions. In the scientific literature, it has often been assumed that people who wear corrective glasses instantaneously account for these distortions when they put their glasses on. We tested this assumption and found that, when people switched between their contact lenses and their glasses, they made the errors that one would predict based on the optics.This shows that people are not immediately adapted to their own glasses when they put them on

Judging an unfamiliar object’s distance from its retinal image size

How do we know how far an object is? If an object's size is known, its retinal image size can be used to judge its distance. To some extent, the retinal image size of an unfamiliar object can also be used to judge its distance, because some object sizes are more likely than others. To examine whether assumptions about object size are used to judge distance, we had subjects indicate the distance of virtual cubes in complete darkness. In separate sessions, the simulated cube size either varied slightly or considerably across presentations. Most subjects indicated a further distance when the simulated cube was smaller, showing that they used retinal image size to judge distance. The cube size that was considered to be most likely depended on the simulated cubes on previous trials. Moreover, subjects relied twice as strongly on retinal image size when the range of simulated cube sizes was small. We conclude that the variability in the perceived cube sizes on previous trials influences the range of sizes that are considered to be likely. © ARVO

The effect of variability in other objects’ sizes on the extent to which people rely on retinal image size as a cue for judging distance

Retinal image size can be used to judge objects’ distances because for any object one can assume that some sizes are more likely than others. It has been shown that an increased variability in the size of otherwise identical target objects over trials reduces the weight given to retinal image size as a distance cue. Here, we examined whether an increased variability in the size of objects of a different color, orientation, or shape reduces the weight given to retinal image size when judging distance. Subjects had to indicate the 3D position of a simulated target object. Retinal image size was given significantly less weight as a cue for judging the target cube’s distance when differently colored and differently oriented target objects appeared in many simulated sizes but not when differently shaped objects had many simulated sizes. We also examined whether increasing the variability in the size of cubes in the surroundings reduces the weight given to retinal image size when judging distance. It does not. We conclude that variability in surrounding or dissimilar objects’ sizes has a negligible influence on the extent to which people rely on retinal image size as a cue for judging distance

The influence of previously seen objects' sizes in distance judgments

An object's retinal image size is determined by a combination of its physical size and its distance, so judgments of an object's size and distance from its retinal image size are coupled. Since one does not have direct access to information about the object's physical size, people may make assumptions about how large it is likely to be. Here we investigated whether the sizes of similar, previously encountered objects influence the assumptions about the physical size of an object and therefore the interpretation of its retinal image size in terms of its distance. Subjects moved their unseen index finger to the positions of binocular simulations of red cubes. For identical target cubes at the same position, they indicated a nearer position of the cube when the preceding cube was small than when it was big. This is in agreement with a tendency to expect the cube to be the same size as that on the previous trial. However, if the expectation were simply adjusted slightly on each trial, the cube would be judged to be nearer when preceded by two consecutive smaller cubes than when preceded by only one smaller cube. It was not, so there must be a more direct influence of the size in the previous trial on distance judgments