A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

Perceptual grouping and distance estimates in typical and atypical development: comparing performance across perception, drawing and construction tasks

Perceptual grouping is a pre-attentive process which serves to group local elements into global wholes, based on shared properties. One effect of perceptual grouping is to distort the ability to estimate the distance between two elements. In this study, biases in distance estimates, caused by four types of perceptual grouping, were measured across three tasks, a perception, a drawing and a construction task in both typical development (TD: Experiment 1) and in individuals with Williams syndrome (WS: Experiment 2). In Experiment 1, perceptual grouping distorted distance estimates across all three tasks. Interestingly, the effect of grouping by luminance was in the opposite direction to the effects of the remaining grouping types. We relate this to differences in the ability to inhibit perceptual grouping effects on distance estimates. Additive distorting influences were also observed in the drawing and the construction task, which are explained in terms of the points of reference employed in each task. Experiment 2 demonstrated that the above distortion effects are also observed in WS. Given the known deficit in the ability to use perceptual grouping in WS, this suggests a dissociation between the pre-attentive influence of and the attentive deployment of perceptual grouping in WS. The typical distortion in relation to drawing and construction points towards the presence of some typical location coding strategies in WS. The performance of the WS group differed from the TD participants on two counts. First, the pattern of overall distance estimates (averaged across interior and exterior distances) across the four perceptual grouping types, differed between groups. Second, the distorting influence of perceptual grouping was strongest for grouping by shape similarity in WS, which contrasts to a strength in grouping by proximity observed in the TD participants. (c) 2008 Elsevier Inc. All rights reserved.

A longitudinal study of perceptual grouping by proximity, luminance and shape in infants at two, four and six months

Grouping by luminance and shape similarity has previously been demonstrated in neonates and at 4 months, respectively. By contrast, grouping by proximity has hitherto not been investigated in infancy. This is also the first study to chart the developmental emergence of perceptual grouping longitudinally. Sixty-one infants were presented with a matrix of local stimuli grouped horizontally or vertically by luminance, shape or proximity at 2, 4, and 6 months. Infants were exposed to each set of stimuli for three presentation durations. Grouping was demonstrated for luminance similarity at the earliest testing age, 2 months, by shape similarity at 4 months, but was not observed for grouping by proximity. Grouping by shape similarity showed a distinctive pattern of grouping ability across exposure durations, which reflected familiarity preferences followed by novelty preferences. This remained stable across age. No link was found between the emergence of perceptual grouping ability and the exposure duration required to elicit grouping. We conclude by stressing the importance of longitudinal studies of infant development in furthering our understanding of human cognition, rather than relying on assumptions from the adult endstate.

The development of perceptual grouping in infants with Williams syndrome

Perceptual grouping by luminance similarity and by proximity was investigated in infants with Williams syndrome (WS) aged between 6 and 36 months (visit 1, N=29). WS infants who were still under 36 months old, 8 months later, repeated the testing procedure (visit 2, N=15). Performance was compared to typically developing (TD) infants aged from 2 to 20 months (N=63). Consistent with the literature, TD participants showed grouping by luminance at the youngest testing age, 2 months. Grouping by proximity had not previous been charted in typical development: this study showed grouping by proximity at 8 months. Infants with WS could group by luminance. Developmental progression of the WS group showed some similarities to typical development, although further investigation is required to further address this in more depth. In contrast, infants with WS were not able to group by proximity. This pattern of emergence and development of grouping abilities is considered in relation to the pattern of grouping abilities observed in adults with WS.

Perceptual grouping ability in Williams syndrome: evidence for deviant patterns of performance

Williams syndrome (WS) is a rare genetic disorder. At a cognitive level, this population display poor visuo-spatial cognition when compared to verbal ability. Within the visuo-spatial domain, it is now accepted that individuals with WS are able to perceive both local and global aspects of an image, albeit at a low level. The present study examines the manner in which local elements are grouped into a global whole in WS. Fifteen individuals with WS and 15 typically developing controls, matched for non-verbal ability, were presented with a matrix of local elements and asked whether these elements were perceptually grouped horizontally or vertically. The WS group was at the same level as the control group when grouping by luminance, closure, and alignment. However, their ability to group by shape, orientation and proximity was significantly poorer than controls. This unusual profile of grouping abilities in WS suggests that these individuals do not form a global percept in a typical manner. (c) 2004 Published by Elsevier Ltd.

Determining feature relevance for the grouping of motor unit action potentials through generative topographic mapping

The study of motor unit action potential (MUAP) activity from electrornyographic signals is an important stage on neurological investigations that aim to understand the state of the neuromuscular system. In this context, the identification and clustering of MUAPs that exhibit common characteristics, and the assessment of which data features are most relevant for the definition of such cluster structure are central issues. In this paper, we propose the application of an unsupervised Feature Relevance Determination (FRD) method to the analysis of experimental MUAPs obtained from healthy human subjects. In contrast to approaches that require the knowledge of a priori information from the data, this FRD method is embedded on a constrained mixture model, known as Generative Topographic Mapping, which simultaneously performs clustering and visualization of MUAPs. The experimental results of the analysis of a data set consisting of MUAPs measured from the surface of the First Dorsal Interosseous, a hand muscle, indicate that the MUAP features corresponding to the hyperpolarization period in the physisiological process of generation of muscle fibre action potentials are consistently estimated as the most relevant and, therefore, as those that should be paid preferential attention for the interpretation of the MUAP groupings.

Perceptual constancy, reverberation, and grouping: within-band effects

Perceptual constancy effects are observed when differing amounts of reverberation are applied to a context sentence and a test‐word embedded in it. Adding reverberation to members of a “sir”‐“stir” test‐word continuum causes temporal‐envelope distortion, which has the effect of eliciting more sir responses from listeners. If the same amount of reverberation is also applied to the context sentence, the number of sir responses decreases again, indicating an “extrinsic” compensation for the effects of reverberation. Such a mechanism would effect perceptual constancy of phonetic perception when temporal envelopes vary in reverberation. This experiment asks whether such effects precede or follow grouping. Eight auditory‐filter shaped noise‐bands were modulated with the temporal envelopes that arise when speech is played through these filters. The resulting “gestalt” percept is the appropriate speech rather than the sound of noise‐bands, presumably due to across‐channel “grouping.” These sounds were played to listeners in “matched” conditions, where reverberation was present in the same bands in both context and test‐word, and in “mismatched” conditions, where the bands in which reverberation was added differed between context and test‐word. Constancy effects were obtained in matched conditions, but not in mismatched conditions, indicating that this type of constancy in hearing precedes across‐channel grouping.

Grouping of 24 apple cultivars on the basis of starch degradation rate and their fruit pattern

The ripening processes of 24 apple cultivars were examined in the United Kingdom National Fruit Collection in 2010. Basically the starch content, and additionally ground colour, water-soluble solids content and flesh firmness were studied during ripening. The degradation of the starch content was evaluated using a 0–10 scale. A starch degradation value of 50% was taken to be the optimum harvest date, with harvest beginning at a value of 40% and finishing at 60%. Depending on the cultivar, this represented a harvest window of 9 to 21 days. Later ripening cultivars matured more slowly, leading to a longer harvesting period, with the exception of cv. Feuillemorte. Pronounced differences were observed among the cultivars on the basis of the starch degradation pattern, allowing them to be divided into four groups. Separate charts were elaborated for each group that are recommended for use in practice.

Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model

This paper develops a bias correction scheme for a multivariate heteroskedastic errors-in-variables model. The applicability of this model is justified in areas such as astrophysics, epidemiology and analytical chemistry, where the variables are subject to measurement errors and the variances vary with the observations. We conduct Monte Carlo simulations to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates. We also give an application to a real data set.