On the mean and variance of response times under the diffusion model with an application to parameter estimation

2009 ◽  
Vol 53 (2) ◽  
pp. 55-68 ◽  
Author(s):  
Raoul P.P.P. Grasman ◽  
Eric-Jan Wagenmakers ◽  
Han L.J. van der Maas
2017 ◽  
Vol 28 (10) ◽  
pp. 1510-1517 ◽  
Author(s):  
Andrey Chetverikov ◽  
Gianluca Campana ◽  
Árni Kristjánsson

Colors are rarely uniform, yet little is known about how people represent color distributions. We introduce a new method for studying color ensembles based on intertrial learning in visual search. Participants looked for an oddly colored diamond among diamonds with colors taken from either uniform or Gaussian color distributions. On test trials, the targets had various distances in feature space from the mean of the preceding distractor color distribution. Targets on test trials therefore served as probes into probabilistic representations of distractor colors. Test-trial response times revealed a striking similarity between the physical distribution of colors and their internal representations. The results demonstrate that the visual system represents color ensembles in a more detailed way than previously thought, coding not only mean and variance but, most surprisingly, the actual shape (uniform or Gaussian) of the distribution of colors in the environment.


Author(s):  
Hung Phuoc Truong ◽  
Thanh Phuong Nguyen ◽  
Yong-Guk Kim

AbstractWe present a novel framework for efficient and robust facial feature representation based upon Local Binary Pattern (LBP), called Weighted Statistical Binary Pattern, wherein the descriptors utilize the straight-line topology along with different directions. The input image is initially divided into mean and variance moments. A new variance moment, which contains distinctive facial features, is prepared by extracting root k-th. Then, when Sign and Magnitude components along four different directions using the mean moment are constructed, a weighting approach according to the new variance is applied to each component. Finally, the weighted histograms of Sign and Magnitude components are concatenated to build a novel histogram of Complementary LBP along with different directions. A comprehensive evaluation using six public face datasets suggests that the present framework outperforms the state-of-the-art methods and achieves 98.51% for ORL, 98.72% for YALE, 98.83% for Caltech, 99.52% for AR, 94.78% for FERET, and 99.07% for KDEF in terms of accuracy, respectively. The influence of color spaces and the issue of degraded images are also analyzed with our descriptors. Such a result with theoretical underpinning confirms that our descriptors are robust against noise, illumination variation, diverse facial expressions, and head poses.


Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 568
Author(s):  
Sabine G. Gebhardt-Henrich ◽  
Ariane Stratmann ◽  
Marian Stamp Dawkins

Group level measures of welfare flocks have been criticized on the grounds that they give only average measures and overlook the welfare of individual animals. However, we here show that the group-level optical flow patterns made by broiler flocks can be used to deliver information not just about the flock averages but also about the proportion of individuals in different movement categories. Mean optical flow provides information about the average movement of the whole flock while the variance, skew and kurtosis quantify the variation between individuals. We correlated flock optical flow patterns with the behavior and welfare of a sample of 16 birds per flock in two runway tests and a water (latency-to-lie) test. In the runway tests, there was a positive correlation between the average time taken to complete the runway and the skew and kurtosis of optical flow on day 28 of flock life (on average slow individuals came from flocks with a high skew and kurtosis). In the water test, there was a positive correlation between the average length of time the birds remained standing and the mean and variance of flock optical flow (on average, the most mobile individuals came from flocks with the highest mean). Patterns at the flock level thus contain valuable information about the activity of different proportions of the individuals within a flock.


Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 955
Author(s):  
Alamir Elsayed ◽  
Mohamed El-Beltagy ◽  
Amnah Al-Juhani ◽  
Shorooq Al-Qahtani

The point kinetic model is a system of differential equations that enables analysis of reactor dynamics without the need to solve coupled space-time system of partial differential equations (PDEs). The random variations, especially during the startup and shutdown, may become severe and hence should be accounted for in the reactor model. There are two well-known stochastic models for the point reactor that can be used to estimate the mean and variance of the neutron and precursor populations. In this paper, we reintroduce a new stochastic model for the point reactor, which we named the Langevin point kinetic model (LPK). The new LPK model combines the advantages, accuracy, and efficiency of the available models. The derivation of the LPK model is outlined in detail, and many test cases are analyzed to investigate the new model compared with the results in the literature.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Roger Ratcliff ◽  
Inhan Kang

AbstractRafiei and Rahnev (2021) presented an analysis of an experiment in which they manipulated speed-accuracy stress and stimulus contrast in an orientation discrimination task. They argued that the standard diffusion model could not account for the patterns of data their experiment produced. However, their experiment encouraged and produced fast guesses in the higher speed-stress conditions. These fast guesses are responses with chance accuracy and response times (RTs) less than 300 ms. We developed a simple mixture model in which fast guesses were represented by a simple normal distribution with fixed mean and standard deviation and other responses by the standard diffusion process. The model fit the whole pattern of accuracy and RTs as a function of speed/accuracy stress and stimulus contrast, including the sometimes bimodal shapes of RT distributions. In the model, speed-accuracy stress affected some model parameters while stimulus contrast affected a different one showing selective influence. Rafiei and Rahnev’s failure to fit the diffusion model was the result of driving subjects to fast guess in their experiment.


1991 ◽  
Vol 28 (3) ◽  
pp. 529-538
Author(s):  
M. P. Quine

Points arrive in succession on an interval and immediately ‘cover' a region of length ½ to each side (less if they are close to the boundary or to a covered part). The location of a new point is uniformly distributed on the uncovered parts. We study the mean and variance of the total number of points ever formed, in particular as a → 0, in which case we also establish asymptotic normality.


2013 ◽  
Vol 23 (1) ◽  
pp. 117-129 ◽  
Author(s):  
Jiawen Bian ◽  
Huiming Peng ◽  
Jing Xing ◽  
Zhihui Liu ◽  
Hongwei Li

This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton-Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton- Raphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators (LSEs) under the same noise conditions, but it outperforms LSEs in terms of the mean squared errors. Finally, the effectiveness of the algorithm is verified by some numerical experiments.


1969 ◽  
Vol 13 (2) ◽  
pp. 117-126 ◽  
Author(s):  
Derek J. Pike

Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.


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