20 papers · ranked by Valyu relevance
Omar Eidous, Mohammad Al-Rawash
In this paper, we introduce a new approximation of the cumulative distribution function of the standard normal distribution based on Tocher's approximation. Also, we assess the quality of the new approximation using two criteria namely the maximum absolute error and the mean absolute error. The approximation is…
Adrian G. Fischer, Robert E. Gaunt, Gesine Reinert, Yvik Swan
In this paper we obtain quantitative Bernstein-von Mises type bounds on the normal approximation of the posterior distribution in exponential family models when centering either around the posterior mode or around the maximum likelihood estimator. Our bounds, obtained through a version of Stein's method, are…
Zoe Shapcott
In this note, we assess the accuracy of CLT-based approximations for the volume of intersection of the ddimensional cube [−1, 1]d and an Lq-ball centred at the origin; this is clearly equivalent to approximating the distribution of the Lq-norm of a random point in a d-dimensional cube centered at 0. The approximations…
Saed Moradi, Denis Laurendeau, Clement Gosselin, Stefano Berretti
Most man-made objects are composed of a few basic geometric primitives (GPs) such as spheres, cylinders, planes, ellipsoids, or cones. Thus, the object recognition problem can be considered as one of geometric primitives extraction. Among the different geometric primitives, cylinders are the most frequently used GPs in…
Asyraf Nadia Mohd Yunus, Nora Muda, Abdul Rahman Othman, Sonia Aïssa + 1 more
'Jiangtao Gou'] In probabilistic modeling across engineering, finance, and telecommunications, sums of lognormal random variables frequently occur, yet no closed-form expression exists for their distribution. This study systematically evaluates three approximation methods-Wilkinson (W), Schwartz & Yeh (SY), and Inverse…
Guangshuai Liu, Xurui Li, Si Sun, Wenyu Yi + 1 more
This paper introduces a robust normal estimation method for point cloud data that can handle both smooth and sharp features. Our method is based on the inclusion of neighborhood recognition into the normal mollification process in the neighborhood of the current point: First, the point cloud surfaces are assigned…
Daniel Herrera-Esposito, Johannes Burge
The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $x$ by its norm $xTx$. The resulting random variable follows a distribution on the unit sphere. No closed-form formulas for the moments of the projected normal distribution…
John Heine, Erin E.E. Fowler, Anders Berglund, Michael J. Schell + 1 more
Proper data modeling in biomedical research requires sufficient data for exploration and reproducibility purposes. A limited sample size can inhibit objective performance evaluation. We are developing a synthetic population (SP) generation technique to address the limited sample size condition. We show how to estimate…
Anna Hlubinová, Pavol Bokes, Abhyudai Singh
This paper examines a structurally symmetric fluctuation test experiment in which cell populations grow from a single cell to a set size before undergoing treatment. During growth, cells may acquire tolerance to treatment through probabilistic events, which are passed to progeny. Motivated by recent research on drug…
Xu Yang, Cai Cheng, Jin Duan, You-Fei Hao + 3 more
'Sylvain Girard'] There are six possible solutions for the surface normal vectors obtained from polarization information during 3D reconstruction. To resolve the ambiguity of surface normal vectors, scholars have introduced additional information, such as shading information. However, this makes the 3D reconstruction…
Sabyasachi Shivkumar, Madeline S. Cappelloni, Ross K. Maddox, Ralf M. Haefner
Perceptual decision-making has been extensively modeled using the ideal observer framework. However, a range of deviations from optimality demand an extension of this framework to characterize the different sources of suboptimality. Prior work has mostly formalized these sources by adding biases and variability in the…
Authors not listed
Vibrational exciton models are widely used for the simulation of biomolecular vibrational spectra, in particular of two-dimensional infrared (2D-IR) spectra. The parameters entering such models, specifically harmonic local-mode frequencies and harmonic coupling constants, are provided by vibrational maps, which have…
Patrick Kramer, Alexander Kreiß
We study regression discontinuity designs with the use of additional covariates for estimation of the average treatment effect. We provide a detailed proof of asymptotic normality of the covariate-adjusted estimator under minimal assumptions, which may serve as an accessible text to the mathematics behind regression…
Jonas Vester, Jógvan Magnus Haugaard Olsen
The partial Hessian approximation is often used to perform vibrational analysis of large QM/MM systems where the high computational cost of calculating the full Hessian is impractical. Here, we investigate the accuracy and applicability of the partial Hessian vibrational analysis (PHVA) approach as it is typically used…
Jiyeon Park, Paul K. Newton
We use the Bernstein polynomials of degree d as the basis for constructing a uniform approximation to the rate of evolution (related to the fixation probability) of a species in a two-component finite-population frequency-dependent evolutionary game setting. The approximation is valid over the full range 0 ≤ w ≤ 1…
Augustijn A.A. de Boer, Seyed Mostafa Kia, Saige Rutherford, Mariam Zabihi + 7 more
Normative modelling is an emerging technique for parsing heterogeneity in clinical cohorts. This can be implemented in practice using hierarchical Bayesian regression, which provides an elegant probabilistic solution to handle site variation in a federated learning framework. However, applications of this method to…
Denis Tikhonov, Yury Vishnevskiy
In this work we discuss the generally applicableWigner sampling and introduce a new, simplified Wigner sampling method, for computationally effective modeling of molecular properties containing nuclear quantum effects and vibrational anharmonicity. For various molecular systems have been performed test calculations of…
Shunzhou Wan, Agastya Bhati, David Wright, Ian Wall + 3 more
Optimization of binding affinities for ligands to their target protein is a primary objective in rational drug discovery. Herein we report on a collaborative study that evaluates various compounds designed to bind to the SET and MYND domain-containing protein 3 (SMYD3). SMYD3 is a histone methyltransferase and plays an…
Andrew McCluskey
The use of mathematical transformations to reduce non-linear functions to linear problems, which can be tackled with analytical linear regression, is commonplace in the chemistry curriculum. The linearization procedure, however, assumes an incorrect statistical model for real experimental data; leading to biased…
Taufik A Valiante
Neuronal size has often been used to explain the “superiority” of the human brain. By deriving the Shannon entropy of different statistical distributions, we show that the entropy of different distributions is solely accounted for by the variance of the distribution. We use total dendritic length of neurons from…