scholarly journals A Fast-Converging Kernel Density Estimator for Dispersion in Horizontally Homogeneous Meteorological Conditions

Atmosphere ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 1343
Author(s):  
Gunther Bijloos ◽  
Johan Meyers
Keyword(s):  
Convergence Rate ◽  
Path Integral ◽  
Concentration Field ◽  
Kernel Density ◽  
Particle Dispersion ◽  
Meteorological Conditions ◽  
Kernel Density Estimator ◽  
Gaussian Kernel ◽  
Density Estimator ◽  
Data Set

Kernel smoothers are often used in Lagrangian particle dispersion simulations to estimate the concentration distribution of tracer gasses, pollutants etc. Their main disadvantage is that they suffer from the curse of dimensionality, i.e., they converge at a rate of 4/(d+4) with d the number of dimensions. Under the assumption of horizontally homogeneous meteorological conditions, we present a kernel density estimator that estimates a 3D concentration field with the faster convergence rate of a 1D kernel smoother, i.e., 4/5. This density estimator has been derived from the Langevin equation using path integral theory and simply consists of the product between a Gaussian kernel and a 1D kernel smoother. Its numerical convergence rate and efficiency are compared with that of a 3D kernel smoother. The convergence study shows that the path integral-based estimator has a superior convergence rate with efficiency, in mean integrated squared error sense, comparable with the one of the optimal 3D Epanechnikov kernel. Horizontally homogeneous meteorological conditions are often assumed in near-field range dispersion studies. Therefore, we illustrate the performance of our method by simulating experiments from the Project Prairie Grass data set.

scholarly journals An evaluation of different measures of dynamically recrystallized grain size for paleopiezometry or paleowattometry studies

Solid Earth ◽  
2015 ◽  
Vol 6 (2) ◽  
pp. 475-495 ◽  
Author(s):  
M. A. Lopez-Sanchez ◽  
S. Llana-Fúnez
Keyword(s):  
Grain Size ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Gaussian Kernel ◽  
Robust Estimator ◽  
Density Estimator ◽  
Lithospheric Deformation ◽  
Single Measure ◽  
Frequency Peak ◽  
Recrystallized Grain Size

Abstract. Paleopiezometry and paleowattometry studies are essential to validate models of lithospheric deformation and therefore increasingly common in structural geology. These studies require a single measure of dynamically recrystallized grain size in natural mylonites to estimate the magnitude of differential paleostress (or the rate of mechanical work). This contribution tests the various measures of grain size used in the literature and proposes the frequency peak of a grain size distribution as the most robust estimator for paleopiezometry or paleowattometry studies. The novelty of the approach resides in the use of the Gaussian kernel density estimator as an alternative to the classical histograms, which improves reproducibility. A free, open-source, easy-to-handle script named GrainSizeTools ( http://www.TEOS-10.org) was developed with the aim of facilitating the adoption of this measure of grain size in paleopiezometry or paleowattometry studies. The major advantage of the script over other programs is that by using the Gaussian kernel density estimator and by avoiding manual steps in the estimation of the frequency peak, the reproducibility of results is improved.

scholarly journals A Bayesian Approach to Parameter Estimation for Kernel Density Estimation via Transformations

2011 ◽  
Vol 5 (2) ◽  
pp. 181-193 ◽  
Author(s):  
Qing Liu ◽  
David Pitt ◽  
Xibin Zhang ◽  
Xueyuan Wu
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Original Data ◽  
Sampling Procedure ◽  
Kernel Density Estimator ◽  
Density Estimator ◽  
Insurance Claim ◽  
Data Set ◽  
Transformation Parameters

AbstractIn this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel. In the current literature, there have been some developments in the area of estimating densities based on transformed data, where bandwidth selection usually depends on pre-determined transformation parameters. Moreover, in the bivariate situation, the transformation parameters were estimated for each dimension individually. We use a Bayesian sampling algorithm and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters simultaneously within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is better captured through the bivariate density estimator based on transformed data.

scholarly journals Gaussian Kernel Density Estimator for Voxel Size Selection in Atom Probe Tomography

2013 ◽  
Vol 19 (S2) ◽  
pp. 992-993 ◽  
Author(s):  
K. Kaluskar ◽  
K. Rajan
Keyword(s):  
Atom Probe Tomography ◽  
Kernel Density ◽  
Atom Probe ◽  
Kernel Density Estimator ◽  
Gaussian Kernel ◽  
Density Estimator ◽  
Voxel Size ◽  
Size Selection

Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.

Online clutter estimation using a Gaussian kernel density estimator for multitarget tracking

2015 ◽  
Vol 9 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Xin Chen ◽  
Ratnasingham Tharmarasa ◽  
Thia Kirubarajan ◽  
Mike McDonald
Keyword(s):  
Kernel Density ◽  
Kernel Density Estimator ◽  
Gaussian Kernel ◽  
Density Estimator ◽  
Multitarget Tracking

A new kernel density estimator based on the minimum entropy of data set

2019 ◽  
Vol 491 ◽  
pp. 223-231 ◽  
Author(s):  
Jie Jiang ◽  
Yu-Lin He ◽  
De-Xin Dai ◽  
Joshua Zhexue Huang
Keyword(s):  
Kernel Density ◽  
Kernel Density Estimator ◽  
Density Estimator ◽  
Minimum Entropy ◽  
Data Set

scholarly journals Estimating the Gait Speed of Older Adults in Smart Home Environments

2022 ◽  
Vol 3 (2) ◽  
Author(s):  
Björn Friedrich ◽  
Enno-Edzard Steen ◽  
Sandra Hellmers ◽  
Jürgen M. Bauer ◽  
Andreas Hein
Keyword(s):  
Older Adults ◽  
Gait Speed ◽  
Smart Home ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Gaussian Kernel ◽  
Measurement Unit ◽  
Density Estimator ◽  
Home Environments ◽  
Smart Home Environments

AbstractMobility is one of the key performance indicators of the health condition of older adults. One important parameter is the gait speed. The mobility is usually assessed under the supervision of a professional by standardised geriatric assessments. Using sensors in smart home environments for continuous monitoring of the gait speed enables physicians to detect early stages of functional decline and to initiate appropriate interventions. This in combination with a floor plan smart home sensors were used to calculate the distance that a person walked in the apartment and the inertial measurement unit data for estimating the actual walking time. A Gaussian kernel density estimator was applied to the computed values and the maximum of the kernel density estimator was considered as the gait speed. The proposed method was evaluated on a real-world dataset and the estimations of the gait speed had a deviation smaller than $$0.10 \, \frac{\mathrm{m}}{\mathrm{s}}$$ 0.10 m s , which is smaller than the minimal clinically important difference, compared to a baseline from a standardised geriatrics assessment.

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