Title Participants Abstract "A note on the behaviour of a kernel-smoothed kernel density estimator" "Paul JANSSEN, Jan SWANEPOEL, Noel VERAVERBEKE" "Kernel density estimators have been studied in great detail. In this note a new family of kernels, depending on a parameter c, is obtained by kernel-smoothing an initial kernel density estimator. Under certain conditions, we show that nonparametric density estimators based on such kernels outperform the initial estimator in terms of minimized asymptotic mean integrated squared error and in kernel efficiency." "A Fast-Converging Kernel Density Estimator for Dispersion in Horizontally Homogeneous Meteorological Conditions" "Gunther Bijloos, Johan Meyers" "Clustering spatio-temporal trajectories based on kernel density estimation" "Min Deng, Nico Van de Weghe" "Kernel Density Estimation for Dynamical Systems" "Johan Suykens" "© 2018 Hanyuan Hang, Ingo Steinwart, Yunlong Feng and Johan A.K. Suykens. We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual mixing concepts may not be appropriate for measuring the dependence among these observations. By employing the C-mixing concept to measure the dependence, we conduct statistical analysis on the consistency and convergence of the kernel density estimator. Our main results are as follows: First, we show that with properly chosen bandwidth, the kernel density estimator is universally consistent under L1-norm; Second, we establish convergence rates for the estimator with respect to several classes of dynamical systems under L1-norm. In the analysis, the density function f is only assumed to be Holder continuous or pointwise Holder controllable which is a weak assumption in the literature of nonparametric density estimation and also more realistic in the dynamical system context. Last but not least, we prove that the same convergence rates of the estimator under L1-norm and L1-norm can be achieved when the density function is Holder continuous, compactly supported, and bounded. The bandwidth selection problem of the kernel density estimator for dynamical system is also discussed in our study via numerical simulations." "The use of kernel density estimation to examine associations between neighborhood destination intensity and walking and physical activity" "Tania L. King, Lukar Thornton, Rebecca J. Bentley, Anne M. Kavanagh" "Background Local destinations have previously been shown to be associated with higher levels of both physical activity and walking, but little is known about how the distribution of destinations is related to activity. Kernel density estimation is a spatial analysis technique that accounts for the location of features relative to each other. Using kernel density estimation, this study sought to investigate whether individuals who live near destinations (shops and service facilities) that are more intensely distributed rather than dispersed: 1) have higher odds of being sufficiently active; 2) engage in more frequent walking for transport and recreation. Methods The sample consisted of 2349 residents of 50 urban areas in metropolitan Melbourne, Australia. Destinations within these areas were geocoded and kernel density estimates of destination intensity were created using kernels of 400m (meters), 800m and 1200m. Using multilevel logistic regression, the association between destination intensity (classified in quintiles Q1(least)-Q5(most)) and likelihood of: 1) being sufficiently active (compared to insufficiently active); 2) walking >= 4/week (at least 4 times per week, compared to walking less), was estimated in models that were adjusted for potential confounders. Results For all kernel distances, there was a significantly greater likelihood of walking >= 4/week, among respondents living in areas of greatest destinations intensity compared to areas with least destination intensity: 400m (Q4 OR 1.41 95% CI 1.02-1.96; Q5 OR 1.49 95% CI 1.06-2.09), 800m (Q4 OR 1.55, 95% CI 1.09-2.21; Q5, OR 1.71, 95% CI 1.18-2.48) and 1200m (Q4, OR 1.7, 95% CI 1.18-2.45; Q5, OR 1.86 95% CI 1.28-2.71). There was also evidence of associations between destination intensity and sufficient physical activity, however these associations were markedly attenuated when walking was included in the models. Conclusions This study, conducted within urban Melbourne, found that those who lived in areas of greater destination intensity walked more frequently, and showed higher odds of being sufficiently physically active-an effect that was largely explained by levels of walking. The results suggest that increasing the intensity of destinations in areas where they are more dispersed; and or planning neighborhoods with greater destination intensity, may increase residents' likelihood of being sufficiently active for health." "Kernel density compression for real-time Bayesian encoding/decoding of unsorted hippocampal spikes" "Davide Ciliberti, Fabian Kloosterman" "To gain a better understanding of how neural ensembles communicate and process information, neural de- coding algorithms are used to extract information encoded in their spiking activity. Bayesian decoding is one of the most used neural population decoding approaches to extract information from the ensemble spiking activity of rat hippocampal neurons. Recently it has been shown howBayesian decoding can be implemented without the intermediate step of sorting spike waveforms into groups of single units. Here we extend the approach in order to make it suitable for online encoding/decoding scenarios that require real-time decoding such as brain-machine interfaces.We propose an online algorithm for the Bayesian decoding that reduces the time required for decoding neural populations, resulting in a real-time capable decoding framework. More specifically,we improve the speed of the probability density estimation step, which is the most essential and the most expensive computation of the spike-sorting-less decoding process, by developing a kernel density compression algorithm. In contrary to existing online kernel compression techniques, rather than optimizing for the minimum estimation error caused by kernels compression, the proposed method compresses kernels on the basis of the distance between the merging component and its most similar neighbor. Thus, without costly optimization, the proposed method has very low compression latency with a small and manageable estimation error. In addition, the proposed bandwidth matchingmethod for Gaussian kernelsmerging has an interesting mathematical property whereby optimization in the estimation of the probability density func- tion can be performed efficiently, resulting in a faster decoding speed.We successfully applied the proposed kernelcompression algorithm to the Bayesian decoding framework to reconstruct positions of a freelymoving rat fromhippocampal unsorted spikes, with significant improvements in the decoding speed and acceptable decoding error." "Using kernel density estimation to understand the influence of neighbourhood destinations on BMI" "Tania L. King, Rebecca J. Bentley, Lukar Thornton, Anne M. Kavanagh" "Objectives: Little is known about how the distribution of destinations in the local neighbourhood is related to body mass index (BMI). Kernel density estimation (KDE) is a spatial analysis technique that accounts for the location of features relative to each other. Using KDE, this study investigated whether individuals living near destinations (shops and service facilities) that are more intensely distributed rather than dispersed, have lower BMIs. Study design and setting: A cross-sectional study of 2349 residents of 50 urban areas in metropolitan Melbourne, Australia. Methods: Destinations were geocoded, and kernel density estimates of destination intensity were created using kernels of 400, 800 and 1200 m. Using multilevel linear regression, the association between destination intensity (classified in quintiles Q1(least)-Q5(most)) and BMI was estimated in models that adjusted for the following confounders: age, sex, country of birth, education, dominant household occupation, household type, disability/injury and area disadvantage. Separate models included a physical activity variable. Results: For kernels of 800 and 1200 m, there was an inverse relationship between BMI and more intensely distributed destinations (compared to areas with least destination intensity). Effects were significant at 1200 m: Q4, beta-0.86, 95% CI -1.58 to -0.13, p= 0.022; Q5, beta-1.03 95% CI -1.65 to -0.41, p= 0.001. Inclusion of physical activity in the models attenuated effects, although effects remained marginally significant for Q5 at 1200 m: beta-0.77 95% CI -1.52, -0.02, p=0.045. Conclusions: This study conducted within urban Melbourne, Australia, found that participants living in areas of greater destination intensity within 1200 m of home had lower BMIs. Effects were partly explained by physical activity. The results suggest that increasing the intensity of destination distribution could reduce BMI levels by encouraging higher levels of physical activity." "Integrating pedestrian-habitat models and network kernel density estimations to measure street pedestrian suitability" "Javier Delso, Belen Martin, Emilio Ortega, Nico Van de Weghe" "Pedestrian-oriented urban designs are sustainable from a mobility perspective, and could therefore be used to improve urban environments. This study proposes an analogy between the ecological idea of habitat and the pedestrian urban environment and introduces the concept of ""pedestrian habitat quality"". We present a methodology based on this concept to measure pedestrian habitat suitability in an urban street network, combining network kernel density estimations with a habitat suitability model. The dimensions of proximity and walkability connectivity are first incorporated in the methodology through network kernel density estimations, and the micro physical environmental factors relevant for pedestrians are considered using a pedestrian habitat quality model. The final outcome of the methodology is an identification of priority streets for action in order to improve pedestrian mobility. The methodology was applied to Vitoria-Gasteiz, a medium-sized city in northern Spain. Our results for Vitoria-Gasteiz show that the streets with a greater potential for improvement are situated in the surroundings of the city centre and in industrial edges that serve as a link to residential zones. It has been demonstrated that the methodology could be a useful tool for urban and transport planners to identify priority streets on which to focus efforts for improving urban environments." "Comparison of presmoothing methods in kernel density estimation under censoring" "Irène Gijbels" "The behavior of the presmoothed density estimator is studied when different ways to estimate the conditional probability of uncensoring are used. The Nadaraya–Watson, local linear and local logistic approach are compared via simulations with the classical Kaplan–Meier estimator. While the local logistic presmoothing estimator presents the best performance, the relative benefits of the local linear versus the Nadaraya–Watson estimator depend very much on the shape of some underlying functions." "Identifying Outliers in Response Quality Assessment by Using Multivariate Control Charts Based on Kernel Density Estimation" "Jiayun Jin, Geert Loosveldt"