Kernel Density Estimation Methods for a Geostatistical Approach in Seismic Risk Analysis: The Case Study of Potenza Hilltop Town (Southern Italy)

This paper focuses on an overview of kernel density estimation especially for what concerns the choice of bandwidth and intensity parameters according to local conditions. A case study inherent seismic risk analysis of the old town centre of Potenza hilltop town has been discussed, with particular attention to the evaluation of the possible local amplifying factors. This first integrated application of kernel density maps to analyse seismic damage scenarios with a geostatistical approach allowed to evaluate the local geological, geomorphological and 1857 earthquake macroseismic data, offering a new point of view of civil protection planning. The aim of geostatistical approach is to know seismic risk variability at local level, modelling and visualizing it.

[1]  J. Marron,et al.  Improved Variable Window Kernel Estimates of Probability Densities , 1995 .

[2]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .

[3]  S. Sheather A data-based algorithm for choosing the window width when estimating the density at a point , 1983 .

[4]  Beniamino Murgante,et al.  Where are the slums? New approaches to urban regeneration , 2008 .

[5]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[6]  A. Cuevas,et al.  A comparative study of several smoothing methods in density estimation , 1994 .

[7]  M. C. Jones,et al.  A Brief Survey of Bandwidth Selection for Density Estimation , 1996 .

[8]  H. Miller A MEASUREMENT THEORY FOR TIME GEOGRAPHY , 2005 .

[9]  Daniel J. Price,et al.  An energy‐conserving formalism for adaptive gravitational force softening in smoothed particle hydrodynamics and N‐body codes , 2006, astro-ph/0610872.

[10]  Colin O. Wu A Cross-Validation Bandwidth Choice for Kernel Density Estimates with Selection Biased Data , 1997 .

[11]  P. Diggle A point process modeling approach to raised incidence of a rare phenomenon in the vicinity of a prespecified point , 1990 .

[12]  J. Simonoff Smoothing Methods in Statistics , 1998 .

[13]  Luc Devroye,et al.  Variable Kernel Estimates: On the Impossibility of Tuning the Parameters , 1998 .

[14]  Ian Abramson On Bandwidth Variation in Kernel Estimates-A Square Root Law , 1982 .

[15]  K. Dixon,et al.  Harmonic mean measure of animal activity areas , 1980 .

[16]  G. Grünthal European macroseismic scale 1998 : EMS-98 , 1998 .

[17]  Stephen M Roberts,et al.  Body Weight Distributions for Risk Assessment , 2007, Risk analysis : an official publication of the Society for Risk Analysis.

[18]  J. Montanero,et al.  ON THE EXISTENCE AND LIMIT BEHAVIOR OF THE OPTIMAL BANDWIDTH FOR KERNEL DENSITY ESTIMATION , 2007 .

[19]  M. C. Jones,et al.  On optimal data-based bandwidth selection in kernel density estimation , 1991 .

[20]  D. Sumner,et al.  Are Farm Size Distributions Bimodal? Evidence from Kernel Density Estimates of Dairy Farm Size Distributions , 2001 .

[21]  Giuseppe Borruso,et al.  Network Density Estimation: Analysis of Point Patterns over a Network , 2005, ICCSA.

[22]  V. A. Epanechnikov Non-Parametric Estimation of a Multivariate Probability Density , 1969 .

[23]  Trevor C. Bailey,et al.  Interactive Spatial Data Analysis , 1995 .

[24]  James Stephen Marron,et al.  On the Amount of Noise Inherent in Bandwidth Selection for a Kernel Density Estimator , 1987 .

[25]  C. Quesenberry,et al.  A nonparametric estimate of a multivariate density function , 1965 .

[26]  M. C. Jones,et al.  E. Fix and J.L. Hodges (1951): An Important Contribution to Nonparametric Discriminant Analysis and Density Estimation: Commentary on Fix and Hodges (1951) , 1989 .

[27]  Neil Stuart,et al.  When is a hotspot a hotspot? A procedure for creating statistically robust hotspot maps of crime , 2002 .

[28]  Jerome Sacks,et al.  ASYMPTOTICALLY OPTIMUM KERNELS FOR DENSITY ESTIMATION AT A POINT , 1981 .

[29]  T. Cacoullos Estimation of a multivariate density , 1966 .

[30]  Giuseppe Borruso,et al.  Network Density and the Delimitation of Urban Areas , 2003, Trans. GIS.

[31]  Roland Schregle,et al.  Bias Compensation for Photon Maps , 2003, Comput. Graph. Forum.

[32]  D. W. Scott,et al.  On Locally Adaptive Density Estimation , 1996 .

[33]  M. Rosenblatt Remarks on Some Nonparametric Estimates of a Density Function , 1956 .

[34]  David Taniar,et al.  Computational Science and Its Applications - ICCSA 2005, International Conference, Singapore, May 9-12, 2005, Proceedings, Part I , 2005, ICCSA.

[35]  Matthew P. Wand,et al.  Kernel Smoothing , 1995 .

[36]  Susan A. Murphy,et al.  Monographs on statistics and applied probability , 1990 .

[37]  P. J. Clark,et al.  Distance to Nearest Neighbor as a Measure of Spatial Relationships in Populations , 1954 .

[38]  Guenter Enderle,et al.  Bias Compensation for Photon Maps , 1985 .

[39]  I Bracken,et al.  Linkage of the 1981 and 1991 UK Censuses Using Surface Modelling Concepts , 1995, Environment & planning A.

[40]  Bernard W. Silverman,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[41]  A. Bowman,et al.  Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations , 1999 .

[42]  L. Breiman,et al.  Variable Kernel Estimates of Multivariate Densities , 1977 .

[43]  B. Worton Kernel methods for estimating the utilization distribution in home-range studies , 1989 .

[44]  Hans-Peter Seidel,et al.  Fast Final Gathering via Reverse Photon Mapping , 2005, Comput. Graph. Forum.

[45]  P. Diggle,et al.  Spatial point pattern analysis and its application in geographical epidemiology , 1996 .

[46]  P. Diggle A Kernel Method for Smoothing Point Process Data , 1985 .

[47]  J. Downs,et al.  Characterising Linear Point Patterns , 2007 .

[48]  David W. S. Wong,et al.  A surface-based approach to measuring spatial segregation , 2007 .

[49]  Martin L. Hazelton,et al.  Optimal rates for local bandwidth selection , 1996 .

[50]  James Stephen Marron,et al.  Variable window width kernel estimates of probability densities , 1992 .

[51]  Chris Brunsdon,et al.  Estimating probability surfaces for geographical point data: an adaptive kernel algorithm , 1995 .

[52]  David W. Macdonald,et al.  Are kernels the mustard? Data from global positioning system (GPS) collars suggests problems for kernel home- range analyses with least-squares cross-validation , 2005 .

[53]  Christopher Worswick,et al.  Adaptation and Inequality: Children of Immigrants in Canadian Schools , 2004 .

[54]  Stephen Chiu,et al.  A Comparative Review of Bandwidth Selection for Kernel Density Estimation , 1996 .

[55]  Jason Dykes,et al.  The use of the landscape metaphor in understanding population data , 1999 .

[56]  J. Burt,et al.  Elementary statistics for geographers , 1995 .

[57]  Huan Liu,et al.  Social Computing, Behavioral Modeling, and Prediction , 2008 .