Rank: 215 based on 457 downloads (last 30 days) and 5 files submitted
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Zdravko Botev

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Company/University
University of New South Wales

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Professional Interests:
Monte Carlo methods: generalized splitting

 

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Files Posted by Zdravko View all
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07 Nov 2012 Screenshot Fractional Brownian field or surface generator Generates fractional Brownian field or surface with a given Hurst parameter using Stein's method. Author: Zdravko Botev circulant matrix, fractional brownian s..., wiener sheet, stationary gaussian p..., circulant embedding 23 2
06 Nov 2012 Screenshot Fractional Brownian motion generator Generates fractional Brownian motion with a given Hurst parameter using the FFT. Author: Zdravko Botev fractional brownian m..., circulant matrix, spectral method, stationary gaussian p... 37 0
02 Nov 2012 Screenshot Circulant Embedding method for generating stationary Gaussian field Implements Dietrich and Newsam's circulant embedding method for fast generation of Gaussian fields. Author: Zdravko Botev random field, stationary gaussian p..., fractional brownian m..., wiener sheet, spatial process 26 0
13 Jan 2011 Screenshot Kernel Density Estimator Reliable and extremely fast kernel density estimator for one-dimensional data Author: Zdravko Botev statistics, probability, kernel smoothing, automatic hitech band..., tdsubha2010, kernel density estima... 199 33
  • 4.72
4.7 | 26 ratings
26 May 2009 Screenshot kernel density estimation fast and accurate state-of-the-art bivariate kernel density estimator Author: Zdravko Botev statistics, probability, kernel density estima..., optimal bandwidth sel... 172 31
  • 4.0
4.0 | 25 ratings
Comments and Ratings by Zdravko View all
Updated File Comments Rating
21 Jan 2011 Kernel Density Estimator Reliable and extremely fast kernel density estimator for one-dimensional data Author: Zdravko Botev

Due to numerical round-off error from the fft.m function, it is possible to get density values of -1.38e-018 (instead of 0) and cdf values slightly larger than 1.
If this is a problem, one can correct the output from kde by overwriting:

density=max(density,0); cdf=min(1,cdf);

15 Oct 2010 Kernel Density Estimator Reliable and extremely fast kernel density estimator for one-dimensional data Author: Zdravko Botev

Dear George, the kde function works as it should. There is no problem with the kde. What you call a problem is actually one of the main strengths of the routine.

By typing data = [d1;d1;d1;d1;d1;d2;d3];
you are creating DISCRETE data, because you create ties (the same values appear multiple times). For a truly continuous data, there can be no ties or repeated values!!!
If you have ties, then the data CANNOT be continuous be definition.

The kde.m CORRECTLY recognizes that the data you have provided is perfectly discrete and since discrete data does not need smoothing, the selected bandwidth should be zero. kde.m is the only routine I am aware of that does this correctly, every other routine fails this BASIC theoretical test.

Comments and Ratings on Zdravko's Files View all
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16 Mar 2014 Fractional Brownian field or surface generator Generates fractional Brownian field or surface with a given Hurst parameter using Stein's method. Author: Zdravko Botev Damodara

Hi Botev,

How can we measure these fractals using box counting dimension method.

Regards
dams

30 Jan 2014 kernel density estimation fast and accurate state-of-the-art bivariate kernel density estimator Author: Zdravko Botev Oliver

I am running the code perfectly on sets of 45 points (each has a X and Y coordinate). But when I try to only use a subset of those 45 points I get:
Error using fzero (line 274)
The function values at the interval endpoints must differ in sign.

Error in kde2d (line 101)
t_star=fzero(@(t)(t-evolve(t)),[0,0.1]);

Is code not able to handle the low sample size? Not sure what is happening. It seems to not be able to find a bandwidth.

26 Jan 2014 kernel density estimation fast and accurate state-of-the-art bivariate kernel density estimator Author: Zdravko Botev sepideh

13 Nov 2013 Kernel Density Estimator Reliable and extremely fast kernel density estimator for one-dimensional data Author: Zdravko Botev Ramesh , Bharath

Dear Botev,

I have encountered a problem with your implementation and seeking your help. The PDFs obtained using translated versions of the signal (image histogram, in this case) is not the same.

data = [23 23 23 22 22 22 21 22 23];
data = [53 53 53 52 52 52 51 52 53];
MIN = 0
MAX = 255
n = 256;

[bandwidth,density,xmesh,cdf]=kde(data,256,MIN,MAX)

This gives a good uni-modal estimate, whereas the second one is incomprehensible.

[bandwidth,density,xmesh,cdf]=kde(data2,256,MIN,MAX)

Please take a look at the density plots in each case.

This might be a problem with the bandwidth estimation but I don't know how to solve it.

Any help is appreciated.

Bharath

For e.g:

24 Sep 2013 Fractional Brownian field or surface generator Generates fractional Brownian field or surface with a given Hurst parameter using Stein's method. Author: Zdravko Botev Luiz

Dear Botev,

Thanks for sharing this file. I am trying to run the file, but Matlab says that is necessary to have a function rho. Could you provide a rho function as an example? You have done it in your other code (stationary_Gaussian_process) and it was great to have a start point.

Thanks!

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