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Painting of Zdravko
Welcome to Zdravko Botev's webpage

Contacts:

School of Mathematics and Physics
The University of Queensland,
Brisbane 4072, Australia
Room 448, Priestley Building #67
Email: botev AT maths.uq.edu.au
Telephone international: +(61) (7) 33461426
Telephone interstate: (07) 33461426

Professional interests

  • Monte Carlo methods in Reliability and Option pricing
  • Kernel density estimation
  • Splitting for estimation of Static Rare event probabilities
  • Cross Entropy methods for combinatorial and continuous optimization
  • Markov Chain Monte Carlo algorithms with stochastic search applications
  • stochastic differential equations

Good Software for Probability Density Estimation

Kernel Density Estimators for Matlab (save the code in an m-file under the names below)

  • for one-dimensional data: kde.m
  • for two-dimensional data: kde2d.m
  • for n-dimensional data: ongoing project

Preprints, Papers and Presentations

  • D. P. Kroese, T. Taimre and Z. I. Botev (2010), Handbook of Monte Carlo Methods, John Wiley & Sons , in press [ Wiley]
  • Botev. Z.I. and Kroese D. P. (2010). Efficient Monte Carlo simulation via the Generalzied Splitting Method. Statistics and Computing. DOI: 10.1007/s11222-010-9201-4
  • Botev. Z.I., Grotowski J.F and Kroese D. P. (2010). Kernel density estimation via diffusion. Annals of Statistics. Volume 38, Number 5, Pages 2916--2957
  • Botev, Z.I., Kroese, D.P. (2009). The Generalized Cross Entropy Method, with Applications to Probability Density Estimation. Methodology and Computing in Applied Probability. DOI: 10.1007/s11009-009-9133-7
  • Botev, Z.I., Kroese, D.P. (2008). Non-asymptotic bandwidth selection for density estimation of discrete data. Methodology and Computing in Applied Probability. Volume 10, Number 3, 435-451,
  • Botev, Z.I., Kroese, D.P. (2008). An Efficient Algorithm for Rare-event Probability Estimation, Combinatorial Optimization, and Counting. Methodology and Computing in Applied Probability. Volume 10, Number 4, 471-505 (pdf)
  • D. P. Kroese, T. Taimre, Z. I. Botev and R. Y. Rubinstein (2007), Solutions Manual for Monte Carlo Methods, Wiley-Interscience, Second edition [ Wiley | Amazon | Barnes and Noble ]
  • Botev, Z.I, Kroese, D.P., Taimre, T. (2007). Generalized Cross-Entropy Methods with Applications to Rare-Event simulation and Optimization. Simulation. Volume 83, Number 11, 785-806
  • Botev, Z.I, Kroese, D.P., Taimre, T. (2006). Generalized Cross-Entropy Methods. Proceedings of RESIM 2006, Bamberg, Germany, 1-30. (pdf)
  • Botev, Z., Kroese, D.P. (2004). Global Likelihood Optimization via the Cross-Entropy Method, with an Application to Mixture Models. Proceedings of the Winter Simulation Conference, Washington DC, pp 529--535. (pdf)
  • Bachelor of Science Honors Project
  • This paper has been used to help write the kernel density estimation software.

Teaching

Teaching projects since my second year of undergraduate study. I have tutored 10 different courses and lectured a 3-rd year level and a 4-th year level course. Teaching feedback: The most frequent complaint of students is that the course material is boring. There is an analogy between boring maths and boring musical exercises. Everybody wants to start playing Beethoven sonatas straight away, but you can't play good music unless you put long boring hours of hard work --- practising fingering, chord progressions, notation reading etc etc. The same is true for maths. It takes a lot of hard work and boring exercises to get to a level where it becomes interesting and fascinating like a Beethoven sonata.