Dirk Kroese

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Dirk P. Kroese
Dirkkroese091019cutout.jpg
Born1963 (age 6061)
Scientific career
Fields Mathematics AND Statistics
Institutions The University of Queensland
Thesis Stochastic Models in Reliability  (1990)

Dirk Pieter Kroese (born 1963) is a Dutch-Australian mathematician and statistician, and Professor at the University of Queensland. He is known for several contributions to applied probability, kernel density estimation, Monte Carlo methods and rare-event simulation. He is, with Reuven Rubinstein, a pioneer of the Cross-Entropy (CE) method.

Contents

Biography

Born in Wapenveld (municipality of Heerde), Dirk Kroese received his MSc (Netherlands Ingenieur (ir) degree) in 1986 and his Ph.D. (cum laude) in 1990, both from the Department of Applied Mathematics at the University of Twente. His dissertation was entitled Stochastic Models in Reliability. His PhD advisors were Joseph H. A. de Smit and Wilbert C. M. Kallenberg. [1] Part of his PhD research was carried out at Princeton University under the guidance of Erhan Çınlar. He has held teaching and research positions at University of Texas at Austin (1986), Princeton University (1988–1989), the University of Twente (1991–1998), the University of Melbourne (1997), and the University of Adelaide (1998–2000). Since 2000 he has been working at the University of Queensland, where he became a full professor in 2010. [2]

Work

Kroese's work spans a wide range of topics in applied probability and mathematical statistics, including telecommunication networks, reliability engineering, point processes, kernel density estimation, Monte Carlo methods, rare-event simulation, cross-entropy methods, randomized optimization, and machine learning. He is a Chief Investigator of the Australian Research Council Centre of Excellence in Mathematical and Statistical Frontiers (ACEMS). [3] He has over 120 peer-reviewed publications, [4] including six monographs. [5]

Publications

Books

Selected articles

Related Research Articles

The following outline is provided as an overview of and topical guide to statistics:

<span class="mw-page-title-main">Monte Carlo method</span> Probabilistic problem-solving algorithm

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanislaw Ulam, was inspired by his uncle's gambling habits.

The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precisely stated prior data.

In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's equilibrium distribution matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution.

Importance sampling is a Monte Carlo method for evaluating properties of a particular distribution, while only having samples generated from a different distribution than the distribution of interest. Its introduction in statistics is generally attributed to a paper by Teun Kloek and Herman K. van Dijk in 1978, but its precursors can be found in statistical physics as early as 1949. Importance sampling is also related to umbrella sampling in computational physics. Depending on the application, the term may refer to the process of sampling from this alternative distribution, the process of inference, or both.

<span class="mw-page-title-main">Monte Carlo integration</span> Numerical technique

In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers. It is a particular Monte Carlo method that numerically computes a definite integral. While other algorithms usually evaluate the integrand at a regular grid, Monte Carlo randomly chooses points at which the integrand is evaluated. This method is particularly useful for higher-dimensional integrals.

<span class="mw-page-title-main">Kernel density estimation</span> Estimator

In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy.

In statistics, resampling is the creation of new samples based on one observed sample. Resampling methods are:

  1. Permutation tests
  2. Bootstrapping
  3. Cross validation
  4. Jackknife

The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective.

Stochastic optimization (SO) are optimization methods that generate and use random variables. For stochastic optimization problems, the objective functions or constraints are random. Stochastic optimization also include methods with random iterates. Some hybrid methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization. Stochastic optimization methods generalize deterministic methods for deterministic problems.

<span class="mw-page-title-main">Truncated normal distribution</span> Type of probability distribution

In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above. The truncated normal distribution has wide applications in statistics and econometrics.

<span class="mw-page-title-main">Computational statistics</span> Interface between statistics and computer science

Computational statistics, or statistical computing, is the study which is the intersection of statistics and computer science, and refers to the statistical methods that are enabled by using computational methods. It is the area of computational science specific to the mathematical science of statistics. This area is fast developing. The view that the broader concept of computing must be taught as part of general statistical education is gaining momentum.

<span class="mw-page-title-main">Reuven Rubinstein</span> Israeli scientist

Reuven Rubinstein (1938–2012) was an Israeli scientist known for his contributions to Monte Carlo simulation, applied probability, stochastic modeling, and stochastic optimization, having authored more than one hundred papers and six books.

In statistics, the antithetic variates method is a variance reduction technique used in Monte Carlo methods. Considering that the error in the simulated signal has a one-over square root convergence, a very large number of sample paths is required to obtain an accurate result. The antithetic variates method reduces the variance of the simulation results.

In probability theory, reflected Brownian motion is a Wiener process in a space with reflecting boundaries. In the physical literature, this process describes diffusion in a confined space and it is often called confined Brownian motion. For example it can describe the motion of hard spheres in water confined between two walls.

Rare event sampling is an umbrella term for a group of computer simulation methods intended to selectively sample 'special' regions of the dynamic space of systems which are unlikely to visit those special regions through brute-force simulation. A familiar example of a rare event in this context would be nucleation of a raindrop from over-saturated water vapour: although raindrops form every day, relative to the length and time scales defined by the motion of water molecules in the vapour phase, the formation of a liquid droplet is extremely rare.

In probability theory, a Cauchy process is a type of stochastic process. There are symmetric and asymmetric forms of the Cauchy process. The unspecified term "Cauchy process" is often used to refer to the symmetric Cauchy process.

Subset simulation is a method used in reliability engineering to compute small failure probabilities encountered in engineering systems. The basic idea is to express a small failure probability as a product of larger conditional probabilities by introducing intermediate failure events. This conceptually converts the original rare-event problem into a series of frequent-event problems that are easier to solve. In the actual implementation, samples conditional on intermediate failure events are adaptively generated to gradually populate from the frequent to rare event region. These 'conditional samples' provide information for estimating the complementary cumulative distribution function (CCDF) of the quantity of interest, covering the high as well as the low probability regions. They can also be used for investigating the cause and consequence of failure events. The generation of conditional samples is not trivial but can be performed efficiently using Markov chain Monte Carlo (MCMC).

<span class="mw-page-title-main">Ilya M. Sobol'</span> Russian mathematician (born 1926)

Ilya Meyerovich Sobol’ is a Russian mathematician, known for his work on Monte Carlo methods. His research spans several applications, from nuclear studies to astrophysics, and has contributed significantly to the field of sensitivity analysis.

References

  1. "Dirk P. Kroese". Mathematics Genealogy Project. Retrieved 14 July 2022.
  2. University of Queensland
  3. ARC Centre of Excellence in Mathematical and Statistical Frontiers (ACEMS)
  4. Google Scholar
  5. Homepage Dirk Kroese