# Computational Statistics Domain

A Computational Statistics Domain is a computational mathematics domain that overlaps with a statistics domain.

**AKA:**Statistical Computing.**Context:**- It can (typically) involve Statistical Algorithms and Statistical Information Systems.
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**Counter-Example(s):****See:**Statistics, Computational Science, Stochastic Finite Element.

## References

### 2011

- http://en.wikipedia.org/wiki/Computational_statistics
**Computational statistics**, or**statistical computing**, is the interface between statistics and computer science. It is the area of computational science (or scientific computing) specific to the mathematical science of statistics.The terms 'computational statistics' and 'statistical computing' are often used interchangeably, although Carlo Lauro (a former president of the International Association for Statistical Computing) proposed making a distinction, defining 'statistical computing' as "the application of computer science to statistics", and 'computational statistics' as "aiming at the design of algorithm for implementing statistical methods on computers, including the ones unthinkable before the computer age (e.g. bootstrap, simulation), as well as to cope with analytically intractable problems".

The term 'Computational statistics' may also be used to refer to computationally

*intensive*statistical methods including resampling methods, Markov chain Monte Carlo methods, local regression, kernel density estimation, artificial neural networks and generalized additive models.

### 2009

- (Gentle, 2009) ⇒ James E. Gentle. (2009). “Computational Statistics." Springer. ISBN:978-0-387-98143-7

### 2005

- (Givens & Hoeting, 2005) ⇒ Geof H. Givens, and Jennifer A. Hoeting. (2005). “Computational Statistics." Wiley. ISBN: 978-0-471-46124-1
- Preface & TOC: http://www.stat.colostate.edu/computationalstatistics/
- BOOK OVERVIEW: This comprehensive introduction enables readers to develop a multifaceted and thorough knowledge of modern statistical computing and computational statistics. … the authors help readers gain a practical understanding of how and why modern statistical methods work, enabling readers to apply these methods effectively. Detailed examples are drawn from diverse fields such as bioinformatics, ecology, medicine, computer vision, and stochastic finance.
The text emphasizes areas that are central to understanding the evolving field of computational statistics including areas where routine application of software often fails to solve complex problems. Topics covered include ordinary and combinatorial optimization, algorithms for missing data, numerical and Monte Carlo integration, simulation, introductory and advanced Markov chain Monte Carlo, bootstrapping, density estimation, and smoothing.

### 2002

- http://www.scs.gmu.edu/~jgentle/compstat/
- Computational Statistics is the area of specialization within statistics that includes statistical visualization and other computationally-intensive methods of statistics. Computational statistics is built on the mathematical theory and methods of statistics, and includes visualization, statistical computing, and Monte Carlo methods. The emphasis in computational statistics is often on exploratory methods.
Research in computational statistics involves the development of visualization and computationally-intensive methods for mining large, nonhomogeneous, multi-dimensional datasets so as to discover knowledge in the data. As in all areas of statistics, probability models are important, and results are qualified by statements of confidence or of probability. An important activity in computational statistics is model building and evaluation.

Examples of research areas in computational statistics:

- Techniques for discovering structure in data. These are usually exploratory or visual, and may involve such things as density estimation, clustering, or classification. In most cases, the emphasis would be on large-dimensional datasets.
- Statistical learning.
- Methods of analysis of extremely large datasets (large number of observations or large number of dimensions).
- Computationally-intensive methods of analysis (Monte Carlo methods or resampling methods).
- Simulation methods.
- Methods for statistical modeling. These may be classical statistical models, models based on differential equations, especially SDEs, or Bayesian hierarchical models.
- Numerical methods for statistical analysis (statistical computing).
- Methods for statistical problems that have a major "computer science" aspect (record matching, for example).

- Computational Statistics is the area of specialization within statistics that includes statistical visualization and other computationally-intensive methods of statistics. Computational statistics is built on the mathematical theory and methods of statistics, and includes visualization, statistical computing, and Monte Carlo methods. The emphasis in computational statistics is often on exploratory methods.

### 1996

- (Lauro, 1996) ⇒ Carlo Lauro. (1996). “Computational Statistics or Statistical Computing, is that the question?" In: Computational Statistics & Data Analysis, 23(1).
- ABSTRACT. Computational statistics, supported by computing power and availability of efficient methodology, techniques and algorithms on the statistical side and by the perception on the need of valid data analysis and data interpretation on the biomedical side, has invaded in a very short time many cutting edge research areas of molecular biomedicine. Two salient cutting edge biomedical research questions demonstrate the increasing role and decisive impact of computational statistics. The role of well designed and well communicated simulation studies is emphasized and computational statistics is put into the framework of the International Association of Statistical Computing (IASC) and special issues on Computational Statistics within Clinical Research launched by the journal Computational Statistics and Data Analysis (CSDA).

### 1988

- (Thisted, 1988) ⇒ Ronald Aaron Thisted. (1988). “Elements of Statistical Computing: Numerical computation." Chapman and Hall. ISBN: 9780412013713
- BOOK OVERVIEW: Statistics and computing share many close relationships. Computing now permeates every aspect of statistics, from pure description to the development of statistical theory. At the same time, the computational methods used in statistical work span much of computer science. Elements of Statistical Computing covers the broad usage of computing in statistics. It provides a comprehensive account of the most important computational statistics. Included are discussions of numerical analysis, numerical integration, and smoothing. The author give special attention to floating point standards and numerical analysis; iterative methods for both linear and nonlinear equation, such as Gauss-Seidel method and successive over-relaxation; and computational methods for missing data, such as the EM algorithm. Also covered are new areas of interest, such as the Kalman filter, projection-pursuit methods, density estimation, and other computer-intensive techniques.