Computational statistics

Computational statistics, also known as statistical computing, is the exciting intersection of statistics and computer science. It focuses on using computers to perform complex statistical methods that would be too difficult to do by hand. This field is part of computational science, which applies computer power to solve scientific problems, but it specifically deals with statistics.

Just like in traditional statistics, the goal is to turn raw data into useful knowledge. However, computational statistics often works with very large amounts of information, called sample size, and with data sets that are not all the same. Computers help scientists analyze these big and complex data sets.

The words 'computational statistics' and 'statistical computing' are often used to mean the same thing. Some experts, like Carlo Lauro, suggest they have slightly different meanings. He says 'statistical computing' is about using computers to apply statistical methods, while 'computational statistics' is about designing new computer algorithms to perform statistical tasks, even ones that were impossible before computers existed, like the bootstrap and simulation.

Computational statistics also includes many powerful methods that need a lot of computer processing time. These include resampling methods, Markov chain Monte Carlo methods, local regression, kernel density estimation, artificial neural networks, and generalized additive models. These tools help scientists understand patterns and make predictions from complex data.

History

Computational statistics has a short but important history. Long ago, statisticians mainly used math to develop their methods. In 1908, William Sealy Gosset used a special computer method called the Monte Carlo method simulation and discovered something called the Student’s t-distribution. Computers later made it easy to repeat his work.

Scientists also found ways to create random numbers using computers. These random numbers help in many types of statistical studies. In 1958, John Tukey created a method called the jackknife to improve statistical results, which also needed computers to work well. Computers have helped make many difficult statistical tasks much easier.

Methods

Computational statistics includes many useful methods for analyzing data. One important method is called maximum likelihood estimation. This method helps us guess the hidden details, or parameters, of how data is created. We do this by finding the settings that make our observed data most likely to happen.

Another useful method is called Monte Carlo. This method uses random numbers to solve problems that might seem fixed and certain. It is especially helpful for tough problems in physics and math. A related technique called Markov chain Monte Carlo uses chains of random steps to create samples that follow a specific pattern. Finally, bootstrapping is a way to repeat samples from our original data to understand how sure we can be about our guesses. There is also a related method called the jackknife.

Applications

Computational statistics is used in many different fields to help solve problems and make discoveries. Some areas where it is applied include computational biology, which studies living things; computational linguistics, which looks at language and how we use it; and machine learning, which helps computers learn from data. Other fields include data science, where we collect and analyze information to find patterns, and econometrics, which uses statistics to understand economics. This shows how important computational statistics is in many areas of science and everyday life.

Computational statistics journals

Here are some important journals where people share their ideas and research about computational statistics:

• Communications in Statistics - Simulation and Computation
• Computational Statistics
• Computational Statistics & Data Analysis
• Journal of Computational and Graphical Statistics
• Journal of Statistical Computation and Simulation
• Journal of Statistical Software
• The R Journal
• The Stata Journal
• Statistics and Computing
• Wiley Interdisciplinary Reviews: Computational Statistics

Associations

Computational statistics is closely linked with groups that bring together experts in statistics and computer science. One such group is the International Association for Statistical Computing, which supports the development and sharing of methods that use computers to advance statistical understanding.