Computational statistics

Computational statistics, also known as statistical computing, is the fun mix of statistics and computer science. It uses computers to do hard statistical methods that are too tricky to calculate by hand. This field is part of computational science, which uses computers to solve science problems, but it focuses on statistics.

Just like in traditional statistics, the goal is to change raw data into useful knowledge. Computers help scientists work with huge amounts of information, called sample size, and with mixed data sets.

The words 'computational statistics' and 'statistical computing' usually mean the same thing. Some experts say they have small differences in meaning. One expert says 'statistical computing' is about using computers to apply statistical methods, while 'computational statistics' is about creating new computer steps to do statistical methods, like the bootstrap and simulation.

Computational statistics has many strong tools that need a lot of computer work. 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 find patterns and make guesses from complicated information.

History

Computational statistics has a short but important history. Long ago, statisticians mainly used math. 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. Later, computers made it easy to repeat his work.

Scientists also learned to create random numbers using computers. These random numbers help in many statistical studies. In 1958, John Tukey created a method called the jackknife to improve results. Computers helped make many difficult tasks 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 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. 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.

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 helps us solve problems and make discoveries in many different fields. It is used in computational biology, which studies living things. It is also used in computational linguistics, which looks at language and how we use it.

Machine learning uses computational statistics to help computers learn from data. In data science, we collect and analyze information to find patterns. Econometrics uses statistics to understand economics. This shows how useful computational statistics is in science and everyday life.