## What is Bayesian statistics?

Author: **John Stevens**

Statistical inference concerns unknown **parameters **that describe certain population characteristics such as the true mean efficacy of a particular treatment. **Inferences **are made using data and a statistical model that links the data to the parameters.

In frequentist statistics, parameters are fixed quantities, whereas in Bayesian statistics the true value of a parameter can be thought of as being a random variable to which we assign a probability distribution, known specifically as **prior information**.

A Bayesian analysis synthesises both sample data, expressed as the **likelihood function**, and the prior distribution, which represents additional information that is available.

The **posterior distribution **expresses what is known about a set of parameters based on both the sample data and prior information.

In frequentist statistics, it is often necessary to rely on large-sample approximations by assuming **asymptomatic normality**. In contrast, Bayesian inferences can be computed exactly, even in highly complex situations.