This website is using cookies to ensure you get the best experience possible on our website.
More info: Privacy & Cookies, Imprint
In Bayesian statistics, estimates are calculated using Bayes' theorem and the concept of conditional probability. Bayes' theorem states that the probability of event A given that event B has occurred divided by the probability of event B given that event A has occurred and the probability of event A divided by the probability of event B.
In Bayesian statistics, estimates are made based on existing information and prior knowledge about the parameter being estimated. The estimation process consists of the following steps:
Determining a priori distribution: Before starting the data analysis, a priori distribution is determined for the parameter to be estimated. The priori distribution expresses the initial knowledge or uncertainty about the parameter before looking at the data.
Collection of data: Data is collected to enable estimation of the parameter. The data can come from experiments, surveys or other observations.
Prior distribution update: Combining the prior distribution with the observed data calculates the posterior distribution. The posterior distribution gives the updated probability distribution of the parameter considering the observed data.
Calculation of the estimate: The estimate of the parameter is derived from the a posteriori distribution. This can be done by various methods, such as choosing the maximum a posteriori (MAP estimation) or calculating the expected value of the a posteriori distribution.
Evaluation of the estimate: The quality of the estimate can be evaluated using various criteria, such as the mean square deviation or the confidence interval.
The Bayesian estimation approach allows existing knowledge to be combined with observed data to improve estimates. By accounting for priori knowledge, Bayesian statistics can be particularly beneficial when data is limited or when estimating rare events.