What are Bayesian intervals and how do they work?

What are Bayesian intervals and how do they work?

Bayesian intervals, also known as credible intervals, are a range of values derived from Bayesian statistics that contain the true parameter value with a certain probability. They provide a way to quantify uncertainty in parameter estimates.

How do they differ from confidence intervals?

The key difference is that confidence intervals are frequentist and interpret the interval in terms of long-run frequency, while Bayesian intervals provide a direct probability statement about the parameter being within the interval.

Can you give me an example of how to calculate a Bayesian interval?

Sure! Suppose we have a posterior distribution for a parameter that is normally distributed. To calculate a 95% credible interval, you would find the values that contain 95% of the distribution's area.

What are some practical applications of Bayesian intervals?

They are widely used in fields like medicine for estimating treatment effects, in finance for risk assessment, and in machine learning for model uncertainty.