1 / 6

Two approaches to statistical inference

Two approaches to statistical inference. “Bayesian approach” & “Frequentist approach”. Principle of Bayesian approach. Probability as a measure of personal uncertainty : degree of belief All information presented with probability

mercia
Download Presentation

Two approaches to statistical inference

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Two approaches to statistical inference “Bayesian approach” & “Frequentist approach”

  2. Principle of Bayesian approach • Probability as a measure of personal uncertainty : degree of belief • All information presented with probability • Information combined and updated by using the rules of probability calculus • Most important output: posterior probability • state of information after seeing the observations

  3. Properties of Bayesian approach • Can assess hypotheses of many kind • Prediction of new observations • Values of unobserved variables • Current, future and past events or propositions • Requires typically high computation power • -> started to gain popularity not before than 15 years ago • Controversial as it breaks the illusion of objectivity

  4. Frequentist approach • Defines probability as “Limiting relative frequency of independent trials” • = Infinite number of trials : imagine that the data set would be collected for very large number of times while the state of nature remains unchanged • Tossing a bottle cap: the relative frequency of tosses in which the cap is upside down within infinite number of tosses. • There is no probability defined for the position of the cap in any specific toss • Frequency probability can be defined only to observables that are thought to vary because of random sampling: the true state of the world can not have frequency probability

  5. Frequentist/classical/sampling approach • Three main areas • Hypothesis testing (p-values) • Point estimation • Interval estimation • Formal inference about hypothetical data: • How often one would get more extreme data if the assumed hypothesis was true and the sampling was infinitely repeated? • How would an estimator behave in future repetitions, if the estimate we have now was equal to the true value • Indirect inference about the state of the world: no measure of uncertainty

  6. Which one to choose for a problem?

More Related