Statistics / Bayesian inference · BEGINNER LESSON
Non-informative
A non-informative prior distribution is a Bayesian prior chosen to have little or no influence on the result, so the current data mostly determine the posterior distribution. In some measurement settings, it is used when only the current observations should be used and no prior information is added.
What it is
In Bayesian inference, a prior distribution is the starting probability description of unknown model parameters before the data are observed. A non-informative prior is selected to keep that starting description from strongly pulling the answer in any direction, so the data can “speak for themselves.” In one measurement framework, a non-informative prior is specifically used when only current observations should contribute to the posterior and no prior information should be used.
[1] Selection of Prior Distributions When Analyzing Clinical Trial Data Using ... [2] 1 March 16, 2011 Only non-informative Bayesian prior distributions ... [3] An Investigation of Non-Informative Priors for Bayesian Dose ... - PMC
How it works
Bayes’ theorem combines the prior distribution with the observed data through the statistical model to produce the posterior distribution, which is the updated distribution after the data are seen. If the prior is non-informative, its role is intended to be small, so posterior results such as a treatment effect estimate depend mainly on the data. A common example mentioned in clinical trial analysis is a normal prior centered at 0, meaning no treatment effect, with a large spread; the wide spread makes the prior diffuse rather than concentrated. In measurement work, a non-informative improper prior may be used for Type A evaluation, where Type A means an evaluation based on repeated observations and conventional statistics; here the goal is an unbiased central measured value from the current observations alone.
[1] Selection of Prior Distributions When Analyzing Clinical Trial Data Using ... [2] 1 March 16, 2011 Only non-informative Bayesian prior distributions ...
Why people use it
People use non-informative priors when they do not want to add subject matter knowledge, historical trial data, or investigator optimism/pessimism to the analysis. This is useful when the analyst wants a more data-driven posterior. In some settings, such priors are used because they can give results close to conventional statistical estimates. However, the sources also note that in some models, such as dose-response analysis, a prior that is intended to be non-informative for one parameter can still influence other quantities, so complete non-informativeness may not be possible for all targets at once.
[1] Selection of Prior Distributions When Analyzing Clinical Trial Data Using ... [3] An Investigation of Non-Informative Priors for Bayesian Dose ... - PMC
Limitations
A non-informative prior is not a magic way to remove assumptions. The choice of prior can still matter, and some priors called non-informative can still add information or create bias for certain questions. One source also notes that some non-informative priors are improper, meaning they do not integrate to one and therefore are not proper probability density functions. Another limitation is that a prior that leaves one parameter largely uninformed may still affect other parameters or other endpoints.
[2] 1 March 16, 2011 Only non-informative Bayesian prior distributions ... [3] An Investigation of Non-Informative Priors for Bayesian Dose ... - PMC
SEE THE IDEA
How a non-informative prior enters Bayesian analysis
Starting description of unknown parameters before data are seen; non-informative means minimal intended influence.
Current measurements or trial results supplied by the study or experiment.
Updated distribution after Bayes’ theorem combines prior and data.
Prior and observed data are combined to produce the posterior; a non-informative prior is chosen to contribute as little as possible.
A non-informative prior is meant to leave most of the updating work to the data, but it may still influence some results.
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.