Bayesian Statistics Flashcards
Compare and contrast classical hypothesis testing and the Bayesian inference approach
Classical hypothesis testing:
Define a null and alternate hypothesis
Calculate a p value, and accept or reject the null hypothesis
Bayesian inference approach:
Define a knowledge prior to the study (e.g., from literature). If not much data exists then you may have a “lowly informative”, or even “non-informative” prior. In this case, the data gathered in the trial will have the greater impact on the posterior than if you have an informative prior.
Acquire the data
Revision of the prior information to form posterior estimates (after the trial)
Interpretations of the resulting posterior estimates
Compare and contrast classical hypothesis testing and the Bayesian inference approach summary statistics
Classical hypothesis testing:
Produces p value - probability. Only provides evidence against H0 (null).
95% confidence interval - there is 95% probability that the true value in the population is likely to lie with 95% confidence
Bayesian inference approach:
Bayes factor - ratio of the likelihood of H0 (null) to H1 (alternate). Provides evidence for and against H0.
Odds ratio - the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure
95% Credible interval - there is a 95% probability that the true value lies within this range.
what is the positive predictive value (PPV)
positive predictive value (PPV) of a test is the proportion of persons who are actually positive out of all those testing positive.
PPV = True Positive / Tested positive
Using Bayes’ therom to calculate PPV if sensitivity, specificity and prevalence are known
What is the posterior probability
The probability of success can be defined as the probability of an event occurring given some prior information and observed data.
The revised or updated probability of an event occurring after taking into consideration new information
What is a conjugate prior?
When the prior and posterior distributions belong to the same family of distributions
Define probability
Probability is the likelihood of an event occurring.
Define conditional probability
Conditional probability is a measure of the probability of an event occurring given that another event has already occurred.
Define voxel
A voxel (volume element) is the 3D version of a pixel (picture element)
Give an example of how Bayes’ theorem is used
Tissue segmentation in neuroimaging
* Bayes’ Theorem is used to determine the probability of tissue types within magnetic resonance images.
