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- bayesian - Flat, conjugate, and hyper- priors. What are they? - Cross . . .
Today, Gelman argues against the automatic choice of non-informative priors, saying in Bayesian Data Analysis that the description "non-informative" reflects his attitude towards the prior, rather than any "special" mathematical features of the prior (Moreover, there was a question in the early literature of at what scale a prior is
- When are Bayesian methods preferable to Frequentist?
The Bayesian, on the other hand, think that we start with some assumption about the parameters (even if unknowingly) and use the data to refine our opinion about those parameters Both are trying to develop a model which can explain the observations and make predictions; the difference is in the assumptions (both actual and philosophical)
- Posterior Predictive Distributions in Bayesian Statistics - Physics Forums
Confessions of a moderate Bayesian, part 4 Bayesian statistics by and for non-statisticians Read part 1: How to Get Started with Bayesian Statistics Read part 2: Frequentist Probability vs Bayesian Probability Read part 3: How Bayesian Inference Works in the Context of Science Predictive distributions
- How to choose prior in Bayesian parameter estimation
The problem is that if you choose non-conjugate priors, you cannot make exact Bayesian inference (simply put, you cannot derive a close-form posterior) Rather, you need to make approximate inference or use sampling methods such as Gibbs sampling, Rejection sampling, MCMC, etc to derive you posterior
- Help me understand Bayesian prior and posterior distributions
See also this reference for a short but imho good overview of Bayesian reasoning and simple analysis A longer introduction for conjugate analyses, especially for binomial data can be found here A general introduction into Bayesian thinking can be found here More slides concerning aspects of Baysian statistics are here
- Should Bayesian inference be avoided with a small sample size and . . .
With small n and no reliable prior, instead of a Bayesian analysis---or even a Frequentist analysis (which may just confirm that "The sample is too small to estimate these parameters with adequate precision")---I would just report descriptive statistics graphs and be very transparent about the study's limitations: due to the sample size, our
- What is the best introductory Bayesian statistics textbook?
My bayesian-guru professor from Carnegie Mellon agrees with me on this having the minimum knowledge of statistics and R and Bugs(as the easy way to DO something with Bayesian stat) Doing Bayesian Data Analysis: A Tutorial with R and BUGS is an amazing start You can compare all offered books easily by their book cover!
- Simple real world examples for teaching Bayesian statistics?
Bayesian statistics allows one to formally incorporate prior knowledge into an analysis I would like to give students some simple real world examples of researchers incorporating prior knowledge into their analysis so that students can better understand the motivation for why one might want to use Bayesian statistics in the first place
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