Bayes Position1 #249335 Bayesian Statistics |
From Wikipedia: Statistical inference Bayesian inference is an approach to statistical inference, that is distinct from the Neo-traditional frequentist inference. (The term Neo-traditional denotes that Bayesian methods pre-date the frequentist inference methods that dominated recent work.) It is specifically based on the use of Bayesian probabilities to summarise evidence. [edit]Statistical modelling The formulation of statistical models for use in Bayesian statistics has the additional feature, not present with other types of statistical techniques, of requiring the formulation of a set of prior distributions for any unknown parameters. Such prior distributions are as much part of the statistical model as the part that expresses the probability distribution of observations given the model parameters. The specification of a set of prior distributions for a problem may involve hyperparameters and hyperprior distributions. [edit]Design of experiments The usual considerations in the design of experiments are extended in the case of Bayesian design of experiments to include the influence of prior beliefs. Importantly, the application of sequential analysis techniques allow the outcome of earlier experiments to influence the design of the next experiment, based on the updating of beliefs as expressed by the prior and posterior distribution. Part of the problem of the design of experiments is that they should make good use of resources of all types: one example of the Bayesian design of experiments aimed at such efficiency is the multi-armed bandit problem. [edit]Statistical graphics Statistical graphics includes methods for data exploration, for model validation, etc. The use of certain modern computational techniques for Bayesian inference, specifically the various types of Markov chain Monte Carlo techniques, have led to the need for checks, often made in graphical form, on the validity of such computations in expressing the required posterior distributions. |
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CitationsAdd new citationList by: CiterankMap Link[1] Think Bayes: Bayesian Statistics Made Simple
Author: Allen B. Downey - Blog: http://allendowney.blo... Publication info: 2013 draft of a book, online Cited by: Jack Park 6:14 PM 5 February 2013 GMT URL: | Excerpt / Summary The premise of this book is that if you know how to program, you can use that skill to help you learn other topics, including Bayesian statistics. Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on distributions are simple loops. This presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without excessive concern about whether the model lends itself to conventional analysis. And while it’s true that the discrete computations I present here yield approximations of the results we would get from continuous functions, it is important to remember that both computations are based on models of a real system, and that any approximation errors (differences between the models) are almost always negligible compared to modeling errors (differences between the models and reality). |
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