Bayesian Analysis Task
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A Bayesian Analysis Task is a statistical analysis that is based on the Bayesian Axiom System (of Bayesian probability and the application of Bayes' rule).
- AKA: Bayesian Statistics.
- Context:
- It can be solved by a Bayesian Analysis System (that implements a Bayesian inferencing algorithm).
- …
- Counter-Example(s):
- See: Bayesian Estimator, Bayesian Inference, Bayesian Experiment, Bayes' Rule, Sequential Analysis, Decision Theory, Bayesian Probability, Likelihood Principle.
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Bayesian_inference Retrieved:2014-5-17.
- In statistics, Bayesian inference is a method of inference in which Bayes' rule is used to update the probability estimate for a hypothesis as additional evidence is acquired. Bayesian updating is an important technique throughout statistics, and especially in mathematical statistics. For some cases, exhibiting a Bayesian derivation for a statistical method automatically ensures that the method works as well as any competing method.
Bayesian updating is especially important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a range of fields including science, engineering, philosophy, medicine and law.
In the philosophy of decision theory, Bayesian inference is closely related to discussions of subjective probability, often called “Bayesian probability”. Bayesian probability provides a rational method for updating beliefs.
- In statistics, Bayesian inference is a method of inference in which Bayes' rule is used to update the probability estimate for a hypothesis as additional evidence is acquired. Bayesian updating is an important technique throughout statistics, and especially in mathematical statistics. For some cases, exhibiting a Bayesian derivation for a statistical method automatically ensures that the method works as well as any competing method.
- (Macke, 2014) ⇒ Jakob H. Macke. (2014). “Electrophysiology Analysis, Bayesian”. In: Encyclopedia of Computational Neuroscience.
- QUOTE: Bayesian statistics is a framework for describing empirical data and modelling empirical data using the mathematical language of probability to model uncertainty. Bayesian statistics provides a principled and flexible framework for combining empirical observations with prior knowledge and for quantifying uncertainty. These features are especially useful for analysis questions in which the dataset sizes are small in comparison to the complexity of the model, which is often the case in neurophysiological data analysis.
- (Klarreich, 2014) ⇒ Erica Klarreich. (2014). “In Search of Bayesian Inference.” In: Communications of the ACM Journal, 58(1). doi:10.1145/2686734
2012
- http://www.uv.es/valenciameeting
- Statistics is primarily concerned with the analysis of data, either to assist in the appreciation of some underlying mechanism, or to reach effective decisions. In both cases, some uncertainty resides in the situation and the statistician's tasks are both to reduce this uncertainty and to explain it clearly. Problems of this type occur throughout all the physical, social and other sciences. One way of looking at statistics stems from the appreciation that all uncertainty must be described by probability: that probability is the only sensible language for a logic that deals with all degrees of uncertainty, and not just with the extremes of truth and falsity. This is called Bayesian Statistics. Decision-making is embraced by introducing a utility function, itself probability-based, and then maximizing expected utility. Bayesian statistics is designed to handle all situations where uncertainty is found. Since some uncertainty is present in most aspects of life, it is held that Bayesian statistics should be appreciated and used by everyone. It is the logic of contemporary society. It is 'common sense reduced to calculation.'
2010
- (Hagan & West, 2010) ⇒ Anthony O' Hagan, and Mike West, editors. (2010). “The Oxford Handbook of Applied Bayesian Analysis." ISBN:0191613894
2006
- (Cox, 2006) ⇒ David R. Cox. (2006). “Principles of Statistical Inference." Cambridge University Press. ISBN:9780521685672
- QUOTE: Key ideas about probability models and the objectives of statistical analysis are introduced. The differences between frequentist and Bayesian analyses are illustrated in a very special case.