Bayesian statistics uses both prior and sample information. Usually something is known about possible parameter values before the experiment is performed.

The Bayesian approach allows direct probability interpretations of the parameters, given the observed data.

One can apply Bayesian analysis for a binomial proportion, a normal mean, the difference between normal means, the difference between proportions, and for a simple linear regression model. Bayesian methods will be contrasted with the comparable frequentist methods

Yes, you can do it with traditional statistical softwares like SAS and R.

There are whole books that attempts to answer these questions. To put it short and simple manner: The Bayesian approach can be presented as a generalization of the classical approach: the parameters are not fixed but unknown values ​​of random variables to specify the distribution. Distribution given at the time of modeling is known a priori. The integration of information provided by the data is done by calculating the so-called posterior distribution, which is none other than the conditional distribution (calculated by the formula of Bayes' theorem) to the values ​​taken by the data.

- Possibility to adapt to each situation,

- Use of all relevant information,

- Provides information for decision making,

- Taking into account the existing information.

The approach is to update the prior beliefs on

event in the light of new information for a quantitative description of current knowledge.

For example we use the statistical tools on count data on the avifauna of the entire coastline. This approach takes into account parameters during data acquisition (eg weather conditions).

These are tools that can be useful in modeling, but still quite complex to implement. The computation time can be very long (several hours to several days).

The reference software is WinBUGS that can be associated with R (R2WinBUGS library).

A books :

- Bayesian Computation with R, Albert, 2009

Thanks a lot Alain for this prosperous information

Thanks Poornima

Is Bayesian statistic is robust with small sample sizes?

@Alessandro, Bayesian methodology does *not* require normality and does *not* require independence. Bayesian methods *do* require careful and appropriate modelling of the joint distribution of the data p(x | theta), and careful and appropriate modelling of your prior beliefs concerning the parameters p(theta). The rest is just an application of Bayes' rule "posterior odds equals prior odds times likelihood ratio", or equivalently: "posterior density p(theta | x) is proportional to prior density p(theta) times likelihood p(x | theta)". The technology of Bayesian statistics in practice is all about clever ways to compute the posterior, and about ways to model data and to model prior information which make the computation of the posterior more easy, and so on.

@Abdullah: no; parametric Bayesian modelling is not robust at small sample sizes. Non-parametric Bayesian modelling is technically challenging and full of mine-fields since a prior for very high dimensional priors might superficially appear to represent ignorance, but actually turn out to represent rather sharp pre-knowledge about some aspects of the parameters. This leads to the phenomenon of inconsistency of non-parametric Bayes estimators unless the prior is subtly adjusted to the sample size.

Richard, how big the sample size should be?

Jochen, what are the correct statements?

Thanks all

@Abdullah: you ask "how big should the sample size be"? Just as in classical frequentist statistics there is no one answer to this question. It depends on everything. You might do some simulation experiments in order to get an idea of how good things are working for your specific situation.

I would not say that Bayesian statisticus generalizes classical, nor even that it is a step beyond... It is quite simply a *different* paradigm. The notion of probability is different, and the notion of inference is different. On top of a different kind of probability one builds a different kind of statistics. I would say that both paradigms are models and I would remind everyone that all models are wrong but some are useful. Models are idealizations. If we idealize our ideas of probability and our ideas of inference in one direction we get to Bayesian statistics, if we go in another direction we get to classical frequentist statistics (in several versions: Fisherian; decision theoretic; ...). A real life problem may or may not fit well into either of these extreme "pure" models. Idealizations, models, ... are simplifications - one discards some features of the real world, one emphasizes others.

In the real world, life is difficult, especially for a good statistician.

Hi,

You may want to check out this GUI for R named R2STATS that can be used to perform mixed-models analyses (with many distribution laws, not only normal law). You will need to take a model comparison approach if you go Bayesian. It also gives the frequentist approach output (for simpler models).

For Bayesian analysis on proportions (binomial distribution and non-numeric independent variables), contingency tables and more (multinomial distribution and non-numeric independent variables), there is AtelieR GUI under R, but to my best knowledge the interface is only available in French.

HTH.

Cheers,

SCM

what is bayesian method in data analysis?with brief and simple explanations pleaseeee

@jochen wilhelm, thank you for ur comments

Bayesian statistics require prior probabilities to enrich the current state of knowledge. All scientific inferences have been drawn on approaches: frequentist (or frequency probability) or Bayesian (or inductive probability). Bayesian analysis is primarily concerned with the analysis of data to assist in arriving at an improved understanding of some underlying mechanism, and statistician’s task is then to explain uncertainty and reduce the extent of possibility. Also, The Bayesian approach to data analysis requires a different set of assumptions and computational tools than the classical approaches in many sciences. However, typical applications of the Bayesian method involve estimation of an unobservable parameter that describes an entire population using observable (objective) data derived by sampling.