There are three fundamental approaches to statistics: the traditional ‘‘classical’’ approach of null hypothesis significance testing, Fisherian statistics and the Bayesian approach. In General, we use null hypothesis significance testing in our regressions models, but what are the assupmtions that let us to use Bayesian approach in regression models ?
Thanks for your answer Professor,
In fact, what i really want to know is that if Bayesian Regression can slove some OLS Problems; like " the problems of multicollinearity" .. please find attached an article of Block, J. et al (2011), they did the same thing ..."Previous studies, due to problems of multicollinearity have been unable to distinguish these effects. Using a Bayesian approach that avoids these problems..."
To my knowledge, sloving this type of problems can be through :Ridge, LARS, LASSO, elastic net, k-Nearest Neighbours, Gaussian mixture model, Support or Relevance Vector Regression, PCA or PLS regression, Select attributes and then run regression (selection by stepwise, ...), Latent Class Regression ...
can Bayesian Regression really slove multicollinearity in regression ?
http://www.sciencedirect.com/science/article/pii/S1877858511000623
Bayesian approach can help with collinearity if you put strong priors on parameters - here is an example - you are imposing information to help the estimation
https://www.researchgate.net/publication/258073418_Bayesian_Informative_Priors_with_Yang_and_Land%27s_Hierarchical_Age-Period-Cohort_model
I have written a long reply to this question posted previously - I focus on estimation of complex models
https://www.researchgate.net/post/What_is_the_practical_rationale_of_Bayesian_statsitics_to_improve_estimation
Article Bayesian Informative Priors with Yang and Land’s Hierarchica...
Bayesian approach together with numerical methods lets you estimate models for panel data without the limitations of the classical approaches. You can specify any parametric distributions for priors and for regression equations and get exact results. So it is a more powerful approach.
With the use of the Bayesian approach it is also possible to incorporate prior judgmental knowledge, let me recommend you this paper:
Technical Report A joint Bayesian forecasting model of judgment and observed data
I think your question sort of misses the point, which is not surprising given how knowledge has become locculated.
bayesian inspired mcmc estimation can handle much more sophisticated (realistic??) model specifications, so for me it is much more flexible.
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