Need a recommendation of a book on Bayesian Inference methods for NON-normal distributions. Weibull and exponential preferred if possible. IE, I need to derive the posterior distribution without using a standard deviation and mean.
I somehow doubt any of you can help... but who knows ;) Shot in the dark as I begin to delve into the subject. I need to be an expert by the beginning of December.
Hmm, well a few years ago turned into over a decade ago on those papers - time sure flies. Not sure how much help I can be - more of a multivariate stats guy - and I didn't go into non-normal distributions with Bayesian stats. There were a couple of references I had to articles that might be relevant. Don't really have a book I can recommend. Sorry I'm not more helpful. Here's the references I came across that might be relevant.
Smith & Naylor (1987) - A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution
Erto (1982) - New practical Bayes estimators for the 2-parameter Weibull distribution
Achcar & Louzada-Neto (1992) A Bayesian approach for accelerated life tests considering the Weibull distribution
Giuntini & Giuntini (1993) Simulating a Weibull posterior using Bayes inference
Well what do ya know, it works :)
Premise is this, given prior information of an exponential distribution (at least it's likely it is.. either that or some weibull form) of a failure rate in terms of reliability, retest with new information and determine the true reliability rate.
The system overall has been modified but only a few subcomponants have changed hardware wise, the rest being software. We are making the assumption that the software changes are not be significantly impacting reliability but we will have tests done to gain that data, but we think that the amount of data gained will be insufficient for classical statistical methods (not enough failures observed)... hence the need to fall back on prior data and bayesian stats.
All methods I could find online are for normally distributed distributions and i'd like to find generalized methods for any distribution. In the end, we are likely going to monte carlo it, but as a precurser to that stage i'd like to understand the theory so I can ensure that our simulation is accurate and I can write up the basis of it.
Wow, never expected to get a Bayesian stats question on this board. I'll look through some of my references and see what's there. I did some papers on Bayesian stats a few years back but frankly haven't thought about it at all since.
Cool thanks! I think I found enough info to use WinBugs intelligently (a program for monte carlo simulations with Bayesian Inferences). The theory sounds simple enough... take your prior distribution and convolute it with your new data set. It's just icky on the actual mechanics of doing so.
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