tag:blogger.com,1999:blog-4453805095942812863.post8189704708619604694..comments2024-02-23T02:14:03.787-08:00Comments on Surprise and Coincidence - musings from the long tail: Sampling Dirichlet DistributionsTed Dunning ... apparently Bayesianhttp://www.blogger.com/profile/02498665124454933570noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-4453805095942812863.post-60758243694801709492011-02-16T06:02:28.447-08:002011-02-16T06:02:28.447-08:00Dear Ted,
Thank you for posting this. My question...Dear Ted,<br /><br />Thank you for posting this. My question may be related to Andrei's and Scott's. <br /><br />I'm implementing a Gibbs sampler for a model which has N Dirichlet distributions (\pi) of which the parameters are like you describe in your post: another Dirichlet (m) and a multiplier which is exponential or gamma (\alpha). I have noticed that the posterior distribution of this multiplier (\alpha) is gamma, and I was wondering whether both its shape and scale parameters could be derived given m and the N \pi's (and the prior of \alpha). Do you have any idea if this is possible? Thank you.Jeroen Janssenshttps://www.blogger.com/profile/01767301744767984619noreply@blogger.comtag:blogger.com,1999:blog-4453805095942812863.post-91039496614306908792010-04-06T18:41:44.106-07:002010-04-06T18:41:44.106-07:00I just started a series of postings that will answ...I just started a series of postings that will answer these questions.Ted Dunning ... apparently Bayesianhttps://www.blogger.com/profile/02498665124454933570noreply@blogger.comtag:blogger.com,1999:blog-4453805095942812863.post-74419143388029481852010-04-05T08:55:11.583-07:002010-04-05T08:55:11.583-07:00The problem I am trying to solve is the following:...The problem I am trying to solve is the following:<br /><br />Assume x - Dir(\pi). From what I understand you present a sampling scheme for a prior on \pi: <br />m - Dir(\beta) <br />\alpha - exp(\beta_0) <br />\pi=\alpha m <br /><br />Can one derive the the posterior distribution of \pi | x in terms of \beta; \beta_0 and x? <br /><br />Where: x,\pi,\beta,m are vector and \beta_0,\alpha are scalars.<br /><br />I hope this makes my question clear.<br />Thank youAndyhttps://www.blogger.com/profile/03703732142037185915noreply@blogger.comtag:blogger.com,1999:blog-4453805095942812863.post-48801073190577598682010-04-04T18:57:48.235-07:002010-04-04T18:57:48.235-07:00Andrei,
Can you be a bit more specific? It is pr...Andrei,<br /><br />Can you be a bit more specific? It is pretty straightforward if you are sampling from a multinomial whose parameters are Dirichlet distributed, but I think you have in mind something more interesting.Ted Dunning ... apparently Bayesianhttps://www.blogger.com/profile/02498665124454933570noreply@blogger.comtag:blogger.com,1999:blog-4453805095942812863.post-82540496331993224762010-04-02T14:24:23.560-07:002010-04-02T14:24:23.560-07:00Related to the post on Andrew Gelman's blog - ...Related to the post on Andrew Gelman's blog - Is there a way to take data into account? Can one derive a posterior sampling scheme for the Dirichlet parameter based on the prior sampling scheme you propose here?<br />Do you know any references for this material besides 'The Bayesian Choice'?<br /><br />Thank youAndyhttps://www.blogger.com/profile/03703732142037185915noreply@blogger.comtag:blogger.com,1999:blog-4453805095942812863.post-89929671013273030222010-01-06T09:53:13.261-08:002010-01-06T09:53:13.261-08:00This seems like a promising approach, but how do y...This seems like a promising approach, but how do you compute the MAP dirichlet parameters, given observed data (probability vectors) ? Even better, how do you sample from the posterior ??<br /><br />thanksUnknownhttps://www.blogger.com/profile/13592538740717806901noreply@blogger.com