[R] MLE for bimodal distribution

[(Ted Harding)]

On 08-Apr-09 23:39:36, Ted Harding wrote:
> On 08-Apr-09 22:10:26, Ravi Varadhan wrote:
>> EM algorithm is a better approach for maximum likelihood estimation
>> of finite-mixture models than direct maximization of the mixture
>> log-likelihood.  Due to its ascent properties, it is guaranteed to
>> converge to a local maximum.  By theoretical construction, it also
>> automatically ensures that all the parameter constraints are
>> satisfied.
>> [snip]
>> Be warned
>> that EM convergence can be excruciatingly slow.  Acceleration methods
>> can be of help in large simulation studies or for bootstrapping.
>> 
>> Best,
>> Ravi.
> 
> [snip]
> As to acceleration: agreed, EM can be slow. Aitken acceleration
> can be dramatically faster. Several outlines of the Aitken procedure
> can be found by googling on "aitken acceleration".
> 
> I recently wrote a short note, describing its general principle
> and outlining its application to the EM algorithm, using the Probit
> model as illustration (with R code). For fitting the location
> parameter alone, Raw EM took 59 iterations, Aitken-accelerated EM
> took 3. For fitting the location and scale paramaters, Raw EM took
> 108, and Aitken took 4.
> 
> If anyone would like a copy (PS or PDF) of this, drop me a line.

I have now placed a PDF copy of this, if anyone is interested
(it was intended as a brief expository note), at:

  http://www.zen89632.zen.co.uk/R/EM_Aitken/em_aitken.pdf

Best wishes to all,
Ted.

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Date: 10-Apr-09                                       Time: 17:15:06
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