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Re: fitting many linear eqs simultaneously with outliers [message #77969 is a reply to message #77967]

Thu, 13 October 2011 22:37

Matt Francis
Messages: 94
Registered: May 2010

Member

I have had reasonable success with noisy outlier full data using
AMOEBA (from IDL Astronomy User's Library) to minimise the following
fitness function derived in "Data Analysis:A Bayesian Tutorial" (D.S.
Sivia) section 8.3.1 (second edition):

F = SUM_i {1/(\sigma * \sqrt(2 \pi)) * [ (1 - exp(-R_i^2/2))/R_i^2]}

where R_i = (model - measured)/\sigma

and \sigma is your best a priori guess of the measurement error.

The fitness function above works remarkably well at toning down the
influence of outliers. The down side is that this doesn't use the
linearity of the equations at all, but AMOEBA works pretty efficiently
and your parameter space probably won't be too multi-modal so a
downhill solver should work fine.

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[Message index]

		Re: fitting many linear eqs simultaneously with outliers By: Jeremy Bailin on Mon, 17 October 2011 23:56
		Re: fitting many linear eqs simultaneously with outliers By: Craig Markwardt on Fri, 14 October 2011 18:46
		Re: fitting many linear eqs simultaneously with outliers By: Bringfried Stecklum on Fri, 14 October 2011 02:32
		Re: fitting many linear eqs simultaneously with outliers By: Matt Francis on Thu, 13 October 2011 22:37

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