[gmx-users] error estimates of free energy calculations

[Berk Hess]

>From: David van der Spoel <spoel at xray.bmc.uu.se>
>Reply-To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>Subject: Re: [gmx-users] error estimates of free energy calculations
>Date: Wed, 16 May 2007 08:12:57 +0200
>-->
>Berk Hess wrote:
>>
>>
>>
>>>From: "David Mobley" <dmobley at gmail.com>
>>>Reply-To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>>>To: "Discussion list for GROMACS users" <gmx-users at gromacs.org>
>>>Subject: Re: [gmx-users] error estimates of free energy calculations
>>>Date: Tue, 15 May 2007 15:55:01 -0700
>>>
>>>Jeroen,
>>>
>>>>However, in my opinion (assuming the total error should be calculated
>>>>from standard error propagation), the way g_analyze calculates the
>>>>total error is incorrect. It results in an overestimation of this
>>>>total error by at least a factor of sqrt((number of lambda points) -
>>>>1). This factor is 4.5 in my case, accounting for the larger part of
>>>>my previoulsy mentioned loss of accuracy. And indeed, as you guys
>>>>already mentioned, the remaining part may be explained from the fact
>>>>that Berk uses twice as many lambda values.
>>>
>>>Whoops! Justifies my paranoia about using other people's analysis
>>>tools. :) The person responsible for the analysis tool should take a
>>>look at this -- if the tool does error analysis for the integral, it
>>>should do it properly.
>>
>>ah, g_analyze indeed seems to print an error estimate of the integral,
>>I didn't know about this.
>>But according to me this is totally wrong.
>>It divides the sum of variances by n-1, whereas this should be n^2.
>>
>>I'll fix it for the next release.
>>
>It is the standard deviation, rigth? Which is what the source code says it 
>is...
>

>David.

I don't think the standard deviation of a integral has a meaning,
unless it means standard error...
The code sums the squares of the stddev's (thus the variance),
but without squaring the weights. This leads to a meaningless result.
And even then the endpoints are not correctly taken into account,
so one can not somehow simply correct the result.

As I said, I'll fix it this afternoon.
Currently I am at a conference.

Berk.

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