On Dec 16, 2015, at 6:54 AM, Leo Fang <leofang@phy.duke.edu> wrote:

Hello, 

I have a follow-up question, which I am not sure if it is rooted in MC simulations, or it is a unique property of the ALPS library.

If a MC simulation is done and results are recorded, and the error estimates of every physical quantities are small enough to be neglected, but the autocorrelation time tau is very large (>10) and becomes even larger when the number of MC steps is increased, should I be worried about the validity of estimated results? Does it make sense if I increase the number of thermalization steps (so that the ratio to the number of MC steps is significant, although for now my observation is that this does not help reduce tau)?

Thank you.

Sincerely,

Leo (Fang Yao-Lung)

Duke Physics 

2015-12-15 16:19 GMT-05:00 Matthias Troyer <troyer@phys.ethz.ch>:

Yes, indeed, it’s also in that paper

On 15 Dec 2015, at 22:18, Leo Fang <leofang@phy.duke.edu> wrote:

Dear Prof. Troyer,

It's very clear, thank you! I also found that the tau() calculation implemented in simplebinning.h is explained in detail in your paper arXiv:0906.0943.

Sincerely,

Leo (Fang Yao-Lung)

Duke Physics 

2015-12-15 13:45 GMT-05:00 Matthias Troyer <troyer@phys.ethz.ch>:

> On Dec 15, 2015, at 19:35, Leo Fang <leofang@phy.duke.edu> wrote:
>
> Hello,
>
>
> After the Monte Carlo simulation is done, the time series as well as the autocorrelation time (tau) for each observable are recorded in the path /simulation/results/ of the hdf5 file. (For example, /simulation/results/observable/timeseries/data gives the time series.) I have two questions:
>
> 1. What determines the length of the time series array? In my experience its typical size is around 100. How does ALPS decide to cut the array?

By default it bins the time series into 64-127 bins, each containing averages of a growing number of measurement as you record more. Thus, at first each bin contains one value each until we get to 128 values, then always two get averaged so that you have 64 bins containing averages of 2. As you go to 256 values this is reduced to 64 bins, each averaging 4, and so on
>
> 2. If the binning method is not specified, what's the default way of calculating tau? I've tried to calculate the integrated autocorrelation time using the recorded time series, but it's not exactly same as tau given by ALPS.

The easiest might be if you look at slides of ALPS talks on MC sampling or at the code in simplebinning.h

>
> Thank you.
>
>
> Sincerely,
> Leo (Fang Yao-Lung)
> Duke Physics