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Re: Re: bug in RandomChoice if weight is zero?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106074] Re: [mg106027] Re: [mg105976] bug in RandomChoice if weight is zero?
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Thu, 31 Dec 2009 03:21:07 -0500 (EST)
  • References: <200912290617.BAA02582@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

> Generally, what you ask for should be possible once you give a specific
> interpretation of what you mean by zero

What's ambiguous about the Integer 0?

Bobby

On Wed, 30 Dec 2009 03:17:21 -0600, Leonid Shifrin <lshifr at gmail.com>  
wrote:

> Hi Matthias,
>
> presumably this is because RandomSample never samples any given element  
> more
> than once - in that case it has no other choice, regardless of the  
> weight.
> Perhaps, the error message might be added for exact symbolic zero  
> appearing
> somewhere in the wieights for the case where the size of the desired  
> sample
> is larger than the number of non-zero weights (non-zero means
> UnsameQ[weight,0]).  It is not clear however whether it is worth it given
> the overhead of such an analysis. Besides, this will be a point solution
> anyway, since some expressions that might be used for weights may be in  
> fact
> identically equal to zero but just not simplified to zero - these cases
> would not be caught by such an analysis.
>
> OTOH, it is hard to make a formal (not based on syntax) distinction  
> between
> zero and some very small weight close to zero (which may be expressed not
> necessarily with machine precision). This of course depends on the
> implementation of the underlying algorithm used to do the sampling -  
> whether
> or not it treats weights smaller than machine epsilon as zero. From the
> point of view of the abstract interface of RandomSample, there is no  
> reason
> why it should do that, even if such events are highly unlikely to be
> sampled.
>
> Generally, what you ask for should be possible once you give a specific
> interpretation of what you mean by zero, but arguably this would add more
> ambiguities/restrictions than it is worth for a kind of a general-purpose
> function that RandomSample is. After all, you can always wrap  
> RandomSample
> in your own wrapper function which will implement this functionality in  
> the
> way you want it (consistent with your definition of zero), while  
> preserving
> the syntax of the original RandomSample.
>
> Regards,
> Leonid
>
>
>
>
>
> On Tue, Dec 29, 2009 at 9:17 AM, Matthias Greiff <greiff at mac.com> wrote:
>
>> If I use RandomChoice with weights of zero the corresponding elements  
>> will
>> never be selected.
>>
>> In[62]:= RandomChoice[{0, 0, 3} -> {3, 2, 1}, 5]
>> Out[62]= {1, 1, 1, 1, 1}
>>
>> Why is it not the same if I use RandomSample?
>> The following command
>>
>> RandomSample[{1, 2, 0} -> Range[3], 2]
>>
>> returns either {1,2} or {2,1}. But when I change the command to sample  
>> size
>> 3  I get the following.
>>
>> In[60]:= RandomSample[{1, 2, 0} -> Range[3], 3]
>> Out[60]= {2, 1, 3}
>>
>> Why is the third element selected? Shouldn't Mathematica return an error
>> message because the sample size is larger than the population size?
>>
>> Appreciate your answers.
>>
>> Merry Christmas!
>>
>> Matthias
>>
>>


-- 
DrMajorBob at yahoo.com


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