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Analyzing Large Numbers of Variables—Microarrays, EEG's, MRI's.  This
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Modeling with R.  Three lessons in three weeks. July 9th to 31st 2010. 

quasi-monte carlo integration for mixed discrete and continuous variables

Re: quasi-monte carlo integration for mixed discrete and continuous variables

Quasirandom sequences typically fall in [0,1]. You can model either 
continuous or discrete variables by scaling (continuous) or 
decision-point discretization (discrete). E.g., for a binary 
variable, code "0" for the quasirandom number < 0.5 and "1" if greater.

I would suggest Halton or Hammersley sequences as an initial method 
to consider.

At 01:22 AM 6/4/2010, Wei Ye wrote:
>Hi, all,
>
>Are there any low-discrepancy sequences to do quasi-monte carlo 
>integration for a multivariate distribution with both discrete and 
>continuous variables?
>For example, the continuous variable (A) follows a normal 
>distribution and the discrete variable (B) is binary. The mean 
>of  the normal distribution  depends on the value of B.
>
>Can S-plus generate such sequences?
>
>Thanks.
>
>
>

================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral <at> lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"
================================================================

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Re: quasi-monte carlo integration for mixed discrete and continuous variables

Thank you.

It is  not a problem to generate the points for either a binary variable or a continuous variable. My question
is how to generate the points for both a binary variable and a continuous variable with the latter
distribution depending on the value of the former.

----- Original Message ----
From: Robert A LaBudde <ral <at> lcfltd.com>
To: Wei Ye <weiye1 <at> yahoo.com>
Cc: s-news <at> wubios.wustl.edu
Sent: Fri, June 4, 2010 2:14:05 AM
Subject: Re: [S] quasi-monte carlo integration for mixed discrete and continuous variables

Quasirandom sequences typically fall in [0,1]. You can model either continuous or discrete variables by
scaling (continuous) or decision-point discretization (discrete). E.g., for a binary variable, code
"0" for the quasirandom number < 0.5 and "1" if greater.

I would suggest Halton or Hammersley sequences as an initial method to consider.

At 01:22 AM 6/4/2010, Wei Ye wrote:
> Hi, all,
> 
> Are there any low-discrepancy sequences to do quasi-monte carlo integration for a multivariate
distribution with both discrete and continuous variables?
> For example, the continuous variable (A) follows a normal distribution and the discrete variable (B) is
binary. The mean of  the normal distribution  depends on the value of B.
> 
> Can S-plus generate such sequences?
> 
> Thanks.
> 
> 
> 

================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral <at> lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"
================================================================

      
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Re: quasi-monte carlo integration for mixed discrete and continuous variables

Thanks. But I am asking how to generate quasi monte carlo points, not pseudo random points. 

Quasi monte carlo points are deterministic.

----- Original Message ----
From: "Benoist, Christophe O." <Christophe_Benoist <at> hms.harvard.edu>
To: Wei Ye <weiye1 <at> yahoo.com>; Robert A LaBudde <ral <at> lcfltd.com>
Cc: "s-news <at> wubios.wustl.edu" <s-news <at> wubios.wustl.edu>
Sent: Fri, June 4, 2010 8:56:29 AM
Subject: RE: [S] quasi-monte carlo integration for mixed discrete and continuous variables

How about:

n_1000
mn_0
std_1
x<-sample(c(-1,1), n, replace=T)
y<-abs(rnorm(n,mn,std))
z<-x*y

where the distribution of z is normal but the sign depends on the binary

-----Original Message-----
From: s-news-owner <at> lists.biostat.wustl.edu [mailto:s-news-owner <at> lists.biostat.wustl.edu] On
Behalf Of Wei Ye
Sent: Friday, June 04, 2010 11:38 AM
To: Robert A LaBudde
Cc: s-news <at> wubios.wustl.edu
Subject: Re: [S] quasi-monte carlo integration for mixed discrete and continuous variables

Thank you.

It is  not a problem to generate the points for either a binary variable or a continuous variable. My question
is how to generate the points for both a binary variable and a continuous variable with the latter
distribution depending on the value of the former.

----- Original Message ----
From: Robert A LaBudde <ral <at> lcfltd.com>
To: Wei Ye <weiye1 <at> yahoo.com>
Cc: s-news <at> wubios.wustl.edu
Sent: Fri, June 4, 2010 2:14:05 AM
Subject: Re: [S] quasi-monte carlo integration for mixed discrete and continuous variables

Quasirandom sequences typically fall in [0,1]. You can model either continuous or discrete variables by
scaling (continuous) or decision-point discretization (discrete). E.g., for a binary variable, code
"0" for the quasirandom number < 0.5 and "1" if greater.

I would suggest Halton or Hammersley sequences as an initial method to consider.

At 01:22 AM 6/4/2010, Wei Ye wrote:
> Hi, all,
> 
> Are there any low-discrepancy sequences to do quasi-monte carlo integration for a multivariate
distribution with both discrete and continuous variables?
> For example, the continuous variable (A) follows a normal distribution and the discrete variable (B) is
binary. The mean of  the normal distribution  depends on the value of B.
> 
> Can S-plus generate such sequences?
> 
> Thanks.
> 
> 
> 

================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral <at> lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"
================================================================

      
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Re: quasi-monte carlo integration for mixed discrete and continuous variables

At 02:05 PM 6/4/2010, Wei Ye wrote:
>Thanks. But I am asking how to generate quasi monte carlo points, 
>not pseudo random points.
>
>Quasi monte carlo points are deterministic.

1. Pseudorandom numbers are also deterministic.

2. To use a Halton sequence:

x1<- (1:N - 0.5)/N
w<- (1:N)*sqrt(2.)
x2<- w - trunc(w)

Now x1 and x2 are the 2-D quasirandom sequence you need.

================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral <at> lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"
================================================================

--------------------------------------------------------------------
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Re: quasi-monte carlo integration for mixed discrete and continuous variables

Sorry: This wasn't a real Halton sequence, as the sqrt(2) sequence is 
not the right way to do this (it should really be a reflection of the 
base-2 number instead).

However, the 2-D sequence as given is still a quasirandom sequence.

To generate real Halton or Hammersley sequences would require 
somewhat more programming.

A very good set of 2-D quasirandom low discrepancy numbers is

F3<- 1
F2<- 1
for (i in 1:?) {
   F1<- F2 + F3
}
x1<- 1:F1/F1
w<- (1:F1)*F3/F1
x2<- w - trunc(w)

i.e., the F's are the Fibonacci sequence.

At 04:18 PM 6/4/2010, Robert A LaBudde wrote:
>At 02:05 PM 6/4/2010, Wei Ye wrote:
>>Thanks. But I am asking how to generate quasi monte carlo points, 
>>not pseudo random points.
>>
>>Quasi monte carlo points are deterministic.
>
>1. Pseudorandom numbers are also deterministic.
>
>2. To use a Halton sequence:
>
>x1<- (1:N - 0.5)/N
>w<- (1:N)*sqrt(2.)
>x2<- w - trunc(w)
>
>Now x1 and x2 are the 2-D quasirandom sequence you need.
>
>================================================================
>Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral <at> lcfltd.com
>Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
>824 Timberlake Drive                     Tel: 757-467-0954
>Virginia Beach, VA 23464-3239            Fax: 757-467-2947
>
>"Vere scire est per causas scire"
>================================================================
>
>--------------------------------------------------------------------
>This message was distributed by s-news <at> lists.biostat.wustl.edu.  To
>unsubscribe send e-mail to s-news-request <at> lists.biostat.wustl.edu with
>the BODY of the message:  unsubscribe s-news

================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral <at> lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"
================================================================

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Peter Hingley is out of the office.

I will be out of the office starting  05-06-2010 and will not return until
15-06-2010.

I will respond to your message when I return.

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Breusch–Godfrey

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Re: Breusch?Godfrey