User:Mark W. Miller

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[edit] Articles written or extensively rewritten

[edit] American Civil War

As of June 2008 the article still largely reflects my contributions. I have been a little amazed at how widely that article has been copied or mentioned on the internet. I have always felt a little bad about mentioning events that surrounded the surrender.

[edit] Math and Statistics

As of June 2008 the article still largely reflects my contributions, which wasn't much. The article remains only a stub.

[edit] Biometrics

As of June 2008 the article still largely reflects my contributions. Capture-recapture is an enormous field that presently involves some extremely complex models. However, the Lincoln-Petersen method is basically the beginning and the method is still used. The references at the bottom of the page will expose readers to the broader world of capture-recapture if they are interested. Quite a few good books are available on the subject. Some can be downloaded for free from the internet.

[edit] Sports

As of June 2008 the article still largely reflects my contributions. Smith's stats are up-to-date, as is his current situation with the Pittsburgh Steelers. Many other people have contributed to his page since I added to it.




[edit] Material below has been helpful to me and hopefully will be helpful to others

[edit] Newton-Raphson Method and Hessian Matrix

NOTE TO SELF: THERE WAS A TYPO IN THE HESSIAN MATRIX IN THE BOOK. THE INVERSE OF THE HESSIAN IS CORRECT, BUT THE HESSIAN ITSELF WAS NOT.

THE HESSIAN NOW IS CORRECT BELOW.


I posted a question recently about the Hessian Matrix on the Math Talk page and received some good replies. I posted a follow-up question later in the Math and Science Question section, but then found the error in the book myself. Below deals with using the Hessian Matrix and Newton-Raphson Method to locate the minima or maxima of a function. The example in REA's Problem Solvers book "Operations Research", p. 739-740, contains an error in the Hessian Matrix.

The function in the example contains two unknowns, x1 and x2, and is:

4x12 + 2x1x2 + 2x22 + x1 + x2.


The problem is to find the values of x1 and x2 that provide the minima.

The matrix of partial derivatives is: f(x) = \begin{bmatrix}8x1 + 2x2 + 1 \\2x1 + 4x2 + 1\end{bmatrix} = 0.

The Hessian Matrix is:

H(x) = \begin{bmatrix}8&2\\2&4\end{bmatrix};

Not:

H(x) = \begin{bmatrix}8&2\\8&4\end{bmatrix} as in the book.

The third matrix is indeed the inverse of the Hessian Matrix, and is given correctly in the book as:

H-1(x) = (1/14) * \begin{bmatrix} 2&-1\\-1&4\end{bmatrix}.


The interative formula used to find the values of x1 and x2 corresponding to the minima of the original function is:

x(n+1) = x(n) - H-1(x) * f(x);


and gives the values x(n+1)1 = -1/14 and x(n+1)2 = -3/14.


I understand, at least mechanically, the substitutions and algebra used to arrive at those answers given the formula for x(n+1).

Note that:

H(x) * H-1(x) = \begin{bmatrix} 1&0\\0&1\end{bmatrix}.


Note that the eigenvalues of the Hessian Matrix are 8.8284271 and 3.1715729, which I think corresponds to a minima, which is what the REA "Operations Research" book said was the case with this particular function.


[edit] Brand New to LaTeX and MiKTeX

Installed MiKTeX on my Windows XP computer today. The MiKTeX download included LaTeX.


http://www.latex-project.org/

http://miktex.org/


I needed approximately three hours to figure out how to run the simplest program, a small file called 'hello.tex'. Eventually I tried opening a DOS window and going to the folder containing 'latex.exe':

C:\Program Files\MiKTex 2.7\mikTex\bin>

then typing 'latex hello':

C:\Program Files\MiKTex 2.7\mikTex\bin>latex hello

and it worked.


Sometimes the hardest part about using a computer is figuring out how to turn it on.

Mark W. Miller (talk) 19:16, 6 June 2008 (UTC)


[edit] Creating a PDF file using LaTeX

The steps immediately above worked to create a file called 'hello.dvi'. I was able to convert 'hello.dvi' into a PDF file using the following two steps:


Step 1. Create a PostScript file:

C:\Program Files\MiKTex 2.7\mikTex\bin>dvips hello.dvi -o hello.ps


Step 2. Create a PDF file using the PostScript file from the first step:

C:\Program Files\MiKTex 2.7\mikTex\bin>ps2pdf hello.ps hello.pdf


Note that the file 'hello.tex' was also in the folder:

C:\Program Files\MiKTex 2.7\mikTex\bin>

as were the executable files 'dvips.exe', 'ps2pdf.exe' and 'latex.exe' which were installed automatically when I installed 'MiKTeX 2.7'.

The file 'hello.tex' was obtained via an internet search, copied, and pasted into MS Wordpad and saved on my computer in plain text format.


Mark W. Miller (talk) 08:17, 7 June 2008 (UTC)


[edit] Graphical User Interface for LaTeX

Installed TeXnicCenter which serves as a shell or text editor or graphical user interface for LaTeX and created another version of 'hello.pdf' from within the TeXnicCenter application.

http://www.toolscenter.org/

Mark W. Miller (talk) 12:36, 7 June 2008 (UTC)


[edit] Questions I Have Posted at the Mathematics Reference Desk

Below are some questions I have posted at the Mathematics and Computing Reference Desks. The answers were helpful and I have periodically gone back to refresh my memory.


1. Derivative and partial derivative of what I called the inverse of the logit function.

http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Mathematics/2007_March_19#derivative_of_the_inverse_of_a_logit_function

Note that the answer was vandalized, but I do not think the content of the question or answer was changed.


2. Estimating the variance-covariance matrix of a multinomial function

http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Mathematics/2007_September_28

Note that I answered my own question. I believe my answer is correct. Hopefully so. If somebody types 'Estimating the variance-covariance matrix of a multinomial function' into Google without the quotation marks, the first hit returned is my question and answer!


3. Poisson Distribution

http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Mathematics/2007_September_22

This question dealt with how to determine whether a variable followed a Poisson Distribution.


4. Displaying the gradient when optimizing in R (programming language)

http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Computing/2008_May_31#Displaying_the_gradient_when_optimizing_in_R

Note that this Question #4 was posted at the Computing Reference Desk, not the Mathematics Reference Desk, and this question remains unanswered. If I learn the answer I will provide it.


Mark W. Miller (talk) 13:24, 8 June 2008 (UTC)