# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.

$key = q/{_inline}$tildez${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=8 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline102" SRC="img18.gif"  > '; 
$key = q/{_inline}$(y_1,y_2)=(2,1)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=119 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline88" SRC="img14.gif"  > '; 
$key = q/{displaymath}theta_2|theta_1,ysimN(y_2+rho(theta_1-y_1),1-rho^2).{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=398 HEIGHT=22 ALIGN=BOTTOM ALT="displaymath124" SRC="img22.gif"  > '; 
$key = q/{_inline}$(theta_1^T,theta_2^T)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=58 HEIGHT=33 ALIGN=MIDDLE ALT="tex2html_wrap_inline130" SRC="img24.gif"  > '; 
$key = q/{_inline}$(y_1,y_2)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=52 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline72" SRC="img8.gif"  > '; 
$key = q/{displaymath}1overTsum_t=1^Th(theta^t)tointh(theta)p(theta),quadmboxas;;Ttoinfty{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=408 HEIGHT=49 ALIGN=BOTTOM ALT="displaymath160" SRC="img28.gif"  > '; 
$key = q/{_inline}$sqrtOmega${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=29 HEIGHT=36 ALIGN=MIDDLE ALT="tex2html_wrap_inline100" SRC="img17.gif"  > '; 
$key = q/{_inline}$rho=-.3${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=64 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline90" SRC="img15.gif"  > '; 
$key = q/{displaymath}left(arraycc1;SPMamp;rhorho;SPMamp;1arrayright){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=284 HEIGHT=48 ALIGN=BOTTOM ALT="displaymath50" SRC="img11.gif"  > '; 
$key = q/{_inline}$theta${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=8 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline78" SRC="img12.gif"  > '; 
$key = q/{_inline}$(y_1,y_2)'${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=57 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline82" SRC="img13.gif"  > '; 
$key = q/{displaymath}p(theta|x_1,cdots,x_N)rightarrowdelta_overlinethetaqquadtextwithprobabilityquad1{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=429 HEIGHT=21 ALIGN=BOTTOM ALT="displaymath48" SRC="img2.gif"  > '; 
$key = q/{_inline}$f(x|theta^**)=f(x|theta^*)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=146 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline66" SRC="img7.gif"  > '; 
$key = q/{_inline}$t=2001,ldots,2500${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=149 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline150" SRC="img27.gif"  > '; 
$key = q/{_inline}$overlinetheta${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=10 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap_inline58" SRC="img4.gif"  > '; 
$key = q/{_inline}$theta^*${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=15 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline54" SRC="img1.gif"  > '; 
$key = q/{_inline}${theta^t}${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=31 HEIGHT=31 ALIGN=MIDDLE ALT="tex2html_wrap_inline166" SRC="img29.gif"  > '; 
$key = q/{_inline}$(theta^0_1,theta^0_2)=(0,0)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=119 HEIGHT=32 ALIGN=MIDDLE ALT="tex2html_wrap_inline140" SRC="img25.gif"  > '; 
$key = q/{displaymath}theta_1|theta_2,ysimN(y_1+rho(theta_2-y_2),1-rho^2){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=394 HEIGHT=22 ALIGN=BOTTOM ALT="displaymath114" SRC="img21.gif"  > '; 
$key = q/{_inline}$delta_overlinetheta${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=15 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline56" SRC="img3.gif"  > '; 
$key = q/{_inline}$tildez=(tildez_1,tildez_2)'${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=92 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline96" SRC="img16.gif"  > '; 
$key = q/{_inline}$theta_1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=15 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline110" SRC="img19.gif"  > '; 
$key = q/{_inline}$(theta_1^0,theta_2^0)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=52 HEIGHT=32 ALIGN=MIDDLE ALT="tex2html_wrap_inline126" SRC="img23.gif"  > '; 
$key = q/{_inline}$theta_2${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=15 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline112" SRC="img20.gif"  > '; 
$key = q/{_inline}$theta^**${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=22 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline62" SRC="img6.gif"  > '; 
$key = q/{_inline}$theta^t${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=14 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap_inline148" SRC="img26.gif"  > '; 
$key = q/{displaymath}overlinetheta=argmin_thetainmboxsupport(p)E_theta^*left{-logfracfleft(x|thetaright)fleft(x|theta^*right)right}.{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=433 HEIGHT=48 ALIGN=BOTTOM ALT="displaymath49" SRC="img5.gif"  > '; 
$key = q/{_inline}$Omega${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=12 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline76" SRC="img10.gif"  > '; 
$key = q/{_inline}$(theta_1,theta_2)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=51 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline74" SRC="img9.gif"  > '; 

1;

