# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{displaymath}logleft(fracPi_i=1^Nf(x_i|theta)Pi_i=1^Nf(x_i|overlinetheta)right)rightarrow-infty.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}fracp(theta|x_1,cdots,x_N)p(theta^**|x_1,cdots,x_N)=fracf(x_1,cdots,x_N|theta)p(theta)f(x_1,cdots,x_N|theta^**)p(theta^**)rightarrow0qquadtextifthetaneqtheta^*text,andthetaneqtheta^**text.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}p(theta|x_1,cdots,x_N)rightarrowleft{arrayldelta_theta^*qquadtextwithprobabilityfracp(theta^*)p(theta^*)+p(theta^**)delta_theta^**qquadtextwithprobabilityfracp(theta^**)p(theta^*)+p(theta^**)arrayright.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta=theta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}fracp(theta|x_1,cdots,x_N)p(theta^*|x_1,cdots,x_N)=fracf(x_1,cdots,x_N|theta)p(theta)f(x_1,cdots,x_N|theta^*)p(theta^*)rightarrow0qquadtextifthetaneqtheta^*text,andthetaneqtheta^**text.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}K(theta,theta^*)=E_theta^*left[logf(x|theta)-logf(x|theta^*)right]leq0.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}E(widehattheta)=left[arrayl1.93701.0330arrayright]qquadCov(widehattheta)=left[arrayrr0.9466;SPMamp;-0.3307;SPMamp;0.9822arrayright].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$-infty${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}logleft(fracPi_i=1^Nf(x_i|theta)Pi_i=1^Nf(x_i|overlinetheta)right)rightarrow-inftyqquadtextifthetaneqoverlinethetatext.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}E(widehattheta)=left[arrayl2.01270.9081arrayright]qquadCov(widehattheta)=left[arrayrr1.1094;SPMamp;-0.3370;SPMamp;0.9797arrayright].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}fracp(theta|x_1,cdots,x_N)p(overlinetheta|x_1,cdots,x_N)=fracf(x_1,cdots,x_N|theta)p(theta)f(x_1,cdots,x_N|overlinetheta)p(overlinetheta)rightarrow0qquadtextifthetaneqoverlinethetatext.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$-K(overlinetheta,theta^*);SPMlt;-K(theta,theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p(theta)(neq0)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}f(x|theta^*)=f(x|theta^**)qquadtextforallx.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}overlinetheta=stackunderthetaintextsupp(p(theta))argminleft[-K(theta,theta^*)right].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}logleft(fracPi_i=1^Nf(x_i|theta)Pi_i=1^Nf(x_i|overlinetheta)right)=Nleft[frac1Nsum_i=1^Nf(x_i|theta)-frac1Nsum_i=1^Nf(x_i|overlinetheta)right],{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p(overlinetheta)(neq0)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}E(widehattheta)=left[arrayl2.07941.0093arrayright]qquadCov(widehattheta)=left[arrayrr0.9842;SPMamp;-0.2834;SPMamp;0.9734arrayright].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}E(widehattheta)=left[arrayl2.03240.9756arrayright]qquadCov(widehattheta)=left[arrayrr0.9716;SPMamp;-0.2389;SPMamp;1.0639arrayright].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}fracf(x_1,cdots,x_N|theta)f(x_1,cdots,x_N|overlinetheta)=fracPi_i=1^Nf(x_i|theta)Pi_i=1^Nf(x_i|overlinetheta)rightarrow0qquadtextifthetaneqoverlinethetatext.{displaymath}/;
$cached_env_img{$key} = ' 
';
1;