# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{_inline}$Y^primeSigma^-1Ysimchi^2left(kright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}p(theta)=p(beta,Omega^-1)=p(beta|beta_0,A_0^-1)p(Omega^-1|rho_0,R_0).{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeepsilon_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_p^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}E{tildeepsilon}=int_-infty^+inftyepsilonexp{-epsilon}expleft{-exp{-epsilon}right}depsilon=alpha+sigmagamma,eqno(11){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}p(Omega^-1|rho_0,R_0)=|R_0|^-rho_02|Omega^-1|^(rho_0-(p-1))2expleft{-1over2mboxtr(R_0^-1Omega^-1)right}over2^rho_0p2pi^p(p-1)4prod_i=1^pGammaleft(rho_0+1-iover2right).{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}tildeu_d=v_d+tildeepsilon_d,quadd=1,ldots,Deqno(1){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$v_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta,sigma^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$max_d{epsilon_d}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Ntimes1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$I{delta(epsilon)=d}=1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ldots${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}f(epsilon|X)=prod_d=1^Dexp{-epsilon_d}expleft{-exp{-epsilon_d}right}.eqno(8){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon=(epsilon_1,ldots,epsilon_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$k_ptimes1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Sigma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}F(x|alpha,sigma)=P{tildeepsilonlex|alpha,sigma}=expleft{-expleft{-(x-alpha)oversigmaright}right}.eqno(12){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$delta(epsilon)=d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p(beta|beta_0,A_0^-1)=N(beta_0,A_0^-1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}y=Xbeta^*+varepsilon{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ktimes1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$delta(epsilon_1,ldots,epsilon_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}f(epsilon)=Kexpleft{-left|epsilonoversqrtsigma^2right|right}.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$R_0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$varepsilon_isimNleft(0,Omegaright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}alpha=sigmalogleft[sum_d=1^Dexp{alpha_dsigma}right]eqno(13){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ptimesp${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehatbeta=left(widehatbeta_1^prime,cdots,widehatbeta_p^primeright)^prime${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ptimes1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$I^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$f(epsilon|X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$alpha${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X=(X_1,ldots,X_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$partialUpartialv_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$varepsilon_i=left(varepsilon_i1,cdots,varepsilon_ipright)^prime${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$rho${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}partialU(v_1,ldots,v_D,X)overpartialv_d=P{d|X}eqno(6){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}U(v_1,ldots,v_D,X)=gamma+logleft[sum_d=1^Dexp{v_d}right].eqno(10){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$A_0^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}f(y_1,ldots,y_N|beta,Omega^-1,X_1,ldots,X_N)=pi^-N2|Omega^-1|^N2expleft{-1over2sum_i=1^N(y_i-X_ibeta)'Omega^-1(y_i-X_ibeta)right}{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma=.577216ldots${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta=(beta,Omega^-1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}P{d|X}=exp{v_d}oversum_d'=1^Dexp{v_d'}.eqno(9){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_1^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(epsilon_1,ldots,epsilon_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$I{delta(epsilon)=d}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}hatbeta_mboxlad=argmin_betasum_i=1^N|y_i-X_ibeta|.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$varepsilonsimNleft(0,Omegaright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Ntimesk${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}y_i=X_ibeta+epsilon_i,quadi=1,ldots,N{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Pleft{d|Xright}=intI{d=delta(epsilon)}f(epsilon|X)depsiloneqno(4){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p(Omega^-1|rho_0,R_0)=W(rho,R_0)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}partialpartialv_dmax_d=1,ldots,D[v_d+epsilon_d]=I{d=delta(epsilon)}.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$int^infty_-inftyf(epsilon)depsilon=1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$left(X^primeOmega^-1Xright)^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$left(beta,Omega^-1right)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}U(v_1,ldots,v_D,X)=Eleft{max_d=1,ldots,D[v_d+tildeepsilon_d]Big|Xright}=int_epsilon_1cdotsint_epsilon_Dmax_d=1,ldots,D[v_d+epsilon_d]f(epsilon_1,ldots,epsilon_D|X)depsilon_1cdotsdepsilon_Deqno(5){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$k_1times1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(alpha_1,ldots,alpha_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$k=sum_i=1^pk_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$delta(epsilon)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$YsimNleft(0,Sigmaright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ktimesk${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$max(epsilon_1,ldots,epsilon_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxtr(AB)=mboxtr(BA)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ptimesk${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}delta(epsilon)=mboxitargmax_d=1,ldots,Dleft[v_d+tildeepsilon_dright]eqno(3){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}v_d=X_dbetaeqno(2){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_mboxlad${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P{d|X}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$varepsilon${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1times1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehatbeta_GLS${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$U(v_1,ldots,v_D,X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeu_d${_inline}/;
$cached_env_img{$key} = ' 
';
1;