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bond_doc_cste.gss
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new;
cls;
library optmum, pgraph;
optset;
@GLOBALS@
sim_start=1;
sim_end=3;
incr=0.3; @increment for probability grid search@
format /m1 /rd 9,5;
/*V1=V1';
V2=V2';
S1=S1';
S2=S2';*/
@load data@
load data[271,7]=bond_and_docmeansbon.txt;
y1=data[1:271,2]/100;
y2=data[1:271,3]/100;
yy=y1~y2;
S1=data[1:271,5];
S2=data[1:271,6];
t=rows(yy);
n=2;
@======================================================================@
proc trans4(c0);
local c1;
c1=c0;
c1[1]=c0[1];
c1[2]=c0[2];
c1[3]=c0[3];
c1[4]=c0[4];
c1[5]=exp(-c0[5]);
c1[6]=exp(-c0[6]);
c1[7]=exp(-c0[7]);
c1[8]=exp(-c0[8]);
c1[9]=(1+exp(-c0[9]))*c1[5];
c1[10]=(1+exp(-c0[10]))*c1[6];
c1[11]=(1+exp(-c0[11]))*c1[7];
c1[12]=(1+exp(-c0[12]))*c1[8];
c1[13]=c0[13];
c1[14]=c0[14];
c1[15]=c0[15];
c1[16]=c0[16];
c1[17]=c0[17];
c1[18]=c0[18];
c1[19]=c0[19];
c1[20]=c0[20];
c1[21:26]= exp(-c0[21:26])./(1+exp(-c0[21:26]));
retp(c1);
endp;
@======================================================================@
@======================================================================@
proc v_prob(EV, HE);
local val;
val=(1/sqrt(((2*pi)^n)*det(HE)))*exp(-0.5*EV'*inv(HE)*EV);
retp(val);
endp;
@======================================================================@
@======================================================================@
proc (8)=filter(prmtr1);
local p_tl1,p_tl2,p_tl3,p_tl4,p_tl5,p_tl6,p_tl7,p_tl8,
p_tt1,p_tt2,p_tt3,p_tt4,p_tt5,p_tt6,p_tt7,p_tt8,
prmtr,sigma_1,sigma_2,sigma_1bar,
sigma_2bar,sigma1c,sigma2c,sigma1cbar,sigma2cbar,d1,d2,d3,d4,
d1bar,d2bar,d3bar,d4bar,cst1,cst2,cst1bar,cst2bar,
p1_11,p1_22,p2_11,p2_22,p3_11,p3_22,
p11,p12,p13,p14,p15,p16,p17,p18,
p21,p22,p23,p24,p25,p26,p27,p28,
p31,p32,p33,p34,p35,p36,p37,p38,
p41,p42,p43,p44,p45,p46,p47,p48,
p51,p52,p53,p54,p55,p56,p57,p58,
p61,p62,p63,p64,p65,p66,p67,p68,
p71,p72,p73,p74,p75,p76,p77,p78,
p81,p82,p83,p84,p85,p86,p87,p88,pr_tr,
sigmat_1,sigmat_2,sigmat_3,sigmat_4,sigmat_5,sigmat_6,sigmat_7,sigmat_8,
A,EN,PROB__T,PR_L1,PR_L2,PR_L3,PR_L4,PR_L5,PR_L6,PR_L7,PR_L8,j_iter,
PR_TL11,PR_TL12,PR_TL13,PR_TL14,PR_TL15,PR_TL16,PR_TL17,PR_TL18,
PR_TL21,PR_TL22,PR_TL23,PR_TL24,PR_TL25,PR_TL26,PR_TL27,PR_TL28,
PR_TL31,PR_TL32,PR_TL33,PR_TL34,PR_TL35,PR_TL36,PR_TL37,PR_TL38,
PR_TL41,PR_TL42,PR_TL43,PR_TL44,PR_TL45,PR_TL46,PR_TL47,PR_TL48,
PR_TL51,PR_TL52,PR_TL53,PR_TL54,PR_TL55,PR_TL56,PR_TL57,PR_TL58,
PR_TL61,PR_TL62,PR_TL63,PR_TL64,PR_TL65,PR_TL66,PR_TL67,PR_TL68,
PR_TL71,PR_TL72,PR_TL73,PR_TL74,PR_TL75,PR_TL76,PR_TL77,PR_TL78,
PR_TL81,PR_TL82,PR_TL83,PR_TL84,PR_TL85,PR_TL86,PR_TL87,PR_TL88,
e11,e12,e13,e14,e15,e16,e17,e18,
e21,e22,e23,e24,e25,e26,e27,e28,
e31,e32,e33,e34,e35,e36,e37,e38,
e41,e42,e43,e44,e45,e46,e47,e48,
e51,e52,e53,e54,e55,e56,e57,e58,
e61,e62,e63,e64,e65,e66,e67,e68,
e71,e72,e73,e74,e75,e76,e77,e78,
e81,e82,e83,e84,e85,e86,e87,e88,
fy11,fy12,fy13,fy14,fy15,fy16,fy17,fy18,
fy21,fy22,fy23,fy24,fy25,fy26,fy27,fy28,
fy31,fy32,fy33,fy34,fy35,fy36,fy37,fy38,
fy41,fy42,fy43,fy44,fy45,fy46,fy47,fy48,
fy51,fy52,fy53,fy54,fy55,fy56,fy57,fy58,
fy61,fy62,fy63,fy64,fy65,fy66,fy67,fy68,
fy71,fy72,fy73,fy74,fy75,fy76,fy77,fy78,
fy81,fy82,fy83,fy84,fy85,fy86,fy87,fy88,fy;
prmtr=trans4(prmtr1);
@Normal Times Parameters@
d1=prmtr[1];
d2=prmtr[2];
d3=prmtr[3];
d4=prmtr[4];
sigma_1=prmtr[5];
sigma_2=prmtr[6];
sigma1c=prmtr[7];
sigma2c=prmtr[8];
cst1=prmtr[17];
cst2=prmtr[18];
@S_1t parameters@
sigma_1bar=prmtr[9];
@S_2t parameters@
sigma_2bar=prmtr[10];
@S_ct=S_3t parameters@
sigma1cbar=prmtr[11];
sigma2cbar=prmtr[12];
d1bar=prmtr[13];
d2bar=prmtr[14];
d3bar=prmtr[15];
d4bar=prmtr[16];
cst1bar=prmtr[19];
cst2bar=prmtr[20];
@Transition Probabilities@
p1_11=prmtr[21];
p1_22=prmtr[22];
p2_11=prmtr[23];
p2_22=prmtr[24];
p3_11=prmtr[25];
p3_22=prmtr[26];
p11=p1_11*p2_11*p3_11;
p12=p1_11*p2_11*(1-p3_11);
p13=p1_11*(1-p2_11)*p3_11;
p14=p1_11*(1-p2_11)*(1-p3_11);
p15=(1-p1_11)*p2_11*p3_11;
p16=(1-p1_11)*p2_11*(1-p3_11);
p17=(1-p1_11)*(1-p2_11)*p3_11;
p18=1-p11-p12-p13-p14-p15-p16-p17;
p21=p1_11*p2_11*(1-p3_22);
p22=p1_11*p2_11*p3_22;
p23=p1_11*(1-p2_11)*(1-p3_22);
p24=p1_11*(1-p2_11)*p3_22;
p25=(1-p1_11)*p2_11*(1-p3_22);
p26=(1-p1_11)*p2_11*p3_22;
p27=(1-p1_11)*(1-p2_11)*(1-p3_22);
p28=1-p21-p22-p23-p24-p25-p26-p27;
p31=p1_11*(1-p2_22)*p3_11;
p32=p1_11*(1-p2_22)*(1-p3_11);
p33=p1_11*p2_22*p3_11;
p34=p1_11*p2_22*(1-p3_11);
p35=(1-p1_11)*(1-p2_22)*p3_11;
p36=(1-p1_11)*(1-p2_22)*(1-p3_11);
p37=(1-p1_11)*p2_22*p3_11;
p38=1-p31-p32-p33-p34-p35-p36-p37;
p41=p1_11*(1-p2_22)*(1-p3_22);
p42=p1_11*(1-p2_22)*p3_22;
p43=p1_11*p2_22*(1-p3_22);
p44=p1_11*p2_22*p3_22;
p45=(1-p1_11)*(1-p2_22)*(1-p3_22);
p46=(1-p1_11)*(1-p2_22)*p3_22;
p47=(1-p1_11)*p2_22*(1-p3_22);
p48=1-p41-p42-p43-p44-p45-p46-p47;
p51=(1-p1_22)*p2_11*p3_11;
p52=(1-p1_22)*p2_11*(1-p3_11);
p53=(1-p1_22)*(1-p2_11)*p3_11;
p54=(1-p1_22)*(1-p2_11)*(1-p3_11);
p55=p1_22*p2_11*p3_11;
p56=p1_22*p2_11*(1-p3_11);
p57=p1_22*(1-p2_11)*p3_11;
p58=1-p51-p52-p53-p54-p55-p56-p57;
p61=(1-p1_22)*p2_11*(1-p3_22);
p62=(1-p1_22)*p2_11*p3_22;
p63=(1-p1_22)*(1-p2_11)*(1-p3_22);
p64=(1-p1_22)*(1-p2_11)*p3_22;
p65=p1_22*p2_11*(1-p3_22);
p66=p1_22*p2_11*p3_22;
p67=p1_22*(1-p2_11)*(1-p3_22);
p68=1-p61-p62-p63-p64-p65-p66-p67;
p71=(1-p1_22)*(1-p2_22)*p3_11;
p72=(1-p1_22)*(1-p2_22)*(1-p3_11);
p73=(1-p1_22)*p2_22*p3_11;
p74=(1-p1_22)*p2_22*(1-p3_11);
p75=p1_22*(1-p2_22)*p3_11;
p76=p1_22*(1-p2_22)*(1-p3_11);
p77=p1_22*p2_22*p3_11;
p78=1-p71-p72-p73-p74-p75-p76-p77;
p81=(1-p1_22)*(1-p2_22)*(1-p3_22);
p82=(1-p1_22)*(1-p2_22)*p3_22;
p83=(1-p1_22)*p2_22*(1-p3_22);
p84=(1-p1_22)*p2_22*p3_22;
p85=p1_22*(1-p2_22)*(1-p3_22);
p86=p1_22*(1-p2_22)*p3_22;
p87=p1_22*p2_22*(1-p3_22);
p88=1-p81-p82-p83-p84-p85-p86-p87;
pr_tr= p11~p12~p13~p14~p15~p16~p17~p18|
p21~p22~p23~p24~p25~p26~p27~p28|
p31~p32~p33~p34~p35~p36~p37~p38|
p41~p42~p43~p44~p45~p46~p47~p48|
p51~p52~p53~p54~p55~p56~p57~p58|
p61~p62~p63~p64~p65~p66~p67~p68|
p71~p72~p73~p74~p75~p76~p77~p78|
p81~p82~p83~p84~p85~p86~p87~p88;
sigmat_1= sigma1c^2+sigma_1^2~sigma1c*sigma2c|
sigma1c*sigma2c~sigma2c^2+sigma_2^2;
sigmat_2= sigma1cbar^2+sigma_1^2~sigma1cbar*sigma2cbar|
sigma1cbar*sigma2cbar~sigma2cbar^2+sigma_2^2;
sigmat_3= sigma1c^2+sigma_1^2~sigma1c*sigma2c|
sigma1c*sigma2c~sigma2c^2+sigma_2bar^2;
sigmat_4= sigma1cbar^2+sigma_1^2~sigma1cbar*sigma2cbar|
sigma1cbar*sigma2cbar~sigma2cbar^2+sigma_2bar^2;
sigmat_5= sigma1c^2+sigma_1bar^2~sigma1c*sigma2c|
sigma1c*sigma2c~sigma2c^2+sigma_2^2;
sigmat_6= sigma1cbar^2+sigma_1bar^2~sigma1cbar*sigma2cbar|
sigma1cbar*sigma2cbar~sigma2cbar^2+sigma_2^2;
sigmat_7= sigma1c^2+sigma_1bar^2~sigma1c*sigma2c|
sigma1c*sigma2c~sigma2c^2+sigma_2bar^2;
sigmat_8= sigma1cbar^2+sigma_1bar^2~sigma1cbar*sigma2cbar|
sigma1cbar*sigma2cbar~sigma2cbar^2+sigma_2bar^2;
A = (eye(8)-pr_tr)|ones(1,8);
EN=(0|0|0|0|0|0|0|0|1);
PROB__T = inv(A'A)*A'EN; @8x1 UNCONDITIONAL PROBABILITIES@
PR_L1=PROB__T[1];
PR_L2=PROB__T[2];
PR_L3=PROB__T[3];
PR_L4=PROB__T[4];
PR_L5=PROB__T[5];
PR_L6=PROB__T[6];
PR_L7=PROB__T[7];
PR_L8=PROB__T[8];
@filter only@
p_tl1={};
p_tl2={};
p_tl3={};
p_tl4={};
p_tl5={};
p_tl6={};
p_tl7={};
p_tl8={};
p_tt1={};
p_tt2={};
p_tt3={};
p_tt4={};
p_tt5={};
p_tt6={};
p_tt7={};
p_tt8={};
j_iter = 1;
do until j_iter>t;
PR_TL11=p11*PR_L1;
PR_TL12=p12*PR_L1;
PR_TL13=p13*PR_L1;
PR_TL14=p14*PR_L1;
PR_TL15=p15*PR_L1;
PR_TL16=p16*PR_L1;
PR_TL17=p17*PR_L1;
PR_TL18=p18*PR_L1;
PR_TL21=p21*PR_L2;
PR_TL22=p22*PR_L2;
PR_TL23=p23*PR_L2;
PR_TL24=p24*PR_L2;
PR_TL25=p25*PR_L2;
PR_TL26=p26*PR_L2;
PR_TL27=p27*PR_L2;
PR_TL28=p28*PR_L2;
PR_TL31=p31*PR_L3;
PR_TL32=p32*PR_L3;
PR_TL33=p33*PR_L3;
PR_TL34=p34*PR_L3;
PR_TL35=p35*PR_L3;
PR_TL36=p36*PR_L3;
PR_TL37=p37*PR_L3;
PR_TL38=p38*PR_L3;
PR_TL41=p41*PR_L4;
PR_TL42=p42*PR_L4;
PR_TL43=p43*PR_L4;
PR_TL44=p44*PR_L4;
PR_TL45=p45*PR_L4;
PR_TL46=p46*PR_L4;
PR_TL47=p47*PR_L4;
PR_TL48=p48*PR_L4;
PR_TL51=p51*PR_L5;
PR_TL52=p52*PR_L5;
PR_TL53=p53*PR_L5;
PR_TL54=p54*PR_L5;
PR_TL55=p55*PR_L5;
PR_TL56=p56*PR_L5;
PR_TL57=p57*PR_L5;
PR_TL58=p58*PR_L5;
PR_TL61=p61*PR_L6;
PR_TL62=p62*PR_L6;
PR_TL63=p63*PR_L6;
PR_TL64=p64*PR_L6;
PR_TL65=p65*PR_L6;
PR_TL66=p66*PR_L6;
PR_TL67=p67*PR_L6;
PR_TL68=p68*PR_L6;
PR_TL71=p71*PR_L7;
PR_TL72=p72*PR_L7;
PR_TL73=p73*PR_L7;
PR_TL74=p74*PR_L7;
PR_TL75=p75*PR_L7;
PR_TL76=p76*PR_L7;
PR_TL77=p77*PR_L7;
PR_TL78=p78*PR_L7;
PR_TL81=p81*PR_L8;
PR_TL82=p82*PR_L8;
PR_TL83=p83*PR_L8;
PR_TL84=p84*PR_L8;
PR_TL85=p85*PR_L8;
PR_TL86=p86*PR_L8;
PR_TL87=p87*PR_L8;
PR_TL88=p88*PR_L8;
@filter only@
p_tl1=p_tl1|PR_TL11+PR_TL21+PR_TL31+PR_TL41+PR_TL51+PR_TL61+PR_TL71+PR_TL81;
p_tl2=p_tl2|PR_TL12+PR_TL22+PR_TL32+PR_TL42+PR_TL52+PR_TL62+PR_TL72+PR_TL82;
p_tl3=p_tl3|PR_TL13+PR_TL23+PR_TL33+PR_TL43+PR_TL53+PR_TL63+PR_TL73+PR_TL83;
p_tl4=p_tl4|PR_TL14+PR_TL24+PR_TL34+PR_TL44+PR_TL54+PR_TL64+PR_TL74+PR_TL84;
p_tl5=p_tl5|PR_TL15+PR_TL25+PR_TL35+PR_TL45+PR_TL55+PR_TL65+PR_TL75+PR_TL85;
p_tl6=p_tl6|PR_TL16+PR_TL26+PR_TL36+PR_TL46+PR_TL56+PR_TL66+PR_TL76+PR_TL86;
p_tl7=p_tl7|PR_TL17+PR_TL27+PR_TL37+PR_TL47+PR_TL57+PR_TL67+PR_TL77+PR_TL87;
p_tl8=p_tl8|PR_TL18+PR_TL28+PR_TL38+PR_TL48+PR_TL58+PR_TL68+PR_TL78+PR_TL88;
e11=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e12=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e13=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e14=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e15=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e16=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e17=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e18=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e21=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e22=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e23=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e24=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e25=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e26=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e27=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e28=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e31=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e32=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e33=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e34=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e35=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e36=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e37=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e38=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e41=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e42=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e43=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e44=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e45=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e46=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e47=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e48=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e51=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e52=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e53=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e54=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e55=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e56=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e57=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e58=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e61=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e62=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e63=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e64=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e65=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e66=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e67=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e68=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e71=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e72=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e73=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e74=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e75=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e76=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e77=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e78=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e81=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e82=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e83=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e84=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e85=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e86=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e87=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e88=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
fy11=v_prob(e11,sigmat_1)*PR_TL11;
fy12=v_prob(e12,sigmat_2)*PR_TL12;
fy13=v_prob(e13,sigmat_3)*PR_TL13;
fy14=v_prob(e14,sigmat_4)*PR_TL14;
fy15=v_prob(e15,sigmat_5)*PR_TL15;
fy16=v_prob(e16,sigmat_6)*PR_TL16;
fy17=v_prob(e17,sigmat_7)*PR_TL17;
fy18=v_prob(e18,sigmat_8)*PR_TL18;
fy21=v_prob(e21,sigmat_1)*PR_TL21;
fy22=v_prob(e22,sigmat_2)*PR_TL22;
fy23=v_prob(e23,sigmat_3)*PR_TL23;
fy24=v_prob(e24,sigmat_4)*PR_TL24;
fy25=v_prob(e25,sigmat_5)*PR_TL25;
fy26=v_prob(e26,sigmat_6)*PR_TL26;
fy27=v_prob(e27,sigmat_7)*PR_TL27;
fy28=v_prob(e28,sigmat_8)*PR_TL28;
fy31=v_prob(e31,sigmat_1)*PR_TL31;
fy32=v_prob(e32,sigmat_2)*PR_TL32;
fy33=v_prob(e33,sigmat_3)*PR_TL33;
fy34=v_prob(e34,sigmat_4)*PR_TL34;
fy35=v_prob(e35,sigmat_5)*PR_TL35;
fy36=v_prob(e36,sigmat_6)*PR_TL36;
fy37=v_prob(e37,sigmat_7)*PR_TL37;
fy38=v_prob(e38,sigmat_8)*PR_TL38;
fy41=v_prob(e41,sigmat_1)*PR_TL41;
fy42=v_prob(e42,sigmat_2)*PR_TL42;
fy43=v_prob(e43,sigmat_3)*PR_TL43;
fy44=v_prob(e44,sigmat_4)*PR_TL44;
fy45=v_prob(e45,sigmat_5)*PR_TL45;
fy46=v_prob(e46,sigmat_6)*PR_TL46;
fy47=v_prob(e47,sigmat_7)*PR_TL47;
fy48=v_prob(e48,sigmat_8)*PR_TL48;
fy51=v_prob(e51,sigmat_1)*PR_TL51;
fy52=v_prob(e52,sigmat_2)*PR_TL52;
fy53=v_prob(e53,sigmat_3)*PR_TL53;
fy54=v_prob(e54,sigmat_4)*PR_TL54;
fy55=v_prob(e55,sigmat_5)*PR_TL55;
fy56=v_prob(e56,sigmat_6)*PR_TL56;
fy57=v_prob(e57,sigmat_7)*PR_TL57;
fy58=v_prob(e58,sigmat_8)*PR_TL58;
fy61=v_prob(e61,sigmat_1)*PR_TL61;
fy62=v_prob(e62,sigmat_2)*PR_TL62;
fy63=v_prob(e63,sigmat_3)*PR_TL63;
fy64=v_prob(e64,sigmat_4)*PR_TL64;
fy65=v_prob(e65,sigmat_5)*PR_TL65;
fy66=v_prob(e66,sigmat_6)*PR_TL66;
fy67=v_prob(e67,sigmat_7)*PR_TL67;
fy68=v_prob(e68,sigmat_8)*PR_TL68;
fy71=v_prob(e71,sigmat_1)*PR_TL71;
fy72=v_prob(e72,sigmat_2)*PR_TL72;
fy73=v_prob(e73,sigmat_3)*PR_TL73;
fy74=v_prob(e74,sigmat_4)*PR_TL74;
fy75=v_prob(e75,sigmat_5)*PR_TL75;
fy76=v_prob(e76,sigmat_6)*PR_TL76;
fy77=v_prob(e77,sigmat_7)*PR_TL77;
fy78=v_prob(e78,sigmat_8)*PR_TL78;
fy81=v_prob(e81,sigmat_1)*PR_TL81;
fy82=v_prob(e82,sigmat_2)*PR_TL82;
fy83=v_prob(e83,sigmat_3)*PR_TL83;
fy84=v_prob(e84,sigmat_4)*PR_TL84;
fy85=v_prob(e85,sigmat_5)*PR_TL85;
fy86=v_prob(e86,sigmat_6)*PR_TL86;
fy87=v_prob(e87,sigmat_7)*PR_TL87;
fy88=v_prob(e88,sigmat_8)*PR_TL88;
fy= fy11+fy12+fy13+fy14+fy15+fy16+fy17+fy18+
fy21+fy22+fy23+fy24+fy25+fy26+fy27+fy28+
fy31+fy32+fy33+fy34+fy35+fy36+fy37+fy38+
fy41+fy42+fy43+fy44+fy45+fy46+fy47+fy48+
fy51+fy52+fy53+fy54+fy55+fy56+fy57+fy58+
fy61+fy62+fy63+fy64+fy65+fy66+fy67+fy68+
fy71+fy72+fy73+fy74+fy75+fy76+fy77+fy78+
fy81+fy82+fy83+fy84+fy85+fy86+fy87+fy88;
PR_L1=(fy11+fy21+fy31+fy41+fy51+fy61+fy71+fy81)/fy;
PR_L2=(fy12+fy22+fy32+fy42+fy52+fy62+fy72+fy82)/fy;
PR_L3=(fy13+fy23+fy33+fy43+fy53+fy63+fy73+fy83)/fy;
PR_L4=(fy14+fy24+fy34+fy44+fy54+fy64+fy74+fy84)/fy;
PR_L5=(fy15+fy25+fy35+fy45+fy55+fy65+fy75+fy85)/fy;
PR_L6=(fy16+fy26+fy36+fy46+fy56+fy66+fy76+fy86)/fy;
PR_L7=(fy17+fy27+fy37+fy47+fy57+fy67+fy77+fy87)/fy;
PR_L8=(fy18+fy28+fy38+fy48+fy58+fy68+fy78+fy88)/fy;
@filter only@
p_tt1=p_tt1|PR_L1;
p_tt2=p_tt2|PR_L2;
p_tt3=p_tt3|PR_L3;
p_tt4=p_tt4|PR_L4;
p_tt5=p_tt5|PR_L5;
p_tt6=p_tt6|PR_L6;
p_tt7=p_tt7|PR_L7;
p_tt8=p_tt8|PR_L8;
j_iter = j_iter+1;
endo;
retp(p_tt1,p_tt2,p_tt3,p_tt4,p_tt5,p_tt6,p_tt7,p_tt8);
endp;
@========================================================================@
proc lik_fcn4(prmtr1);
local likv,
prmtr,sigma_1,sigma_2,sigma_1bar,
sigma_2bar,sigma1c,sigma2c,sigma1cbar,sigma2cbar,d1,d2,d3,d4,
d1bar,d2bar,d3bar,d4bar,cst1,cst2,cst1bar,cst2bar,
p1_11,p1_22,p2_11,p2_22,p3_11,p3_22,
p11,p12,p13,p14,p15,p16,p17,p18,
p21,p22,p23,p24,p25,p26,p27,p28,
p31,p32,p33,p34,p35,p36,p37,p38,
p41,p42,p43,p44,p45,p46,p47,p48,
p51,p52,p53,p54,p55,p56,p57,p58,
p61,p62,p63,p64,p65,p66,p67,p68,
p71,p72,p73,p74,p75,p76,p77,p78,
p81,p82,p83,p84,p85,p86,p87,p88,pr_tr,
sigmat_1,sigmat_2,sigmat_3,sigmat_4,sigmat_5,sigmat_6,sigmat_7,sigmat_8,
A,EN,PROB__T,PR_L1,PR_L2,PR_L3,PR_L4,PR_L5,PR_L6,PR_L7,PR_L8,j_iter,
PR_TL11,PR_TL12,PR_TL13,PR_TL14,PR_TL15,PR_TL16,PR_TL17,PR_TL18,
PR_TL21,PR_TL22,PR_TL23,PR_TL24,PR_TL25,PR_TL26,PR_TL27,PR_TL28,
PR_TL31,PR_TL32,PR_TL33,PR_TL34,PR_TL35,PR_TL36,PR_TL37,PR_TL38,
PR_TL41,PR_TL42,PR_TL43,PR_TL44,PR_TL45,PR_TL46,PR_TL47,PR_TL48,
PR_TL51,PR_TL52,PR_TL53,PR_TL54,PR_TL55,PR_TL56,PR_TL57,PR_TL58,
PR_TL61,PR_TL62,PR_TL63,PR_TL64,PR_TL65,PR_TL66,PR_TL67,PR_TL68,
PR_TL71,PR_TL72,PR_TL73,PR_TL74,PR_TL75,PR_TL76,PR_TL77,PR_TL78,
PR_TL81,PR_TL82,PR_TL83,PR_TL84,PR_TL85,PR_TL86,PR_TL87,PR_TL88,
e11,e12,e13,e14,e15,e16,e17,e18,
e21,e22,e23,e24,e25,e26,e27,e28,
e31,e32,e33,e34,e35,e36,e37,e38,
e41,e42,e43,e44,e45,e46,e47,e48,
e51,e52,e53,e54,e55,e56,e57,e58,
e61,e62,e63,e64,e65,e66,e67,e68,
e71,e72,e73,e74,e75,e76,e77,e78,
e81,e82,e83,e84,e85,e86,e87,e88,
fy11,fy12,fy13,fy14,fy15,fy16,fy17,fy18,
fy21,fy22,fy23,fy24,fy25,fy26,fy27,fy28,
fy31,fy32,fy33,fy34,fy35,fy36,fy37,fy38,
fy41,fy42,fy43,fy44,fy45,fy46,fy47,fy48,
fy51,fy52,fy53,fy54,fy55,fy56,fy57,fy58,
fy61,fy62,fy63,fy64,fy65,fy66,fy67,fy68,
fy71,fy72,fy73,fy74,fy75,fy76,fy77,fy78,
fy81,fy82,fy83,fy84,fy85,fy86,fy87,fy88,fy;
prmtr=trans4(prmtr1);
@Normal Times Parameters@
d1=prmtr[1];
d2=prmtr[2];
d3=prmtr[3];
d4=prmtr[4];
sigma_1=prmtr[5];
sigma_2=prmtr[6];
sigma1c=prmtr[7];
sigma2c=prmtr[8];
cst1=prmtr[17];
cst2=prmtr[18];
@S_1t parameters@
sigma_1bar=prmtr[9];
@S_2t parameters@
sigma_2bar=prmtr[10];
@S_ct=S_3t parameters@
sigma1cbar=prmtr[11];
sigma2cbar=prmtr[12];
d1bar=prmtr[13];
d2bar=prmtr[14];
d3bar=prmtr[15];
d4bar=prmtr[16];
cst1bar=prmtr[19];
cst2bar=prmtr[20];
@Transition Probabilities@
p1_11=prmtr[21];
p1_22=prmtr[22];
p2_11=prmtr[23];
p2_22=prmtr[24];
p3_11=prmtr[25];
p3_22=prmtr[26];
p11=p1_11*p2_11*p3_11;
p12=p1_11*p2_11*(1-p3_11);
p13=p1_11*(1-p2_11)*p3_11;
p14=p1_11*(1-p2_11)*(1-p3_11);
p15=(1-p1_11)*p2_11*p3_11;
p16=(1-p1_11)*p2_11*(1-p3_11);
p17=(1-p1_11)*(1-p2_11)*p3_11;
p18=1-p11-p12-p13-p14-p15-p16-p17;
p21=p1_11*p2_11*(1-p3_22);
p22=p1_11*p2_11*p3_22;
p23=p1_11*(1-p2_11)*(1-p3_22);
p24=p1_11*(1-p2_11)*p3_22;
p25=(1-p1_11)*p2_11*(1-p3_22);
p26=(1-p1_11)*p2_11*p3_22;
p27=(1-p1_11)*(1-p2_11)*(1-p3_22);
p28=1-p21-p22-p23-p24-p25-p26-p27;
p31=p1_11*(1-p2_22)*p3_11;
p32=p1_11*(1-p2_22)*(1-p3_11);
p33=p1_11*p2_22*p3_11;
p34=p1_11*p2_22*(1-p3_11);
p35=(1-p1_11)*(1-p2_22)*p3_11;
p36=(1-p1_11)*(1-p2_22)*(1-p3_11);
p37=(1-p1_11)*p2_22*p3_11;
p38=1-p31-p32-p33-p34-p35-p36-p37;
p41=p1_11*(1-p2_22)*(1-p3_22);
p42=p1_11*(1-p2_22)*p3_22;
p43=p1_11*p2_22*(1-p3_22);
p44=p1_11*p2_22*p3_22;
p45=(1-p1_11)*(1-p2_22)*(1-p3_22);
p46=(1-p1_11)*(1-p2_22)*p3_22;
p47=(1-p1_11)*p2_22*(1-p3_22);
p48=1-p41-p42-p43-p44-p45-p46-p47;
p51=(1-p1_22)*p2_11*p3_11;
p52=(1-p1_22)*p2_11*(1-p3_11);
p53=(1-p1_22)*(1-p2_11)*p3_11;
p54=(1-p1_22)*(1-p2_11)*(1-p3_11);
p55=p1_22*p2_11*p3_11;
p56=p1_22*p2_11*(1-p3_11);
p57=p1_22*(1-p2_11)*p3_11;
p58=1-p51-p52-p53-p54-p55-p56-p57;
p61=(1-p1_22)*p2_11*(1-p3_22);
p62=(1-p1_22)*p2_11*p3_22;
p63=(1-p1_22)*(1-p2_11)*(1-p3_22);
p64=(1-p1_22)*(1-p2_11)*p3_22;
p65=p1_22*p2_11*(1-p3_22);
p66=p1_22*p2_11*p3_22;
p67=p1_22*(1-p2_11)*(1-p3_22);
p68=1-p61-p62-p63-p64-p65-p66-p67;
p71=(1-p1_22)*(1-p2_22)*p3_11;
p72=(1-p1_22)*(1-p2_22)*(1-p3_11);
p73=(1-p1_22)*p2_22*p3_11;
p74=(1-p1_22)*p2_22*(1-p3_11);
p75=p1_22*(1-p2_22)*p3_11;
p76=p1_22*(1-p2_22)*(1-p3_11);
p77=p1_22*p2_22*p3_11;
p78=1-p71-p72-p73-p74-p75-p76-p77;
p81=(1-p1_22)*(1-p2_22)*(1-p3_22);
p82=(1-p1_22)*(1-p2_22)*p3_22;
p83=(1-p1_22)*p2_22*(1-p3_22);
p84=(1-p1_22)*p2_22*p3_22;
p85=p1_22*(1-p2_22)*(1-p3_22);
p86=p1_22*(1-p2_22)*p3_22;
p87=p1_22*p2_22*(1-p3_22);
p88=1-p81-p82-p83-p84-p85-p86-p87;
pr_tr= p11~p12~p13~p14~p15~p16~p17~p18|
p21~p22~p23~p24~p25~p26~p27~p28|
p31~p32~p33~p34~p35~p36~p37~p38|
p41~p42~p43~p44~p45~p46~p47~p48|
p51~p52~p53~p54~p55~p56~p57~p58|
p61~p62~p63~p64~p65~p66~p67~p68|
p71~p72~p73~p74~p75~p76~p77~p78|
p81~p82~p83~p84~p85~p86~p87~p88;
sigmat_1= sigma1c^2+sigma_1^2~sigma1c*sigma2c|
sigma1c*sigma2c~sigma2c^2+sigma_2^2;
sigmat_2= sigma1cbar^2+sigma_1^2~sigma1cbar*sigma2cbar|
sigma1cbar*sigma2cbar~sigma2cbar^2+sigma_2^2;
sigmat_3= sigma1c^2+sigma_1^2~sigma1c*sigma2c|
sigma1c*sigma2c~sigma2c^2+sigma_2bar^2;
sigmat_4= sigma1cbar^2+sigma_1^2~sigma1cbar*sigma2cbar|
sigma1cbar*sigma2cbar~sigma2cbar^2+sigma_2bar^2;
sigmat_5= sigma1c^2+sigma_1bar^2~sigma1c*sigma2c|
sigma1c*sigma2c~sigma2c^2+sigma_2^2;
sigmat_6= sigma1cbar^2+sigma_1bar^2~sigma1cbar*sigma2cbar|
sigma1cbar*sigma2cbar~sigma2cbar^2+sigma_2^2;
sigmat_7= sigma1c^2+sigma_1bar^2~sigma1c*sigma2c|
sigma1c*sigma2c~sigma2c^2+sigma_2bar^2;
sigmat_8= sigma1cbar^2+sigma_1bar^2~sigma1cbar*sigma2cbar|
sigma1cbar*sigma2cbar~sigma2cbar^2+sigma_2bar^2;
A = (eye(8)-pr_tr)|ones(1,8);
EN=(0|0|0|0|0|0|0|0|1);
PROB__T = inv(A'A)*A'EN; @8x1 UNCONDITIONAL PROBABILITIES@
PR_L1=PROB__T[1];
PR_L2=PROB__T[2];
PR_L3=PROB__T[3];
PR_L4=PROB__T[4];
PR_L5=PROB__T[5];
PR_L6=PROB__T[6];
PR_L7=PROB__T[7];
PR_L8=PROB__T[8];
likv=0;
j_iter = 1;
do until j_iter>t;
PR_TL11=p11*PR_L1;
PR_TL12=p12*PR_L1;
PR_TL13=p13*PR_L1;
PR_TL14=p14*PR_L1;
PR_TL15=p15*PR_L1;
PR_TL16=p16*PR_L1;
PR_TL17=p17*PR_L1;
PR_TL18=p18*PR_L1;
PR_TL21=p21*PR_L2;
PR_TL22=p22*PR_L2;
PR_TL23=p23*PR_L2;
PR_TL24=p24*PR_L2;
PR_TL25=p25*PR_L2;
PR_TL26=p26*PR_L2;
PR_TL27=p27*PR_L2;
PR_TL28=p28*PR_L2;
PR_TL31=p31*PR_L3;
PR_TL32=p32*PR_L3;
PR_TL33=p33*PR_L3;
PR_TL34=p34*PR_L3;
PR_TL35=p35*PR_L3;
PR_TL36=p36*PR_L3;
PR_TL37=p37*PR_L3;
PR_TL38=p38*PR_L3;
PR_TL41=p41*PR_L4;
PR_TL42=p42*PR_L4;
PR_TL43=p43*PR_L4;
PR_TL44=p44*PR_L4;
PR_TL45=p45*PR_L4;
PR_TL46=p46*PR_L4;
PR_TL47=p47*PR_L4;
PR_TL48=p48*PR_L4;
PR_TL51=p51*PR_L5;
PR_TL52=p52*PR_L5;
PR_TL53=p53*PR_L5;
PR_TL54=p54*PR_L5;
PR_TL55=p55*PR_L5;
PR_TL56=p56*PR_L5;
PR_TL57=p57*PR_L5;
PR_TL58=p58*PR_L5;
PR_TL61=p61*PR_L6;
PR_TL62=p62*PR_L6;
PR_TL63=p63*PR_L6;
PR_TL64=p64*PR_L6;
PR_TL65=p65*PR_L6;
PR_TL66=p66*PR_L6;
PR_TL67=p67*PR_L6;
PR_TL68=p68*PR_L6;
PR_TL71=p71*PR_L7;
PR_TL72=p72*PR_L7;
PR_TL73=p73*PR_L7;
PR_TL74=p74*PR_L7;
PR_TL75=p75*PR_L7;
PR_TL76=p76*PR_L7;
PR_TL77=p77*PR_L7;
PR_TL78=p78*PR_L7;
PR_TL81=p81*PR_L8;
PR_TL82=p82*PR_L8;
PR_TL83=p83*PR_L8;
PR_TL84=p84*PR_L8;
PR_TL85=p85*PR_L8;
PR_TL86=p86*PR_L8;
PR_TL87=p87*PR_L8;
PR_TL88=p88*PR_L8;
e11=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e12=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e13=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e14=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e15=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e16=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e17=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e18=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e21=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e22=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e23=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e24=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e25=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e26=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e27=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e28=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e31=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e32=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e33=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e34=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e35=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e36=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e37=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e38=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e41=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e42=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e43=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e44=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e45=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e46=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e47=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e48=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e51=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e52=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e53=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e54=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e55=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e56=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e57=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e58=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e61=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e62=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e63=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e64=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e65=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e66=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e67=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e68=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e71=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e72=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e73=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e74=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e75=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e76=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e77=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e78=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e81=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e82=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e83=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e84=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e85=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e86=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
e87=yy[j_iter,1:2]'-(cst1+d1*S1[j_iter]+d2*S2[j_iter]|cst2+d3*S1[j_iter]+d4*S2[j_iter]);
e88=yy[j_iter,1:2]'-(cst1bar+d1bar*S1[j_iter]+d2bar*S2[j_iter]|cst2bar+d3bar*S1[j_iter]+d4bar*S2[j_iter]);
fy11=v_prob(e11,sigmat_1)*PR_TL11;
fy12=v_prob(e12,sigmat_2)*PR_TL12;
fy13=v_prob(e13,sigmat_3)*PR_TL13;
fy14=v_prob(e14,sigmat_4)*PR_TL14;
fy15=v_prob(e15,sigmat_5)*PR_TL15;
fy16=v_prob(e16,sigmat_6)*PR_TL16;
fy17=v_prob(e17,sigmat_7)*PR_TL17;
fy18=v_prob(e18,sigmat_8)*PR_TL18;
fy21=v_prob(e21,sigmat_1)*PR_TL21;
fy22=v_prob(e22,sigmat_2)*PR_TL22;
fy23=v_prob(e23,sigmat_3)*PR_TL23;
fy24=v_prob(e24,sigmat_4)*PR_TL24;
fy25=v_prob(e25,sigmat_5)*PR_TL25;
fy26=v_prob(e26,sigmat_6)*PR_TL26;
fy27=v_prob(e27,sigmat_7)*PR_TL27;
fy28=v_prob(e28,sigmat_8)*PR_TL28;
fy31=v_prob(e31,sigmat_1)*PR_TL31;
fy32=v_prob(e32,sigmat_2)*PR_TL32;
fy33=v_prob(e33,sigmat_3)*PR_TL33;
fy34=v_prob(e34,sigmat_4)*PR_TL34;
fy35=v_prob(e35,sigmat_5)*PR_TL35;
fy36=v_prob(e36,sigmat_6)*PR_TL36;
fy37=v_prob(e37,sigmat_7)*PR_TL37;
fy38=v_prob(e38,sigmat_8)*PR_TL38;
fy41=v_prob(e41,sigmat_1)*PR_TL41;
fy42=v_prob(e42,sigmat_2)*PR_TL42;
fy43=v_prob(e43,sigmat_3)*PR_TL43;
fy44=v_prob(e44,sigmat_4)*PR_TL44;
fy45=v_prob(e45,sigmat_5)*PR_TL45;
fy46=v_prob(e46,sigmat_6)*PR_TL46;
fy47=v_prob(e47,sigmat_7)*PR_TL47;
fy48=v_prob(e48,sigmat_8)*PR_TL48;
fy51=v_prob(e51,sigmat_1)*PR_TL51;
fy52=v_prob(e52,sigmat_2)*PR_TL52;
fy53=v_prob(e53,sigmat_3)*PR_TL53;
fy54=v_prob(e54,sigmat_4)*PR_TL54;
fy55=v_prob(e55,sigmat_5)*PR_TL55;
fy56=v_prob(e56,sigmat_6)*PR_TL56;
fy57=v_prob(e57,sigmat_7)*PR_TL57;
fy58=v_prob(e58,sigmat_8)*PR_TL58;
fy61=v_prob(e61,sigmat_1)*PR_TL61;
fy62=v_prob(e62,sigmat_2)*PR_TL62;
fy63=v_prob(e63,sigmat_3)*PR_TL63;
fy64=v_prob(e64,sigmat_4)*PR_TL64;
fy65=v_prob(e65,sigmat_5)*PR_TL65;
fy66=v_prob(e66,sigmat_6)*PR_TL66;
fy67=v_prob(e67,sigmat_7)*PR_TL67;
fy68=v_prob(e68,sigmat_8)*PR_TL68;
fy71=v_prob(e71,sigmat_1)*PR_TL71;
fy72=v_prob(e72,sigmat_2)*PR_TL72;
fy73=v_prob(e73,sigmat_3)*PR_TL73;
fy74=v_prob(e74,sigmat_4)*PR_TL74;
fy75=v_prob(e75,sigmat_5)*PR_TL75;
fy76=v_prob(e76,sigmat_6)*PR_TL76;
fy77=v_prob(e77,sigmat_7)*PR_TL77;
fy78=v_prob(e78,sigmat_8)*PR_TL78;
fy81=v_prob(e81,sigmat_1)*PR_TL81;
fy82=v_prob(e82,sigmat_2)*PR_TL82;
fy83=v_prob(e83,sigmat_3)*PR_TL83;
fy84=v_prob(e84,sigmat_4)*PR_TL84;
fy85=v_prob(e85,sigmat_5)*PR_TL85;
fy86=v_prob(e86,sigmat_6)*PR_TL86;
fy87=v_prob(e87,sigmat_7)*PR_TL87;
fy88=v_prob(e88,sigmat_8)*PR_TL88;
fy= fy11+fy12+fy13+fy14+fy15+fy16+fy17+fy18+
fy21+fy22+fy23+fy24+fy25+fy26+fy27+fy28+
fy31+fy32+fy33+fy34+fy35+fy36+fy37+fy38+
fy41+fy42+fy43+fy44+fy45+fy46+fy47+fy48+
fy51+fy52+fy53+fy54+fy55+fy56+fy57+fy58+
fy61+fy62+fy63+fy64+fy65+fy66+fy67+fy68+
fy71+fy72+fy73+fy74+fy75+fy76+fy77+fy78+
fy81+fy82+fy83+fy84+fy85+fy86+fy87+fy88;