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Copy pathML_fitbigN.m
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ML_fitbigN.m
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function [pbest, BIC, AIC, negLLfit] = ML_fitbigN(theta, tsamp, Ninit,Vinit, N,mudatavec, vardatavec, modelcode)
switch modelcode
case 1
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit, Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit, Vinit, modelcode);
modelfun_V4= @(p)gen_model_v4bigN(p, tsamp, Ninit, Vinit, modelcode);
var_in_mean = @(p)(1/N).*(modelfun_V(p)); % vertical
var_in_var = @(p)(1/N).*(modelfun_V4(p)-(((N-3)./(N-1)).*(modelfun_V(p).^2)));
% PERFORM FITTING OF ALL DATA TO SINGLE EXPONENTIAL MODEL
pfxform = @(pval)[1 1].*log(pval); %'forward' parameter transform into Reals
pbxform = @(phat)[1 1].*exp(phat); %'backward' parameter transform into model space
yfxform = @(y)log(y); % 'forward' transform for data and model output
ybxform = @(yhat)exp(yhat); % 'inverse' transform for data and model output
J = @(phat) (0.99*sum(((mudatavec-modelfun_mu(pbxform(phat))).^2)./(2.*sqrt(var_in_mean(pbxform(phat)))) + log(sqrt(var_in_mean(pbxform(phat)))) + 0.5*log(2*pi))+...
0.01*sum(((vardatavec-modelfun_V(pbxform(phat))).^2)./(2.*sqrt(var_in_var(pbxform(phat)))) + log(sqrt(var_in_var(pbxform(phat)))) + 0.5*log(2*pi)));
objfun_J = @(phat)(J(phat));
lb = [0 0 ];
ub = [ Inf Inf ];
options = optimset('TolX', 1e-8, 'MaxFunEvals', 1000);
[phatbest_J,fval,exitflag] = fminsearch(objfun_J, pfxform(theta), options);% need a better way to search parameter space,i.e. montecarlo
negLLguess= objfun_J(pfxform(theta));
negLLfit= objfun_J(phatbest_J);
params_best_J= pbxform(phatbest_J);
pbest = params_best_J;
k = 2;
n = length(mudatavec)*length(Ninit);
AIC = 2*J(pfxform(params_best_J)) + 2*k;
BIC = 2*J(pfxform(params_best_J)) +log(n)*k;
case 2
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit,Vinit, modelcode);
modelfun_V4= @(p)gen_model_v4bigN(p, tsamp, Ninit,Vinit, modelcode);
var_in_mean = @(p)(1/N).*(modelfun_V(p)); % vertical
var_in_var = @(p)(1/N).*(modelfun_V4(p)-(((N-3)./(N-1)).*(modelfun_V(p).^2)));
% PERFORM FITTING OF ALL DATA TO SINGLE EXPONENTIAL MODEL
pfxform = @(pval)[1 1 1].*log(pval); %'forward' parameter transform into Reals
pbxform = @(phat)[1 1 1].*exp(phat); %'backward' parameter transform into model space
yfxform = @(y)log(y); % 'forward' transform for data and model output
ybxform = @(yhat)exp(yhat); % 'inverse' transform for data and model output
J = @(phat) (0.99*sum(((mudatavec-modelfun_mu(pbxform(phat))).^2)./(2.*sqrt(var_in_mean(pbxform(phat)))) + log(sqrt(var_in_mean(pbxform(phat)))) + 0.5*log(2*pi))+...
0.01*sum(((vardatavec-modelfun_V(pbxform(phat))).^2)./(2.*sqrt(var_in_var(pbxform(phat)))) + log(sqrt(var_in_var(pbxform(phat)))) + 0.5*log(2*pi)));
objfun_J = @(phat)(J(phat));
lb = [0 0 0];
ub = [ Inf Inf Inf ];
options = optimset('TolX', 1e-8, 'MaxFunEvals', 1000);
[phatbest_J,fval,exitflag] = fminsearch(objfun_J, pfxform(theta), options);% need a better way to search parameter space,i.e. montecarlo
negLLguess= objfun_J(pfxform(theta));
negLLfit= objfun_J(phatbest_J);
params_best_J= pbxform(phatbest_J);
pbest = params_best_J;
k = 3;
n = length(mudatavec)*length(Ninit);
AIC = 2*J(pfxform(params_best_J)) + 2*k;
BIC = 2*J(pfxform(params_best_J)) +log(n)*k;
case 3 % strong Allee model Allee death
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit, Vinit,modelcode);
modelfun_V4= @(p)gen_model_v4bigN(p, tsamp, Ninit, Vinit,modelcode);
var_in_mean = @(p)(1/N).*(modelfun_V(p)); % vertical
var_in_var = @(p)(1/N).*(modelfun_V4(p)-(((N-3)./(N-1)).*(modelfun_V(p).^2)));
pfxform = @(pval)[1 1 1].*log(pval); %'forward' parameter transform into Reals
pbxform = @(phat)[1 1 1].*exp(phat); %'backward' parameter transform into model space
yfxform = @(y)log(y); % 'forward' transform for data and model output
ybxform = @(yhat)exp(yhat); % 'inverse' transform for data and model output
J = @(phat) (0.99*sum(((mudatavec-modelfun_mu(pbxform(phat))).^2)./(2.*sqrt(var_in_mean(pbxform(phat)))) + log(sqrt(var_in_mean(pbxform(phat)))) + 0.5*log(2*pi))+...
0.11*sum(((vardatavec-modelfun_V(pbxform(phat))).^2)./(2.*sqrt(var_in_var(pbxform(phat)))) + log(sqrt(var_in_var(pbxform(phat)))) + 0.5*log(2*pi)));
objfun_J = @(phat)(J(phat));
lb = [0 0 -Inf 0];
ub = [ Inf Inf Inf];
options = optimset('TolX', 1e-8, 'MaxFunEvals', 1000);
[phatbest_J,fval,exitflag] = fminsearch(objfun_J, pfxform(theta), options);% need a better way to search parameter space,i.e. montecarlo
negLLguess= objfun_J(pfxform(theta));
negLLfit= objfun_J(phatbest_J);
params_best_J= pbxform(phatbest_J);
pbest = params_best_J;
k = 3;
n = length(mudatavec)*length(Ninit);
AIC = 2*J(pfxform(params_best_J)) + 2*k;
BIC = 2*J(pfxform(params_best_J)) +log(n)*k;
case 4 % strong Allee model Allee on birth & death
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit,Vinit, modelcode);
modelfun_V4= @(p)gen_model_v4bigN(p, tsamp, Ninit,Vinit, modelcode);
var_in_mean = @(p)(1/N).*(modelfun_V(p)); % vertical
var_in_var = @(p)(1/N).*(modelfun_V4(p)-(((N-3)./(N-1)).*(modelfun_V(p).^2)));
pfxform = @(pval)[1 1 1].*log(pval); %'forward' parameter transform into Reals
pbxform = @(phat)[1 1 1].*exp(phat); %'backward' parameter transform into model space
yfxform = @(y)log(y); % 'forward' transform for data and model output
ybxform = @(yhat)exp(yhat); % 'inverse' transform for data and model output
J = @(phat) (0.99*sum(((mudatavec-modelfun_mu(pbxform(phat))).^2)./(2.*sqrt(var_in_mean(pbxform(phat)))) + log(sqrt(var_in_mean(pbxform(phat)))) + 0.5*log(2*pi))+...
0.01*sum(((vardatavec-modelfun_V(pbxform(phat))).^2)./(2.*sqrt(var_in_var(pbxform(phat)))) + log(sqrt(var_in_var(pbxform(phat)))) + 0.5*log(2*pi)));
objfun_J = @(phat)(J(phat));
lb = [0 0 -Inf 0];
ub = [ Inf Inf Inf];
options = optimset('TolX', 1e-8, 'MaxFunEvals', 1000);
[phatbest_J,fval,exitflag] = fminsearch(objfun_J, pfxform(theta), options);% need a better way to search parameter space,i.e. montecarlo
negLLguess= objfun_J(pfxform(theta));
negLLfit= objfun_J(phatbest_J);
params_best_J= pbxform(phatbest_J);
pbest = params_best_J;
k = 3;
n = length(mudatavec)*length(Ninit);
AIC = 2*J(pfxform(params_best_J)) + 2*k;
BIC = 2*J(pfxform(params_best_J)) +log(n)*k;
case 5 % weak Allee model Allee on birth
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit,Vinit, modelcode);
modelfun_V4= @(p)gen_model_v4bigN(p, tsamp, Ninit,Vinit, modelcode);
var_in_mean = @(p)(1/N).*(modelfun_V(p)); % vertical
var_in_var = @(p)(1/N).*(modelfun_V4(p)-(((N-3)./(N-1)).*(modelfun_V(p).^2)));
lb = [0 0 -10 0];
ub = [ 2 2 10 10];
pfxform = @(pval)[1 1 1 1].*(pval-lb)./(ub-lb); %'forward' parameter transform (normalized)
pbxform = @(phat) [1 1 1 1].*((ub-lb).*(phat))+lb;
%yfxform = @(y)log(y); % 'forward' transform for data and model output
%ybxform = @(yhat)exp(yhat); % 'inverse' transform for data and model output
J = @(phat) (0.99*sum(((mudatavec-modelfun_mu(pbxform(phat))).^2)./(sqrt(var_in_mean(pbxform(phat)))) + log(sqrt(var_in_mean(pbxform(phat)))) + 0.5*log(2*pi))+...
0.01*sum(((vardatavec-modelfun_V(pbxform(phat))).^2)./(2.*sqrt(var_in_var(pbxform(phat)))) + log(sqrt(var_in_var(pbxform(phat)))) + 0.5*log(2*pi)));
objfun_J = @(phat)(J(phat));
LB = [0 0 0 0];
UB = [1 1 1 1];
options = optimset('TolX', 1e-8, 'MaxFunEvals', 2000);
[phatbest_J,fval,exitflag] = fminsearchbnd(objfun_J, pfxform(theta),LB, UB, options);
%[phatbest_J,fval,exitflag] = fminsearchbnd(objfun_J, (theta),lb, ub, options);% need a better way to search parameter space,i.e. montecarlo
negLLguess= objfun_J(pfxform(theta));
negLLfit= objfun_J(phatbest_J);
params_best_J= pbxform(phatbest_J);
pbest = params_best_J;
k = 4;
n = length(mudatavec)*length(Ninit);
AIC = 2*J(pfxform(params_best_J)) + 2*k;
BIC = 2*J(pfxform(params_best_J)) +log(n)*k;
case 6 % weak Allee model Allee on birth
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit, Vinit,modelcode);
modelfun_V4= @(p)gen_model_v4bigN(p, tsamp, Ninit,Vinit, modelcode);
var_in_mean = @(p)(1/N).*(modelfun_V(p)); % vertical
var_in_var = @(p)(1/N).*(modelfun_V4(p)-(((N-3)./(N-1)).*(modelfun_V(p).^2)));
lb = [0 0 -10 0];
ub = [ 2 2 10 10];
pfxform = @(pval)[1 1 1 1].*(pval-lb)./(ub-lb); %'forward' parameter transform (normalized)
pbxform = @(phat) [1 1 1 1].*((ub-lb).*(phat))+lb;
%yfxform = @(y)log(y); % 'forward' transform for data and model output
%ybxform = @(yhat)exp(yhat); % 'inverse' transform for data and model output
J = @(phat) (0.99*sum(((mudatavec-modelfun_mu(pbxform(phat))).^2)./(2.*sqrt(var_in_mean(pbxform(phat)))) + log(sqrt(var_in_mean(pbxform(phat)))) + 0.5*log(2*pi))+...
0.01*sum(((vardatavec-modelfun_V(pbxform(phat))).^2)./(2.*sqrt(var_in_var(pbxform(phat)))) + log(sqrt(var_in_var(pbxform(phat)))) + 0.5*log(2*pi)));
objfun_J = @(phat)(J(phat));
LB = [0 0 0 0];
UB = [1 1 1 1];
options = optimset('TolX', 1e-8, 'MaxFunEvals', 2000);
[phatbest_J,fval,exitflag] = fminsearchbnd(objfun_J, pfxform(theta),LB, UB, options);
%[phatbest_J,fval,exitflag] = fminsearchbnd(objfun_J, (theta),lb, ub, options);% need a better way to search parameter space,i.e. montecarlo
negLLguess= objfun_J(pfxform(theta));
negLLfit= objfun_J(phatbest_J);
params_best_J= pbxform(phatbest_J);
pbest = params_best_J;
k = 4;
n = length(mudatavec)*length(Ninit);
AIC = 2*J(pfxform(params_best_J)) + 2*k;
BIC = 2*J(pfxform(params_best_J)) +log(n)*k;
case 7 % weak Allee model Allee on birth & death
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit,Vinit, modelcode);
modelfun_V4= @(p)gen_model_v4bigN(p, tsamp, Ninit,Vinit, modelcode);
var_in_mean = @(p)(1/N).*(modelfun_V(p)); % vertical
var_in_var = @(p)(1/N).*(modelfun_V4(p)-(((N-3)./(N-1)).*(modelfun_V(p).^2)));
lb = [0 0 -10 0];
ub = [ 2 2 10 10];
pfxform = @(pval)[1 1 1 1].*(pval-lb)./(ub-lb); %'forward' parameter transform (normalized)
pbxform = @(phat) [1 1 1 1].*((ub-lb).*(phat))+lb;
%yfxform = @(y)log(y); % 'forward' transform for data and model output
%ybxform = @(yhat)exp(yhat); % 'inverse' transform for data and model output
J = @(phat) (0.99*sum(((mudatavec-modelfun_mu(pbxform(phat))).^2)./(2.*sqrt(var_in_mean(pbxform(phat)))) + log(sqrt(var_in_mean(pbxform(phat)))) + 0.5*log(2*pi))+...
0.01*sum(((vardatavec-modelfun_V(pbxform(phat))).^2)./(2.*sqrt(var_in_var(pbxform(phat)))) + log(sqrt(var_in_var(pbxform(phat)))) + 0.5*log(2*pi)));
objfun_J = @(phat)(J(phat));
LB = [0 0 0 0];
UB = [1 1 1 1];
options = optimset('TolX', 1e-8, 'MaxFunEvals', 2000);
[phatbest_J,fval,exitflag] = fminsearchbnd(objfun_J, pfxform(theta),LB, UB, options);
%[phatbest_J,fval,exitflag] = fminsearchbnd(objfun_J, (theta),lb, ub, options);% need a better way to search parameter space,i.e. montecarlo
negLLguess= objfun_J(pfxform(theta));
negLLfit= objfun_J(phatbest_J);
params_best_J= pbxform(phatbest_J);
pbest = params_best_J;
k = 4;
n = length(mudatavec)*length(Ninit);
AIC = 2*J(pfxform(params_best_J)) + 2*k;
BIC = 2*J(pfxform(params_best_J)) +log(n)*k;
end