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fit_largeN0_to7_models.m
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%% Load in selected mudatavec
% Want to calculate BIC and AIC value from the fitting
% Need to make one big matrix of mu and vardata with corresponding time vecs in order
% Load in raw data, not down sampled
clear all; close all; clc
mudatavec = [];
vardatavec = [];
timevec = [];
mudatavecall = [];
vardatavecall = [];
timevecall = [];
N0vec = [];
numsamps = 0;
S1 = load('../out/BTsumfit.mat');
BTsum1= S1.BTsum;
S = load('../out/BTsumfitps.mat');
BTsum= S.BTsum;
N0list = [512; 1024];
%%
for j = 1:length(N0list)
for i = 1:length(BTsum)
if BTsum(i).N0==N0list(j)
mudata = BTsum(i).mu_t(2:end);
ind = 1:1:length(mudata);
ind = 1:1:43;
mudatasmall= mudata(ind);
mudatavec = vertcat(mudatavec, mudatasmall);
vardata = BTsum(i).var_t(2:end);
vardatasmall = vardata(ind);
vardatavec = vertcat(vardatavec, vardatasmall);
time = BTsum(i).timevec(2:end);
timesmall = time(ind);
timevec = vertcat(timevec, timesmall);
vardatavecall = vertcat(vardatavecall, BTsum(i).var_t(2:end));
mudatavecall = vertcat(mudatavecall, BTsum(i).mu_t(2:end));
timevecall = vertcat(timevecall, BTsum(i).timevec(2:end));
numsamps = BTsum(i).num + numsamps;
end
end
end
%% confirm it's same
figure;
for j = 1:length(N0list)
plot(timevecall, mudatavecall, 'r*')
hold on
plot(timevec, mudatavec, 'b.')
end
xlabel('time (hours)')
ylabel('cell numer')
title('down sampled data for fitting')
%% Perform fitting: fit all data to a single b & d
% For each fitting, we want to write functions in terms of the functions
% that run the model we are fitting to forward. The gen_model_mu runs the
% system of ODEs for the parameters and generates an expected model mean
% and variance for the input p parameters
% information
modelcode = 1;
tsamp = BTsum(1).timevec; % set sample time (if data is down sampled change accordingly
tsampfit = tsamp(2:end);
tsampnew = tsampfit(ind);
tsamp = [0 ;tsampnew];
% Initial guess
dguess = 0.005;
bguess = (log(mudatavec(end-2))-log(mudatavec(end-4)))/(timevec(end-2)-timevec(end-4)) + dguess;
theta = [bguess,dguess];
Ninit = N0list;
Vinit= [BTsum(1).V0, BTsum(2).V0];
% Vinit = 0;
N= numsamps;
[pbestbd, BICbd, AICbd,negLLfitbd] = ML_fitbigN(theta, tsamp, Ninit,Vinit, N,mudatavec, vardatavec, modelcode)
% need to define th inline functions that run forward the mean and the
% variance
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit, Vinit, modelcode);
%% Plot the data compared to best fit model
figure;
subplot(1,2,1)
hold on
plot(timevec, mudatavec, 'r*')
for j = 1:length(N0list)
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_mu(pbestbd), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel('<n> time')
legend('data', 'best fit b-d')
legend boxoff
title(['Mean in data fit to simple birth-death model, BIC= ', num2str(BICbd)])
xlim([ 0 332])
subplot(1,2,2)
hold on
plot(timevec, vardatavec, 'g*')
for j = 1:length(N0list)
modelfun_V =@(p)gen_model_varbigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_V(pbestbd), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel(' Variance in time')
legend('data', 'best fit b-d')
legend boxoff
title(['Variance in data fit to simple birth-death model, BIC= ', num2str(BICbd)])
xlim([ 0 332])
%% Profile likelihood of b-d model
% Use these to determine parameter certainty and find the 95 % CI on the
% b and d parameter estimate from all data
num_params = 2;
% Check fxn
fbest = negLLfitbd;
factor = 0.01;
numpoints = 10;
params = pbestbd;
[profilesbd] = profile_likelihood(params, tsamp, N0list, numsamps ,mudatavec, vardatavec, modelcode, factor, numpoints);
threshold = chi2inv(0.95,length(params))/2 + fbest;
ilo1=find(profilesbd(:,2,1)<threshold);
if ilo1(end) ==numpoints*2 ||ilo1(1)==1
display('All negLL vals below threshold. Increase factor.')
CIbd(1,:) = [NaN, NaN];
else
CIbd(1,:) = [profilesbd(ilo1(1),1,1), profilesbd(ilo1(end),1,1)];
end
ilo2 = find(profilesbd(:,2,2)<threshold);
if ilo2(end) ==numpoints*2 ||ilo1(1)==1
display('All negLL vals below threshold. Increase factor.')
CIbd(2,:)= [NaN NaN];
else
CIbd(2,:) = [profilesbd(ilo2(1),1,2), profilesbd(ilo2(end),1,2)];
end
% this output a profiles 3D matrix whose first z dimension contains the
% profiled parameters and the corresponding negLL
% the CI contains the upper and lower CI on first the b parameter than
% the d parameter
%% Plot profiles to view CI
figure;
subplot(1, 2,1)
plot(profilesbd(:,1,1), profilesbd(:,2,1))
hold on
plot(pbestbd(1),negLLfitbd,'r*','LineWidth',2)
plot([profilesbd(1,1,1) profilesbd(end,1,1)],[threshold threshold],'r--')
xlabel(' profiles param values')
ylabel('Cost Function Value')
title(['Profile Likelihood of b CI = [',num2str(CIbd(1,:)),']'])
subplot(1,2,2)
plot(profilesbd(:,1,2), profilesbd(:,2,2))
hold on
plot(pbestbd(2),negLLfitbd,'r*','LineWidth',2)
plot([profilesbd(1,1,2) profilesbd(end,1,2)],[threshold threshold],'r--')
xlabel(' profiles param values')
ylabel('Cost Function Value')
title([' Profile Likelihood of d CI = [',num2str(CIbd(2,:)),']'])
%% Perform fitting: fit all data to strong Allee model on birth
% For each fitting, we want to write functions in terms of the functions
% that run the model we are fitting to forward. The gen_model_mu runs the
% system of ODEs for the parameters and generates an expected model mean
% and variance for the input p parameters
% information
modelcode = 2;
% Initial guess
bguess = (log(mudatavec(end-2))-log(mudatavec(end-4)))/(timevec(end-2)-timevec(end-4)) + 0.002;
dguess = 0.002;
Aguess = 2;
theta = [bguess,dguess, Aguess];
Ninit = N0list;
N= numsamps;
[pbeststrAb, BICstrAb, AICstrAb,negLLfitstrAb] = ML_fitbigN(theta, tsamp, Ninit,Vinit, N,mudatavec, vardatavec, modelcode);
% need to define th inline functions that run forward the mean and the
% variance
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit, Vinit,modelcode);
%% Plot the data compared to best fit model for strong Allee on birth
modelcode = 2;
figure;
subplot(1,2,1)
hold on
plot(timevec, mudatavec, 'r*')
for j = 1:length(N0list)
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_mu(pbeststrAb), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel('<n> time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Mean in data fit to strong Allee (b), BIC= ', num2str(BICstrAb)])
xlim([ 0 332])
subplot(1,2,2)
hold on
plot(timevec, vardatavec, 'g*')
for j = 1:length(N0list)
modelfun_V =@(p)gen_model_varbigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_V(pbeststrAb), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel(' Variance in time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Variance in data fit to strong Allee(b) model, BIC= ', num2str(BICstrAb)])
xlim([ 0 332])
%% Profile likelihood of strong Allee on birth model
% Use these to determine parameter certainty and find the 95 % CI on the
% b and d parameter estimate from all data
num_params = 3;
% Check fxn
fbest = negLLfitstrAb;
factor = 0.05;
numpoints = 10;
params = pbeststrAb;
[profilesstrAb] = profile_likelihood(params, tsamp, N0list, numsamps ,mudatavec, vardatavec, modelcode, factor, numpoints);
threshold = chi2inv(0.95,length(params))/2 + fbest;
ilo1=find(profilesstrAb(:,2,1)<threshold);
if ilo1(end) ==numpoints*2 ||ilo1(1)==1
display('All negLL vals below threshold. Increase factor.')
CIstrAb(1,:) = [NaN, NaN];
else
CIstrAb(1,:) = [profilesstrAb(ilo1(1),1,1), profilesstrAb(ilo1(end),1,1)];
end
ilo2 = find(profilesstrAb(:,2,2)<threshold);
if ilo2(end) ==numpoints*2 ||ilo2(1)==1
display('All negLL vals below threshold. Increase factor.')
CIstrAb(2,:)= [NaN NaN];
else
CIstrAb(2,:) = [profilesstrAb(ilo2(1),1,2), profilesstrAb(ilo2(end),1,2)];
end
ilo3 = find(profilesstrAb(:,2,3)<threshold);
if ilo3(end) ==numpoints*2 ||ilo3(1)==1
display('All negLL vals below threshold. Increase factor.')
CIstrAb(3,:)= [NaN NaN];
else
CIstrAb(3,:) = [profilesstrAb(ilo3(1),1,3), profilesstrAb(ilo3(end),1,3)];
end
% this output a profiles 3D matrix whose first z dimension contains the
% profiled parameters and the corresponding negLL
% the CI contains the upper and lower CI on first the b parameter than
% the d parameter
%% Plot profiles of strong Allee on birth to view CI
figure;
subplot(1, 3,1)
plot(profilesstrAb(:,1,1), profilesstrAb(:,2,1))
hold on
plot(pbeststrAb(1),negLLfitstrAb,'r*','LineWidth',2)
plot([profilesstrAb(1,1,1) profilesstrAb(end,1,1)],[threshold threshold],'r--')
xlabel(' profiled b values')
xlim([profilesstrAb(1,1,1) profilesstrAb(end,1,1)])
ylabel('Cost Function Value')
title(['Profile Likelihood of b CI = [',num2str(CIstrAb(1,:)),']'])
subplot(1,3,2)
plot(profilesstrAb(:,1,2), profilesstrAb(:,2,2))
hold on
plot(pbeststrAb(2),negLLfitstrAb,'r*','LineWidth',2)
plot([profilesstrAb(1,1,2) profilesstrAb(end,1,2)],[threshold threshold],'r--')
xlabel(' profiles d values')
xlim ([profilesstrAb(1,1,2) profilesstrAb(end,1,2)])
ylabel('Cost Function Value')
title([' Profile Likelihood of d CI = [',num2str(CIstrAb(2,:)),']'])
subplot(1,3,3)
plot(profilesstrAb(:,1,3), profilesstrAb(:,2,3))
hold on
plot(pbeststrAb(3),negLLfitstrAb,'r*','LineWidth',2)
plot([profilesstrAb(1,1,3) profilesstrAb(end,1,3)],[threshold threshold],'r--')
xlabel(' profiled A values')
xlim([profilesstrAb(1,1,3) profilesstrAb(end,1,3)])
ylabel('Cost Function Value')
title([' Profile Likelihood of A CI = [',num2str(CIstrAb(3,:)),']'])
%% Perform fitting: fit all data to strong Allee model on death
% For each fitting, we want to write functions in terms of the functions
% that run the model we are fitting to forward. The gen_model_mu runs the
% system of ODEs for the parameters and generates an expected model mean
% and variance for the input p parameters
% information
modelcode = 3;
% Initial guess
bguess = (log(mudatavec(end-2))-log(mudatavec(end-4)))/(timevec(end-2)-timevec(end-4)) + 0.002;
dguess = 0.002;
Aguess = 2;
theta = [bguess,dguess, Aguess];
Ninit = N0list;
N= numsamps;
[pbeststrAd, BICstrAd, AICstrAd,negLLfitstrAd] = ML_fitbigN(theta, tsamp, Ninit,Vinit, N,mudatavec, vardatavec, modelcode);
% need to define th inline functions that run forward the mean and the
% variance
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit, Vinit,modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit,Vinit, modelcode);
%% Plot the data compared to best fit model
figure;
subplot(1,2,1)
hold on
plot(timevec, mudatavec, 'r*')
for j = 1:length(N0list)
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_mubigN(pbeststrAd), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel('<n> time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Mean in data fit to strong Allee (d), BIC= ', num2str(BICstrAd)])
xlim([ 0 332])
subplot(1,2,2)
hold on
plot(timevec, vardatavec, 'g*')
for j = 1:length(N0list)
modelfun_V =@(p)gen_model_varbigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_V(pbeststrAd), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel(' Variance in time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Variance in data fit to strong Allee(d) model, BIC= ', num2str(BICstrAd)])
xlim([ 0 332])
%% Profile likelihood of strong Allee on death model
% Use these to determine parameter certainty and find the 95 % CI on the
% b and d parameter estimate from all data
num_params = 3;
% Check fxn
fbest = negLLfitstrAd;
factor = 0.05;
numpoints = 10;
params = pbeststrAd;
[profilesstrAd] = profile_likelihood(params, tsamp, N0list, numsamps ,mudatavec, vardatavec, modelcode, factor, numpoints);
threshold = chi2inv(0.95,length(params))/2 + fbest;
ilo1=find(profilesstrAd(:,2,1)<threshold);
if ilo1(end) ==numpoints*2 ||ilo1(1)==1
display('All negLL vals below threshold. Increase factor.')
CIstrAd(1,:) = [NaN, NaN];
else
CIstrAd(1,:) = [profilesstrAd(ilo1(1),1,1), profilesstrAd(ilo1(end),1,1)];
end
ilo2 = find(profilesstrAd(:,2,2)<threshold);
if ilo2(end) ==numpoints*2 ||ilo2(1)==1
display('All negLL vals below threshold. Increase factor.')
CIstrAd(2,:)= [NaN NaN];
else
CIstrAd(2,:) = [profilesstrAd(ilo2(1),1,2), profilesstrAd(ilo2(end),1,2)];
end
ilo3 = find(profilesstrAd(:,2,3)<threshold);
if ilo3(end) ==numpoints*2 ||ilo3(1)==1
display('All negLL vals below threshold. Increase factor.')
CIstrAd(3,:)= [NaN NaN];
else
CIstrAd(3,:) = [profilesstrAd(ilo3(1),1,3), profilesstrAd(ilo3(end),1,3)];
end
% this output a profiles 3D matrix whose first z dimension contains the
% profiled parameters and the corresponding negLL
% the CI contains the upper and lower CI on first the b parameter than
% the d parameter
%% Plot profiles of strong Allee on death to view CI
figure;
subplot(1, 3,1)
plot(profilesstrAd(:,1,1), profilesstrAd(:,2,1))
hold on
plot(pbeststrAd(1),negLLfitstrAd,'r*','LineWidth',2)
plot([profilesstrAd(1,1,1) profilesstrAd(end,1,1)],[threshold threshold],'r--')
xlabel(' profiled b values')
% xlim([profilesstrAd(1,1,1) profilesstrAd(end,1,1)])
ylabel('Cost Function Value')
title(['Profile Likelihood of b CI = [',num2str(CIstrAd(1,:)),']'])
subplot(1,3,2)
plot(profilesstrAd(:,1,2), profilesstrAd(:,2,2))
hold on
plot(pbeststrAd(2),negLLfitstrAd,'r*','LineWidth',2)
plot([profilesstrAd(1,1,2) profilesstrAd(end,1,2)],[threshold threshold],'r--')
xlabel(' profiles d values')
xlim ([profilesstrAd(1,1,2) profilesstrAd(end,1,2)])
ylabel('Cost Function Value')
title([' Profile Likelihood of d CI = [',num2str(CIstrAd(2,:)),']'])
subplot(1,3,3)
plot(profilesstrAd(:,1,3), profilesstrAd(:,2,3))
hold on
plot(pbeststrAd(3),negLLfitstrAd,'r*','LineWidth',2)
plot([profilesstrAd(1,1,3) profilesstrAd(end,1,3)],[threshold threshold],'r--')
xlabel(' profiled A values')
xlim([profilesstrAd(1,1,3) profilesstrAd(end,1,3)])
ylabel('Cost Function Value')
title([' Profile Likelihood of A CI = [',num2str(CIstrAd(3,:)),']'])
%% Perform fitting: fit all data to strong Allee model on birth & death
% For each fitting, we want to write functions in terms of the functions
% that run the model we are fitting to forward. The gen_model_mu runs the
% system of ODEs for the parameters and generates an expected model mean
% and variance for the input p parameters
% information
modelcode = 4;
% Initial guess
bguess = (log(mudatavec(end-2))-log(mudatavec(end-4)))/(timevec(end-2)-timevec(end-4)) + 0.002;
dguess = 0.002;
Aguess = 1;
theta = [bguess,dguess, Aguess];
Ninit = N0list;
N= numsamps;
[pbeststrAbd, BICstrAbd, AICstrAbd,negLLfitstrAbd] = ML_fitbigN(theta, tsamp, Ninit,Vinit, N,mudatavec, vardatavec, modelcode)
% need to define th inline functions that run forward the mean and the
% variance
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit,Vinit, modelcode);
%% Plot the data compared to best fit model
figure;
subplot(1,2,1)
hold on
plot(timevec, mudatavec, 'r*')
for j = 1:length(N0list)
modelfun_mu =@(p)gen_model_mu(p,tsamp, Ninit(j), modelcode);
plot(tsamp(2:end), modelfun_mu(pbeststrAbd), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel('<n> time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Mean in data fit to strong Allee ( b & d), BIC= ', num2str(BICstrAbd)])
xlim([ 0 332])
subplot(1,2,2)
hold on
plot(timevec, vardatavec, 'g*')
for j = 1:length(N0list)
modelfun_V =@(p)gen_model_var(p,tsamp, Ninit(j), modelcode);
plot(tsamp(2:end), modelfun_V(pbeststrAbd), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel(' Variance in time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Variance in data fit to strong Allee(b & d) model, BIC= ', num2str(BICstrAbd)])
xlim([ 0 332])
%% Profile likelihood of strong Allee on birth & death model
% Use these to determine parameter certainty and find the 95 % CI on the
% b and d parameter estimate from all data
num_params = 3;
% Check fxn
fbest = negLLfitstrAbd;
factor = 0.05;
numpoints = 10;
params = pbeststrAbd;
[profilesstrAbd] = profile_likelihood(params, tsamp, N0list, numsamps ,mudatavec, vardatavec, modelcode, factor, numpoints);
threshold = chi2inv(0.95,length(params))/2 + fbest;
ilo1=find(profilesstrAbd(:,2,1)<threshold);
if ilo1(end) ==numpoints*2 ||ilo1(1)==1
display('All negLL vals below threshold. Increase factor.')
CIstrAbd(1,:) = [NaN, NaN];
else
CIstrAbd(1,:) = [profilesstrAbd(ilo1(1),1,1), profilesstrAbd(ilo1(end),1,1)];
end
ilo2 = find(profilesstrAbd(:,2,2)<threshold);
if ilo2(end) ==numpoints*2 ||ilo2(1)==1
display('All negLL vals below threshold. Increase factor.')
CIstrAbd(2,:)= [NaN NaN];
else
CIstrAbd(2,:) = [profilesstrAbd(ilo2(1),1,2), profilesstrAbd(ilo2(end),1,2)];
end
ilo3 = find(profilesstrAbd(:,2,3)<threshold);
if ilo3(end) ==numpoints*2 ||ilo3(1)==1
display('All negLL vals below threshold. Increase factor.')
CIstrAbd(3,:)= [NaN NaN];
else
CIstrAbd(3,:) = [profilesstrAbd(ilo3(1),1,3), profilesstrAbd(ilo3(end),1,3)];
end
% this output a profiles 3D matrix whose first z dimension contains the
% profiled parameters and the corresponding negLL
% the CI contains the upper and lower CI on first the b parameter than
% the d parameter
%% Plot the profiles for strong Allee model on birth & death
figure;
subplot(1, 3,1)
plot(profilesstrAbd(:,1,1), profilesstrAbd(:,2,1))
hold on
plot(pbeststrAbd(1),negLLfitstrAbd,'r*','LineWidth',2)
plot([profilesstrAbd(1,1,1) profilesstrAbd(end,1,1)],[threshold threshold],'r--')
xlabel(' profiled b values')
% xlim([profilesstrAd(1,1,1) profilesstrAd(end,1,1)])
ylabel('Cost Function Value')
title(['Profile Likelihood of b CI = [',num2str(CIstrAbd(1,:)),']'])
subplot(1,3,2)
plot(profilesstrAbd(:,1,2), profilesstrAbd(:,2,2))
hold on
plot(pbeststrAbd(2),negLLfitstrAbd,'r*','LineWidth',2)
plot([profilesstrAbd(1,1,2) profilesstrAbd(end,1,2)],[threshold threshold],'r--')
xlabel(' profiles d values')
%xlim ([profilesstrAbd(1,1,2) profilesstrAbd(end,1,2)])
ylabel('Cost Function Value')
title([' Profile Likelihood of d CI = [',num2str(CIstrAbd(2,:)),']'])
subplot(1,3,3)
plot(profilesstrAbd(:,1,3), profilesstrAbd(:,2,3))
hold on
plot(pbeststrAbd(3),negLLfitstrAbd,'r*','LineWidth',2)
plot([profilesstrAbd(1,1,3) profilesstrAbd(end,1,3)],[threshold threshold],'r--')
xlabel(' profiled A values')
xlim([profilesstrAbd(1,1,3) profilesstrAbd(end,1,3)])
ylabel('Cost Function Value')
title([' Profile Likelihood of A CI = [',num2str(CIstrAbd(3,:)),']'])
%% Perform fitting: fit all data to weak/strong Allee on birth
% For each fitting, we want to write functions in terms of the functions
% that run the model we are fitting to forward. The gen_model_mu runs the
% system of ODEs for the parameters and generates an expected model mean
% and variance for the input p parameters
% information
modelcode = 5;
% Initial guess
bguess = (log(mudatavec(end-2))-log(mudatavec(end-4)))/(timevec(end-2)-timevec(end-4)) + 0.002;
dguess = 0.002;
Aguess = -1;
tauguess = 2;
theta = [bguess,dguess, Aguess, tauguess];
Ninit = N0list;
N= numsamps;
[pbestwkAb, BICwkAb, AICwkAb,negLLfitwkAb] = ML_fitbigN(theta, tsamp, Ninit, Vinit, N,mudatavec, vardatavec, modelcode)
% need to define th inline functions that run forward the mean and the
% variance
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit,Vinit, modelcode);
%% Plot the data compared to best fit model
figure;
subplot(1,2,1)
hold on
plot(timevec, mudatavec, 'r*')
for j = 1:length(N0list)
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_mu(pbestwkAb), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel('<n> time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Mean in data fit to weak Allee (b), BIC= ', num2str(BICwkAb)])
xlim([ 0 332])
subplot(1,2,2)
hold on
plot(timevec, vardatavec, 'g*')
for j = 1:length(N0list)
modelfun_V =@(p)gen_model_varbigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_V(pbestwkAb), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel(' Variance in time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Variance in data fit to weak Allee(b) model, BIC= ', num2str(BICwkAb)])
xlim([ 0 332])
%% Profile likelihood of weak/strong Allee on birth
% Use these to determine parameter certainty and find the 95 % CI on the
% b and d parameter estimate from all data
num_params = 4;
% Check fxn
fbest = negLLfitwkAb;
factor = 0.05;
numpoints = 10;
params = pbestwkAb;
[profileswkAb] = profile_likelihood(params, tsamp, N0list, numsamps ,mudatavec, vardatavec, modelcode, factor, numpoints);
threshold = chi2inv(0.95,length(params))/2 + fbest;
ilo1=find(profileswkAb(:,2,1)<threshold);
if ilo1(end) ==numpoints*2 ||ilo1(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAb(1,:) = [NaN, NaN];
else
CIwkAb(1,:) = [profileswkAb(ilo1(1),1,1), profileswkAb(ilo1(end),1,1)];
end
ilo2 = find(profileswkAb(:,2,2)<threshold);
if ilo2(end) ==numpoints*2 ||ilo2(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAb(2,:)= [NaN NaN];
else
CIwkAb(2,:) = [profileswkAb(ilo2(1),1,2), profileswkAb(ilo2(end),1,2)];
end
ilo3 = find(profileswkAb(:,2,3)<threshold);
if ilo3(end) ==numpoints*2 ||ilo3(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAb(3,:)= [NaN NaN];
else
CIwkAb(3,:) = [profileswkAb(ilo3(1),1,3), profileswkAb(ilo3(end),1,3)];
end
ilo4 = find(profileswkAb(:,2,4)<threshold);
if ilo4(end) ==numpoints*2 ||ilo4(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAb(4,:)= [NaN NaN];
else
CIwkAb(4,:) = [profileswkAb(ilo4(1),1,4), profileswkAb(ilo4(end),1,4)];
end
% this output a profiles 3D matrix whose first z dimension contains the
% profiled parameters and the corresponding negLL
% the CI contains the upper and lower CI on first the b parameter than
% the d parameter
%% Plot profiles for weak/strong Allee on birth
figure;
subplot(1, 4,1)
plot(profileswkAb(:,1,1), profileswkAb(:,2,1))
hold on
plot(pbestwkAb(1),negLLfitwkAb,'r*','LineWidth',2)
plot([profileswkAb(1,1,1) profileswkAb(end,1,1)],[threshold threshold],'r--')
xlabel(' profiled b values')
% xlim([profilesstrAd(1,1,1) profilesstrAd(end,1,1)])
ylabel('Cost Function Value')
title(['Profile Likelihood of b CI = [',num2str(CIwkAb(1,:)),']'])
subplot(1,4,2)
plot(profileswkAb(:,1,2), profileswkAb(:,2,2))
hold on
plot(pbestwkAb(2),negLLfitwkAb,'r*','LineWidth',2)
plot([profileswkAb(1,1,2) profileswkAb(end,1,2)],[threshold threshold],'r--')
xlabel(' profiles d values')
xlim ([profileswkAb(1,1,2) profileswkAb(end,1,2)])
ylabel('Cost Function Value')
title([' Profile Likelihood of d CI = [',num2str(CIwkAb(2,:)),']'])
subplot(1,4,3)
plot(profileswkAb(:,1,3), profileswkAb(:,2,3))
hold on
plot(pbestwkAb(3),negLLfitwkAb,'r*','LineWidth',2)
plot([profileswkAb(1,1,3) profileswkAb(end,1,3)],[threshold threshold],'r--')
xlabel(' profiled A values')
xlim([profileswkAb(1,1,3) profileswkAb(end,1,3)])
ylabel('Cost Function Value')
title([' Profile Likelihood of A CI = [',num2str(CIwkAb(3,:)),']'])
subplot(1,4,4)
plot(profileswkAb(:,1,4), profileswkAb(:,2,4))
hold on
plot(pbestwkAb(4),negLLfitwkAb,'r*','LineWidth',2)
plot([profileswkAb(1,1,4) profileswkAb(end,1,4)],[threshold threshold],'r--')
xlabel(' profiled tau values')
xlim([profileswkAb(1,1,4) profileswkAb(end,1,4)])
ylabel('Cost Function Value')
title([' Profile Likelihood of \tau CI = [',num2str(CIwkAb(4,:)),']'])
%% Perform fitting: fit all data to weak/strong Allee on death
% For each fitting, we want to write functions in terms of the functions
% that run the model we are fitting to forward. The gen_model_mu runs the
% system of ODEs for the parameters and generates an expected model mean
% and variance for the input p parameters
% information
modelcode = 6;
tsamp = 0:4:332; % set sample time (if data is down sampled change accordingly
tsampfit = tsamp(2:end);
tsampnew = tsampfit(ind);
tsamp = [0 tsampnew];
% Initial guess
bguess = (log(mudatavec(end-2))-log(mudatavec(end-10)))/(timevec(end-2)-timevec(end-10)) + 0.002;
dguess = 0.002;
Aguess = -1;
tauguess = 2;
theta = [bguess,dguess, Aguess, tauguess];
Ninit = N0list;
N= numsamps;
[pbestwkAd, BICwkAd, AICwkAd,negLLfitwkAd] = ML_fitbigN(theta, tsamp, Ninit,Vinit, N,mudatavec, vardatavec, modelcode)
% need to define th inline functions that run forward the mean and the
% variance
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit,Vinit, modelcode);
%% Plot the data compared to best fit model
figure;
subplot(1,2,1)
hold on
plot(timevec, mudatavec, 'r*')
for j = 1:length(N0list)
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_mu(pbestwkAd), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel('<n> time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Mean in data fit to weak Allee (d), BIC= ', num2str(BICwkAd)])
xlim([ 0 332])
subplot(1,2,2)
hold on
plot(timevec, vardatavec, 'g*')
for j = 1:length(N0list)
modelfun_V =@(p)gen_model_varbigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_V(pbestwkAd), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel(' Variance in time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Variance in data fit to weak Allee(d) model, BIC= ', num2str(BICwkAd)])
xlim([ 0 332])
%% Profile likelihood of weak/strong Allee on death
% Use these to determine parameter certainty and find the 95 % CI on the
% b and d parameter estimate from all data
num_params = 4;
% Check fxn
fbest = negLLfitwkAd;
factor = 0.05;
numpoints = 10;
params = pbestwkAd;
[profileswkAd] = profile_likelihood(params, tsamp, N0list, numsamps ,mudatavec, vardatavec, modelcode, factor, numpoints);
threshold = chi2inv(0.95,length(params))/2 + fbest;
ilo1=find(profileswkAd(:,2,1)<threshold);
if ilo1(end) ==numpoints*2 ||ilo1(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAd(1,:) = [NaN, NaN];
else
CIwkAd(1,:) = [profileswkAd(ilo1(1),1,1), profileswkAd(ilo1(end),1,1)];
end
ilo2 = find(profileswkAd(:,2,2)<threshold);
if ilo2(end) ==numpoints*2 ||ilo2(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAd(2,:)= [NaN NaN];
else
CIwkAd(2,:) = [profileswkAd(ilo2(1),1,2), profileswkAd(ilo2(end),1,2)];
end
ilo3 = find(profileswkAd(:,2,3)<threshold);
if ilo3(end) ==numpoints*2 ||ilo3(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAd(3,:)= [NaN NaN];
else
CIwkAd(3,:) = [profileswkAd(ilo3(1),1,3), profileswkAd(ilo3(end),1,3)];
end
ilo4 = find(profileswkAd(:,2,4)<threshold);
if ilo4(end) ==numpoints*2 ||ilo4(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAd(4,:)= [NaN NaN];
else
CIwkAd(4,:) = [profileswkAd(ilo4(1),1,4), profileswkAd(ilo4(end),1,4)];
end
% this output a profiles 3D matrix whose first z dimension contains the
% profiled parameters and the corresponding negLL
% the CI contains the upper and lower CI on first the b parameter than
% the d parameter
%%
save('../out/profilesbd.mat', 'profilesbd')
save('../out/profilesstrAb.mat', 'profilesstrAb')
save('../out/profilesstrAd.mat', 'profilesstrAd')
save('../out/profilesstrAbd.mat', 'profilesstrAbd')
save('../out/profileswkAb.mat', 'profileswkAb')
save('../out/profileswkAd.mat', 'profileswkAd')
%% Plot profiles for weak/strong Allee on death
figure;
subplot(1, 4,1)
plot(profileswkAd(:,1,1), profileswkAd(:,2,1))
hold on
plot(pbestwkAd(1),negLLfitwkAd,'r*','LineWidth',2)
plot([profileswkAd(1,1,1) profileswkAd(end,1,1)],[threshold threshold],'r--')
xlabel(' profiled b values')
% xlim([profilesstrAd(1,1,1) profilesstrAd(end,1,1)])
ylabel('Cost Function Value')
title(['Profile Likelihood of b CI = [',num2str(CIwkAd(1,:)),']'])
subplot(1,4,2)
plot(profileswkAd(:,1,2), profileswkAd(:,2,2))
hold on
plot(pbestwkAd(2),negLLfitwkAd,'r*','LineWidth',2)
plot([profileswkAd(1,1,2) profileswkAd(end,1,2)],[threshold threshold],'r--')
xlabel(' profiles d values')
%xlim ([profileswkAd(1,1,2) profileswkAd(end,1,2)])
ylabel('Cost Function Value')
title([' Profile Likelihood of d CI = [',num2str(CIwkAd(2,:)),']'])
subplot(1,4,3)
plot(profileswkAd(:,1,3), profileswkAd(:,2,3))
hold on
plot(pbestwkAd(3),negLLfitwkAd,'r*','LineWidth',2)
plot([profileswkAd(1,1,3) profileswkAd(end,1,3)],[threshold threshold],'r--')
xlabel(' profiled A values')
xlim([profileswkAd(1,1,3) profileswkAd(end,1,3)])
ylabel('Cost Function Value')
title([' Profile Likelihood of A CI = [',num2str(CIwkAd(3,:)),']'])
subplot(1,4,4)
plot(profileswkAd(:,1,4), profileswkAd(:,2,4))
hold on
plot(pbestwkAd(4),negLLfitwkAd,'r*','LineWidth',2)
plot([profileswkAd(1,1,4) profileswkAd(end,1,4)],[threshold threshold],'r--')
xlabel(' profiled tau values')
xlim([profileswkAd(1,1,4) profileswkAd(end,1,4)])
ylabel('Cost Function Value')
title([' Profile Likelihood of \tau CI = [',num2str(CIwkAd(4,:)),']'])
%% Perform fitting: fit all data to weak/strong Allee on birth & death
% For each fitting, we want to write functions in terms of the functions
% that run the model we are fitting to forward. The gen_model_mu runs the
% system of ODEs for the parameters and generates an expected model mean
% and variance for the input p parameters
% information
modelcode = 7;
% Initial guess
bguess = (log(mudatavec(end-2))-log(mudatavec(end-4)))/(timevec(end-2)-timevec(end-4)) + 0.002;
dguess = 0.002;
Aguess = -1;
tauguess = 2;
theta = [bguess,dguess, Aguess, tauguess];
Ninit = N0list;
N= numsamps;
[pbestwkAbd, BICwkAbd, AICwkAbd,negLLfitwkAbd] = ML_fitbigN(theta, tsamp, Ninit,Vinit, N,mudatavec, vardatavec, modelcode)
% need to define th inline functions that run forward the mean and the
% variance
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit,Vinit, modelcode);
modelfun_V = @(p)gen_model_varbigN(p, tsamp, Ninit,Vinit, modelcode);
%% Plot the data compared to best fit model
figure;
subplot(1,2,1)
hold on
plot(timevec, mudatavec, 'r*')
for j = 1:length(N0list)
modelfun_mu =@(p)gen_model_mubigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_mu(pbestwkAbd), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel('<n> time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Mean in data fit to weak Allee (b & d), BIC= ', num2str(BICwkAbd)])
xlim([ 0 332])
subplot(1,2,2)
hold on
plot(timevec, vardatavec, 'g*')
for j = 1:length(N0list)
modelfun_V =@(p)gen_model_varbigN(p,tsamp, Ninit(j),Vinit(j), modelcode);
plot(tsamp(2:end), modelfun_V(pbestwkAbd), 'b-', 'LineWidth', 2) % test model expected
end
xlabel('time (hours)')
ylabel(' Variance in time')
legend('data', 'best fit strong Allee')
legend boxoff
title(['Variance in data fit to weak Allee(b & d) model, BIC= ', num2str(BICwkAbd)])
xlim([ 0 332])
%% Profile likelihood of weak/strong Allee on birth & death
% Use these to determine parameter certainty and find the 95 % CI on the
% b and d parameter estimate from all data
num_params = 4;
% Check fxn
fbest = negLLfitwkAbd;
factor = 0.05;
numpoints = 10;
params = pbestwkAbd;
[profileswkAbd] = profile_likelihood(params, tsamp, N0list, numsamps ,mudatavec, vardatavec, modelcode, factor, numpoints);
threshold = chi2inv(0.95,length(params))/2 + fbest;
ilo1=find(profileswkAbd(:,2,1)<threshold);
if ilo1(end) ==numpoints*2 ||ilo1(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAbd(1,:) = [NaN, NaN];
else
CIwkAbd(1,:) = [profileswkAbd(ilo1(1),1,1), profileswkAbd(ilo1(end),1,1)];
end
ilo2 = find(profileswkAbd(:,2,2)<threshold);
if ilo2(end) ==numpoints*2 ||ilo2(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAbd(2,:)= [NaN NaN];
else
CIwkAbd(2,:) = [profileswkAbd(ilo2(1),1,2), profileswkAbd(ilo2(end),1,2)];
end
ilo3 = find(profileswkAbd(:,2,3)<threshold);
if ilo3(end) ==numpoints*2 ||ilo3(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAbd(3,:)= [NaN NaN];
else
CIwkAbd(3,:) = [profileswkAbd(ilo3(1),1,3), profileswkAd(ilo3(end),1,3)];
end
ilo4 = find(profileswkAbd(:,2,4)<threshold);
if ilo4(end) ==numpoints*2 ||ilo4(1)==1
display('All negLL vals below threshold. Increase factor.')
CIwkAbd(4,:)= [NaN NaN];
else
CIwkAbd(4,:) = [profileswkAbd(ilo4(1),1,4), profileswkAbd(ilo4(end),1,4)];
end
% this output a profiles 3D matrix whose first z dimension contains the
% profiled parameters and the corresponding negLL
% the CI contains the upper and lower CI on first the b parameter than
% the d parameter
%% Plot profiles for weak/strong Allee on birth death
figure;
subplot(1, 4,1)
plot(profileswkAbd(:,1,1), profileswkAbd(:,2,1))
hold on
plot(pbestwkAbd(1),negLLfitwkAbd,'r*','LineWidth',2)
plot([profileswkAbd(1,1,1) profileswkAbd(end,1,1)],[threshold threshold],'r--')
xlabel(' profiled b values')
% xlim([profilesstrAd(1,1,1) profilesstrAd(end,1,1)])
ylabel('Cost Function Value')
title(['Profile Likelihood of b CI = [',num2str(CIwkAbd(1,:)),']'])
subplot(1,4,2)
plot(profileswkAbd(:,1,2), profileswkAbd(:,2,2))
hold on
plot(pbestwkAbd(2),negLLfitwkAbd,'r*','LineWidth',2)
plot([profileswkAbd(1,1,2) profileswkAbd(end,1,2)],[threshold threshold],'r--')
xlabel(' profiles d values')
%xlim ([profileswkAd(1,1,2) profileswkAd(end,1,2)])
ylabel('Cost Function Value')
title([' Profile Likelihood of d CI = [',num2str(CIwkAbd(2,:)),']'])
subplot(1,4,3)
plot(profileswkAbd(:,1,3), profileswkAbd(:,2,3))
hold on
plot(pbestwkAbd(3),negLLfitwkAbd,'r*','LineWidth',2)
plot([profileswkAbd(1,1,3) profileswkAbd(end,1,3)],[threshold threshold],'r--')
xlabel(' profiled A values')
xlim([profileswkAbd(1,1,3) profileswkAbd(end,1,3)])
ylabel('Cost Function Value')
title([' Profile Likelihood of A CI = [',num2str(CIwkAbd(3,:)),']'])
subplot(1,4,4)
plot(profileswkAbd(:,1,4), profileswkAbd(:,2,4))
hold on
plot(pbestwkAbd(4),negLLfitwkAbd,'r*','LineWidth',2)
plot([profileswkAbd(1,1,4) profileswkAbd(end,1,4)],[threshold threshold],'r--')
xlabel(' profiled tau values')
xlim([profileswkAbd(1,1,4) profileswkAbd(end,1,4)])
ylabel('Cost Function Value')
title([' Profile Likelihood of \tau CI = [',num2str(CIwkAbd(4,:)),']'])
save('../out/profileswkAbd.mat', 'profileswkAbd')
%% Make vector of BIC values, negLL values, and parameter numbers
num_params = [ 2, 3, 3, 3, 4, 4, 4];
modellist = [1, 2, 3, 4, 5, 6, 7];
BICvals = [ BICbd, BICstrAb, BICstrAd, BICstrAbd, BICwkAb, BICwkAd, BICwkAbd];
negLLvals = [negLLfitbd, negLLfitstrAb, negLLfitstrAd, negLLfitstrAbd, negLLfitwkAb, negLLfitwkAd, negLLfitwkAbd];