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ABC_mu1a.m
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%% This function is for generating MCMC posterior samples of
%% piece-wise constant mutation rates and changing time point based on bMBP model
% Input: theta_mu: prior for theta, log scale
% theta_sigma: prior variance for theta, 0 if parameter is not
% estimated in this case.
% param_range; a structure storing range of each parameter
% obs_X: observed data
% model_spec: model specifications, including:
% num_training_theta: vector of 2, the number of training data points
% for initial training and additional trainings.
% eps: accuracy threshold,
% psi: error threshold
% N: sample size
% chkt: time checking point
% a: parameter for birth-death process
% num_rep: number of replicates at each training point
% time_update: for showing progress
% init_param: initial values of GP's hyperparameters.
% theta_old: the initial values of parameters to be estimated.
% model: the model version, "2" indicates the model with piece-wise constant rates.
% bounds: bounds for the parameters to be estimated
% trans_step: stepwidth for proposal distribution
function [Sample, runningTime, initTime] = ABC_mu1a(theta_mu, theta_sigma, dt_range, p_range, obs_X, model_spec)
S0 = model_spec.num_training_theta(1,:);
delta = model_spec.num_training_theta(2,:);
p = length(theta_mu); %length(theta_mu)
ksi = model_spec.ksi;
eps = model_spec.eps ;
M = model_spec.M;
N = model_spec.N;
a = model_spec.a;
chkt = model_spec.chkt;
Z0 = model_spec.Z0;
constraint = model_spec.constraint;
num_rep = model_spec.num_rep;
time_update = model_spec.time_update;
%kern_param = [0.01,0.4];
init_param = model_spec.init_param;
bounds = model_spec.bounds;
%trans_step = [0.08,0.08,0.08];
trans_step = model_spec.trans_step;
param_range = [dt_range; p_range];
Y_m = mean(obs_X);
Y_sd = std(obs_X);
Feat = [Y_m, Y_sd];
if model_spec.init == 0
startTime = tic;
[theta_list, X] = getIniX1a(a, dt_range,p_range,chkt,S0, num_rep,time_update, Z0);
theta_list_s = (theta_list - repmat(param_range(:,1)',size(theta_list,1),1)) ./...
repmat((param_range(:,2) - param_range(:,1))',size(theta_list,1),1);
[param, model] = mleHomGP(theta_list_s,mean(X,3),init_param,bounds);
[param_sd, model_sd] = mleHomGP(theta_list_s, std(X,[],3), init_param,bounds);
initTime = toc(startTime);
if model_spec.saveSample == 1
save('post/init1a.mat','theta_list', 'theta_list_s', "X", "initTime",'param','model','param_sd','model_sd');
end
else
load(model_spec.init);
initTime == 0.0;
end
J = size(Feat,2); % number of the features
theta_old = model_spec.theta_old;
Sample = NaN(N,p);
startTime = tic;
%h = waitbar(0,'Please wait...');
for ss = 1:N
if mod(ss, time_update) == 0 % screen print to show progress.
fprintf(['ss=', int2str(ss),'\n']);
end
[theta_new,dt_range_new,p_range_new] = get_theta1a(trans_step,theta_old,dt_range,p_range);
theta = [theta_new;theta_old];
theta_s = (theta - repmat(param_range(:,1)',2,1)) ./...
repmat((param_range(:,2) - param_range(:,1))',2,1);
for iter = 1:5000
alpha = NaN(M,J);
for j = 1:J
if j == 1
[Mu_cond, Var_cond,nugs] = GPHomPrediction(theta_s,model,param);
elseif j == 2
[Mu_cond, Var_cond,nugs] = GPHomPrediction(theta_s,model_sd,param_sd);
end
Yj = Feat(:,j);
% Muj = Mu_cond(:,j);
% Sigmaj = diag(Var_cond(:,j));
% sample = randmvn(Muj,Sigmaj,M,eps)';
% alpha(:,j) = -0.5 * (Yj - sample(:,1)).^2./(nugs(1)/num_rep+eps^2) + 0.5 * (Yj - sample(:,2)).^2./(nugs(2)/num_rep+eps^2);
sample1 = randn(M,1)*sqrt(Var_cond(1))+repmat(Mu_cond(1),M,1);
sample2 = randn(M,1)*sqrt(Var_cond(2))+repmat(Mu_cond(2),M,1);
alpha(:,j) = -0.5 * (Yj - sample1).^2./(nugs(1)/num_rep+eps^2) + 0.5 * (Yj - sample2).^2./(nugs(2)/num_rep+eps^2);
end
log_prior_dens = NaN(size(param_range,1),2);
for p = 1:size(param_range,1)
log_prior_dens(p,:) = tnorm([theta_new(p),theta_old(p)], theta_mu(p), theta_sigma(p), param_range(p,:));
end
log_prior_ratio = sum(log_prior_dens(:,1) - log_prior_dens(:,2));
%log_prior_ratio = 0;
log_like_ratio = sum(alpha,2);
log_trans_dens_new = NaN(size(param_range,1),2);
log_trans_dens_old = NaN(size(param_range,1),2);
for p = 1:size(param_range,1)
log_trans_dens_new(p,:) = tnorm(theta_new(p), theta_old(p), trans_step(p), param_range(p,:));
log_trans_dens_old(p,:) = tnorm(theta_old(p), theta_new(p), trans_step(p), param_range(p,:));
end
log_trans_ratio = sum(log_trans_dens_old - log_trans_dens_new); % all cancell out except the jacobian.
Alpha =min([ones(M,1) exp(log_prior_ratio + log_like_ratio + log_trans_ratio)],[],2);
[Eps,Tau] = unconditionError(Alpha,0.001);
if Eps <= ksi
break
else
[n_training,~,num_rep] = size(X);
[Theta_new, X_delta] = getIniX1a(a,dt_range_new,p_range_new,chkt,delta, num_rep,time_update,Z0);
[n_training_delta,~,num_rep] = size(X_delta);
feat_delta = NaN(n_training_delta + n_training,1,num_rep);
for k = 1:num_rep
feat_delta((n_training + 1):(n_training_delta + n_training),:,k) = X_delta(:,:,k);
feat_delta(1:n_training,:,k) = X(:,:,k);
end
X = feat_delta;
theta_list_new = [theta_list;Theta_new];
theta_list = theta_list_new;
Theta_new_s = (Theta_new - repmat(param_range(:,1)',delta,1)) ./...
repmat((param_range(:,2) - param_range(:,1))',delta,1);
theta_list_new_s = [theta_list_s; Theta_new_s];
theta_list_s = theta_list_new_s;
[param, model] = mleHomGP(theta_list_s,mean(X,3),init_param,bounds);
[param_sd, model_sd] = mleHomGP(theta_list_s,std(X,[],3),init_param,bounds);
for j = 1:size(p_range_new,1)
p_range_new(j,:) = [p_range_new(j,1) - 0.001*iter, p_range_new(j,2)+0.001*iter];
end
if length(dt_range_new) == 2
dt_range_new = [dt_range_new(1) - 0.001*iter, dt_range_new(2)+0.001*iter];
end
end
end
if rand(1) < Tau
Sample(ss,:) = theta_new;
else
Sample(ss,:) = theta_old;
end
theta_old = Sample(ss,:);
%h = waitbar(ss/N,h,['remaining sample =',num2str(N-ss),'samples']);
end
runningTime = toc(startTime);
%if model_spec.saveSample == 1
% save('init_1a_final.mat','theta_list', 'theta_list_s','X');
%end
close(gcf)