1.已知对数似然函数，利用fminunc函数搜索极值。^【1】

function [ll] = neg_loglike(theta,Y,X)  %定义neg_loglike.m方程mu = X*theta(1:2);ll = -1*sum(log(normpdf(Y,mu,theta(3))));  %fminunc默认求最小值，调整
end

%% 假设每次观测独立,代入f(观测|参数)数据。
data = csvread('/tmp/data.csv');  X = data(:,[3 1]);
Y = data(:,2);% Optimization设置，详见help
opt = optimset('GradObj','off',...'Hessian','off',...'LargeScale','off',...'Display','off',...'MaxIter', 100000,...'MaxFunEvals', 1000000, ...'TolFun', 1.000e-006,...'TolX', 1.000e-006,...'FunValCheck','off',...'DerivativeCheck','off',...'Diagnostics','off',...'Algorithm','trust-region-reflective');% 设置初始值，求解
theta_start=.5*ones(size(X,2)+1,1);
[theta,fval,flag,out,grad,hess] = fminunc(@(theta) neg_loglike(theta,Y,X),theta_start, opt);
se = sqrt(diag(inv(hess)));ans = [theta se]

2.已知对数似然函数，利用fminsearch函数搜索极值。^【2】

相似度，matlab代码见参考文献【2】.

function ml = t_var(param)
rng default;
data = random('norm',0,1,[400,1]);
z = (data - param(1)) ./ param(2);
L = -.5.*z.*z - log(sqrt(2.*pi).*param(2));
ml = -sum(numel(data).*L);
endx0 =[0 0]
[x,fval] = fminsearch(@t_var,x0,optimset('TolX',1e-19,'MaxFunEvals',1000,'MaxIter',1000))

3利用遗传算法求取似然函数的极值

matlab自带的遗传算法。
待续，方法发生了变化。

参考文献

【1】https://rlhick.people.wm.edu/posts/estimating-custom-mle.html
【2】https://www.656463.com/wenda/yMATLABbxzdsrgjsf_187