estimate normal learning model and see how parameters update over time

Question

Joshua Scott 2022-10-25

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1835128-estimate-normal-learning-model-and-see-how-parameters-update-over-time

评论： Ayush Anand 2023-9-13

I want to estimate a normal learning model by simulating a variable via draws from a normal distribution and get the posterior, expected value, and variance of the expected value. A baseline I would like to run is this: https://www2.bcs.rochester.edu/sites/jacobslab/cheat_sheet/bayes_Normal_Normal.pdf

Here is my sample code I have from text. However, it starts with a linear regression. How can I adapt this so it just is a simple case where I am sampling from one variable? Do I just set this up so x=mu and xi=mu in the log likelihood?

Code:

n=831741; k=3; % set number of obs and n number of vars
y = data.Pi;
x = data.X; b = ones(k,1); % generate data set
y = x*b + randn(n,1);
r = [1.0 1.0 1.0]'; % prior means
R = eye(k); T = eye(k); % prior variance
Q = chol(inv(T)); q = Q*r;
b0 = (x'*x)\(x'*y); % use ols as initial values
sige = (y-x*b0)'*(y-x*b0)/(n-k);
xpx = x'*x; xpy = x'*y; % calculate x’x, x’y (just once)
qpq = Q'*Q; qpv = Q'*q; % calculate Q’Q, Q’q (just once)
ndraw = 5000;
bsave = zeros(ndraw,k); % allocate storage for results
ssave = zeros(ndraw,1);
for i=1:ndraw % Start the sampling
xpxi = inv(xpx + sige*qpq);
b = xpxi*(xpy + sige*qpv); % update b
b = norm_rnd(sige*xpxi) + b; % draw MV normal with mean(b), var(b)
bsave(i,:) = b'; % save b draws
e = y - x*b; ssr = e'*e; % update sige
chi = chis_rnd(1,n); % do chisquared(n) draw
sige = ssr/chi;
ssave(i,1) = sige; % save sige draws
end % End the sampling

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Ayush Anand 2023-9-13

Hi Joshua, I don't exactly understand what do you mean by "sampling from just one variable". If you mean that you do not want the linear regression setup, you can use the "normrnd" function to generate Gaussian distributed numbers. You can also use the "normpdf" function to generate Gaussian distributed numbers from a chosen vector in accordance with the pdf. Let me know if I am misunderstanding your question or if you are trying to do something else

请先登录，再进行评论。

请先登录，再回答此问题。

estimate normal learning model and see how parameters update over time

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

回答（0 个）

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

estimate normal learning model and see how parameters update over time

1 个评论 显示 -1更早的评论隐藏 -1更早的评论

回答（0 个）

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

1 个评论
显示 -1更早的评论隐藏 -1更早的评论