A question about conditional mean

In summary, the conversation discusses the conditional distribution of a multivariate normal variable and provides a formula for calculating it. The formula involves the mean and covariance matrix of the variable, as well as a subset of the variables and a given value. The conversation also mentions that this concept is well-known in basic statistics and can be found in any standard textbook.
  • #1
lequan
6
0
X (n by 1) follows a multivariate normal distribution, i.e.,

X ~ N(mu, Sigma). mu is n by 1, Sigma is n by n.

What is

E(X|X_{sub}=A)?

where the index 'sub' (m by 1) is a subset of {1,2,..,n}, A is m by 1, 1 <= m < n.
 
Physics news on Phys.org
  • #3
Thanks a lot for the reference! This is the right answer. Actually, this is about the conditional distribution of multivariate normal variables, and well known in any standard textbook of basic statistics. However, I failed to realize this early. :(
 

What is a conditional mean and how is it calculated?

A conditional mean is a statistical measure that represents the average value of a dependent variable given a specific value of an independent variable. It is calculated by dividing the sum of the product of each value of the dependent variable and its probability by the total number of observations.

Why is conditional mean important in statistics?

Conditional mean is important in statistics because it allows us to understand how the average value of a dependent variable changes as the independent variable changes. This can provide insight into relationships between variables and can help in making predictions.

Can conditional mean be used for both discrete and continuous variables?

Yes, conditional mean can be used for both discrete and continuous variables. However, the calculation method may differ depending on the type of variable.

What is the difference between conditional mean and overall mean?

The conditional mean is calculated for a specific value of the independent variable, while the overall mean is calculated for all values of the independent variable. The conditional mean can provide more specific information about the relationship between variables, while the overall mean provides a general overview.

Are there any limitations to using conditional mean?

One limitation of using conditional mean is that it assumes a linear relationship between the variables. It may not accurately represent the relationship if the data follows a non-linear pattern. Additionally, outliers in the data can also affect the accuracy of the conditional mean.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
987
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
779
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
873
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
12
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
530
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
941
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
Replies
0
Views
234
Back
Top