# EM algorithms - confidence interval estimation

Does anybody know how to find the confidence intervals for estimated parameters of a mixture of Gaussians by using EM algorithm?

• Could you be somewhat more clear? Why do you think EM is interesting in this case? What have you tried yourself? Also, can you describe your data clearly and specify which parameters you actually want estimated? This may help us understand exactly what you expect. – Nick Sabbe May 2 '13 at 12:59
• @NickSabbe: Hi Nick, sorry for my unclear question, I'm not good at math... :). My data come from a mixture of normal distributions (the number of components is known), I have used EM algorithm to estimate the proportion, mean and variance of each component. Suppose that the dataset is big enough, what I want to know is how to find the confident interval for each estimated proportion, mean and variance. – An Mai May 2 '13 at 13:20
• @AnMai I had a similiar problem as you have, check my posts: stats.stackexchange.com/questions/54736/… and stats.stackexchange.com/questions/54726/… The basic point is, that for confidence intervals you will need the standard errors. You can get them via boot.se but the problem is (see my posts) that this is not consistent, you get different values every time you run the code. The better solution is to use bootstrap ci: projecteuclid.org/… – Stat Tistician May 2 '13 at 14:48
• see also this paper: citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.203 – Stat Tistician May 2 '13 at 14:53
• @Stat Tistician I also encounted the same problem. Thanks for your sharing, I have downloaded all the documents you list above. However, I am bad at math, so could you just tell me whether I can use bootstrap or other tools to calculate the confidence intervals of the normal distribution component which is obtained by EM algorithm??? – user26940 Jun 16 '13 at 6:30