# Questions tagged [convergence]

Convergence generally means that a sequence of a certain sample quantity approaches a constant as the sample size tends to infinity. Convergence is also a property of an iterative algorithm to stabilize on some aim value.

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### Issues with using Expectation Maximization algorithm

I was using the EM algorithm to maximize a partially observed likelihood. However, I have certain doubts. Normally, the algorithm works fine. I could print the value of the log likelihood of the ...
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### R's coxph won't converge when I include factor (categorical) variables

I have a dataset of 371 observations. When I run coxph with numeric variables it works fine. However, when I try to add factor (categorical) variables it returns “...
2k views

### MCMC autocorrelation convergence diagnostic

I use MCMC (Metropolis-Hastings) to sample posterior distributions of three parameters using a nonlinear least-squares objective function to calculate the likelihood of a parameter sets. I want ...
267 views

### MCMC and terrible convergence

The code and data I am borrowing come from http://www.perossi.org/home/bsm-1 under CS 5 from the book Bayesian Statitics and Marketing. I tried applying their model to another dataset and am getting ...
256 views

### How to visually show the convergence of a process?

I have some set of measurements that I have represented as vectors $x^t$ for $t \in \{ 1, 2, ...\}$. I want to test "convergence" of the process (visually) in some sense. I thought maybe I could run ...
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### Confusion related to the derivation of a dual of a problem

I have this confusion related to the derivation of the dual. I was referring to these lecture slides. I didn't get how the dual was derived. I didn't get how the dual was derived. I am ok up to the ...
384 views

### pLSA using tempered EM

In an article by Hofmann pdf, he proposes: initialize $β$ to one, run until convergence, then rescale $β$ by a factor $η<1$, run again until convergence, and iterate this until changing $β$ ...
3k views

### (interacting) MCMC for multimodal posterior

I am trying to sample from a posterior having many modes particularly far from each others using MCMC. It appears that in most cases, only one of these modes contains the 95% hpd I am looking for. I ...
244 views

### Convergence rate of a non-linear function of the sample mean

We have a iid sequence of random variables $X_1, X_2, \dots, X_n$, where $E(X_i) = \mu$ and $var(X_i) = \sigma^2$. The sample mean $\bar{X}$ converges to $\mu$ at rate $\sqrt{n}$ thanks to the LLN. ...
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### On the uniform convergence of relative frequencies of events to their probabilities

I have read the article by Vapnik, Chervonenkis "On the uniform convergence of relative frequencies of events to their probabilities" Theory of Probability and Its Applications, vol XVI, n. , 1971. ...
188 views

### Best practices for MCMC early stopping?

What are best and / or standard practices for MCMC early stopping? I have an algorithm which I want to compare with existing non-MCMC algorithms for accuracy and speed. When assessing the speed it's ...
24k views

### Why doesn't k-means give the global minimum?

I read that the k-means algorithm only converges to a local minimum and not to a global minimum. Why is this? I can logically think of how initialization could affect the final clustering and there is ...
3k views

### Variables that do not converge in winbugs

I conducted a Bayesian analysis in winbugs and then checked the convergence from the history plots. The regression coefficients look stabilized, but the variance parameters don't. I got the number of ...
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### Convergence in distribution and CDF

Suppose $X_n$ converges in distribution to $X$ , $x_n \rightarrow x$, also the cumulative distribution function for $X$ is continuous at $x$. Show that $P(X_n \leq x_n) \rightarrow P(X \leq x)$. PS:...
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### A problem on a.s. convergence

I'm preparing for an exam and I came across this problem from old exams. I'm really clueless on how to solve it. Consider a sequence of random variables $\{X_n\}_{n=1} ^\infty$ defined on the ...
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### Find the limiting distribution of Sum over Sum of Squares

Having a little trouble with this one: Suppose $X_1, X_2, \ldots$ are iid standard normal random variables. Let $W_n = \sqrt{n} \frac{X_1 + \cdots + X_n}{X_1^2 + \cdots + X_n^2}$. Find the limiting ...