# 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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### Using Multiple MCMC Chains in Higher Dimensions For Convergence Diagnostics

I have an MCMC problem where I sample from mixture of two multinormal distributions with dimension D. I use Random-Walk Metropolis-Hastings algorithm to sample from that mixture. For the mixture of ...
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### Loss function on the training set reaches baseline value and settles

I am training a neural network that needs to solve a regression problem. To give some context, the network needs to predict a target value that lies in the range [0, 0.25] given as input features 4 ...
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### Stop stan when it reaches convergence (Rhat = 1) [closed]

I'm doing a Bayesian analysis, which involves changing the warmup and iterations (many times per day). I wanted to know if there is a loop to automatically change warmups and interactions and stop the ...
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### Convergence in $L_1$ counterexample

I am looking for an example of a sequence of r.v. $X_n$ that converges to $X$ in $L_1$, but such that $X_n^2$ does not converge to $X^2$ in $L_1$. Anyone has something in mind?
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### Different regularity conditions for finite population CLT

I am having trouble understanding the different regularity conditions for different versions of the finite population central limit theorem. I would greatly appreciate any help or insight anyone has. ...
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### Does a Binomial converge to Poisson or Normal?

I have read the answer here. Here the distinction is that If $n\to\infty$ and $p\to0$ while $np$ approaches some positive number $\lambda,$ then the binomial distribution approaches a Poisson ...
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### Bounding the uniform deviation of the empirical risk from the risk over a finite function class

I am having difficulty interpreting the following theorem from here as a probability statement: Theorem. For all $\delta$ such that $0 < \delta < 1/2$, with proability at least $1 - \delta$ the ...
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