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Variance of marginal posterior distribution

I had some thought about it, implemented some non-trivial Bayesian examples (i.e. with not conjugate posteriors) in R, and every example seems to support your argument. So, I'll try to give some ...
Fiodor1234's user avatar
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1 vote

Variance of marginal posterior distribution

While this is probably true for most relevant examples an easy counterexample exist in that $\theta$ and $\phi$ can be independent in both prior and likelihood. I have constructed a realistic example ...
Lukas Lohse's user avatar
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0 votes

How to derive Diffusion Model's reverse conditional probability when it's tractable via conditioning on $x_0$

It seems you've already understood up to the step of the exact conditional probability of the reverse diffusion process $q(\mathbf{x}_{t-1}|\mathbf{x}_t, \mathbf{x}_0)$ which is proportional to the ...
cinch's user avatar
  • 426
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How to calculate the Expected maximum likelihood variance and mean for gaussian?

This is a late answer, but I was just trying to show the same thing, so here it is. It's quite similar to the derivation suggested by the other answer (Wikipedia), but I found this easier to ...
Shivay Vadhera's user avatar
1 vote

Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for linear regression?

The very purpose to check if a given data is normal, if we use t-tests or analysis of variance to find significant difference between groups of data. If we apply t-tests or ANOVA without knowing if ...
Gene Uniana's user avatar
0 votes

What is the distribution of $X_i-\bar{X}$ when $X_1,...,X_n \sim \text{IID N}(\mu,\sigma)$?

Here is the multivariate extension using the centring matrix While there are other answers here that solve your problem, you might be interested to know that this problem is closely related to the ...
Ben's user avatar
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3 votes
Accepted

Approximation of the expected value of the $i$-th standard normal order statistic in a sample of size n

Here is an example of using numerical integration to find the expected values using Mathematica which is more accurate than Blom's equation. (Note: to make a "nice" table there are ...
JimB's user avatar
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5 votes

Equivalence of inverse transformations under distributional equivalence

Since the unit standard multivariate normal $\mathcal{N}(0, I)$ is rotationally symmetric, let $R$ be any orthogonal matrix, that is, $R^TR = R R^T =I$, then also $RY \sim \mathcal{N}(0, I)$. Since $g$...
kjetil b halvorsen's user avatar
2 votes

Is it possible for some p-values to be impossible? (because statistic generated by parametric bootstrap is mostly the same value.)

If $A_n$ differs substantially from the identity matrix - where "substantially" depends upon the sample size - the MLE of $\lambda$ will be driven to zero quite often, and your results will ...
jbowman's user avatar
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4 votes

Is it possible for some p-values to be impossible? (because statistic generated by parametric bootstrap is mostly the same value.)

As others have mentioned, yes there are cases where some p-values are impossible. But I don't think that is the case here. It is also possible that there is an error in your calculations. But it is ...
Greg Snow's user avatar
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1 vote

How do companies decide the warranty period for a product?

The answer you are looking for falls under the topic of "Tolerance Intervals" (TI). Tolerance intervals for normal populations are a well covered topic, particularly in industry. You can ...
jginestet's user avatar
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2 votes
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Worst-case analysis using confidence intervals

Your intuition that you are double counting the uncertainty is indeed correct. What you are looking for is a Tolerance Interval, that is a confidence interval for a proportion. Let's assume that your ...
jginestet's user avatar
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