# Tag Info

Accepted

### Is the invariance property of the ML estimator nonsensical from a Bayesian perspective?

As Xi'an says, the question is moot, but I think that many people are nevertheless led to consider the maximum-likelihood estimate from a Bayesian perspective because of a statement that appears in ...
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### Doubt in the Invariance Property of Consistent Estimators

$X_{n+1}$ converges not to a constant, but to a distribution with variance 1. Therefore, Slutsky's theorem (with the two "estimators" $\dfrac{1}{2}\overline{X}_n$ and $\dfrac{1}{2}X_{n+1}$ ...
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### Is the invariance property of the ML estimator nonsensical from a Bayesian perspective?

From a non-Bayesian view point, there is no definition of quantities like $$p(x|\theta = -\sqrt \eta \lor \theta = \sqrt \eta)$$ because $\theta$ is then a fixed parameter and the conditioning ...
• 106k

### Neural network to read short strings - translational invariance in CNNs

If you really want to use deep learning for this, then I'd consider a character-level recurrent neural network (such as a bidirectional LSTM) or if you want a transformer, which would take as the ...
• 33k

### Neural network to read short strings - translational invariance in CNNs

You don't need deep learning for that. You have a list of keywords and need to match them. The problem is that they may be misspelled. Another problem is that sometimes you need to match a keyword ...
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### Is there any difference between estimating $\sigma^2$ and $\sigma$ in a simulation study?

I find this question of interest because it highlights the artificial nature of seeking unbiasedness above everything else. A few points: the variance $\sigma^2$ allows for an unbiased estimator, ...
• 106k
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### Are HPD intervals invariant to reparameterization?

In general, they are not, even under the hypothesis that the transformation is monotonic. This is due to the fact that, when we transform variables, the density of the transformed variable is the ...
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### Jeffreys' prior invariance under reparametrization

The "invariance" of Jeffreys' priors should have been called "equivariance" to avoid confusion. It does not mean that it does not change under reparameterisation but rather that ...
• 106k
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### Ways of implementing Translation invariance

This answer by Matt Krause on What is translation invariance in computer vision and convolutional netral network? contain some pointers: One can show that the convolution operator commutes with ...
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### Why is invariance (in relation to neural networks) called invariance?

The term "invariance" or "invariant" in this context is not directly related to the statistical meaning of the term "variance" - it is using the basic English meaning of the words variant/varying/etc: ...
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### Is it alright to place equality constraints on the items loadings for assessing configural invariance using effect coding approach?

Is it alright to place equality constraints on the items loadings for assessing configural invariance using effect coding approach? Yes, invariance/equality of measurement parameters can be tested ...
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### Invariance of mutual information (two-dimensional Gaussian)

This is just a calculation error. Your first D should be $D=log(\sigma_1/\sigma_2)$. So they are the same.
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### What is Exact definition of Invariance principle

The basic intuition behind invariance is that statistical conclusions should not depend on choice of measurement scale. Some examples: Measurement of distance in meters or parsecs. Angle measurement ...
• 79.6k
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### Intuitive explanation of "invariance"

Invariance is a relative property not an absolute one. Something is described as invariant under some manipulation. For a non-mathematical (and hence non-statistical) example we consider the egg. The ...
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### Multi-group SEM - constraints and regression paths

The regression slope coefficients in your structural (latent variable) model only involve the covariance structure (latent variances and covariances). Therefore, loading (metric/weak) invariance is ...
• 3,561