Questions tagged [information]

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44
votes
7answers
5k views

Why would someone use a Bayesian approach with a 'noninformative' improper prior instead of the classical approach?

If the interest is merely estimating the parameters of a model (pointwise and/or interval estimation) and the prior information is not reliable, weak, (I know this is a bit vague but I am trying to ...
53
votes
10answers
15k views

Measuring entropy/ information/ patterns of a 2d binary matrix

I want to measure the entropy/ information density/ pattern-likeness of a two-dimensional binary matrix. Let me show some pictures for clarification: This display should have a rather high entropy: ...
4
votes
1answer
634 views

How to interpret the divergence of Fisher information expectation?

Consider translated Weibull distribution with probability density function: $$ f(x ; k, \lambda, \theta) = \frac{k}{\lambda} \left( \frac{x-\theta}{\lambda} \right)^{k-1} \exp\left( - \left(\frac{...
4
votes
1answer
380 views

Item information in IRT

According to item information curves, item information for a 2PL IRT model is $I(\theta)=a^2_i p_i(\theta) q_i(\theta)$ To determine $p_i(\theta)$ and $q_i(\theta)$, do you just use the observed ...
16
votes
2answers
3k views

Observed information matrix is a consistent estimator of the expected information matrix?

I am trying to prove that the observed information matrix evaluated at the weakly consistent maximum likelihood estimator (MLE), is a weakly consistent estimator of the expected information matrix. ...
20
votes
2answers
599 views

Fisher information in a hierarchical model

Given the following hierarchical model, $$ X \sim {\mathcal N}(\mu,1), $$ and, $$ \mu \sim {\rm Laplace}(0, c) $$ where $\mathcal{N}(\cdot,\cdot)$ is a normal distribution. Is there a way to get an ...
5
votes
1answer
8k views

Why is variance (instead of standard deviation) the default measure of information content in principal components?

The information content of principal components is almost always expressed as a variance (e.g., in scree plots or in statements like "the first three PCs contain 95% of the total data variance"). The ...
2
votes
2answers
278 views

Bayesian Statistics -Prior and Posterior distributions

Please is it ever possible for the prior distribution to contain more information about parameter(s) than the posterior distribution? If yes, when can that occur? Is it the same concept as the ...
7
votes
1answer
2k views

Is it appropriate to use the term “bits” to discuss a log-base-2 likelihood ratio?

I'm quite enamoured with likelihood ratios as a means of quantifying relative evidence in scientific endeavours. However, in practice I find that the raw likelihood ratio can get unprintably large, so ...
1
vote
0answers
75 views

Information about parameters using priors distributions [duplicate]

When using the "non-informative" prior $\pi(\mu,\sigma)\propto\frac{1}{\sigma^2}$ where $\pi(\mu)\propto1$ and $\pi(\sigma^2)\propto\frac{1}{\sigma^2}$ Where is the no information for the ...