# Questions tagged [theory]

For questions about statistical theory. Always include a more specific tag as well.

76 questions with no upvoted or accepted answers
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### Cox's Theorem: ignorance, objective priors, and the Mind Projection Fallacy

I've been trying to understand Cox's Theorem and the problems surrounding it. There's so much information on this topic that I've become confused as to the exact state of the theorem. I've gathered ...
141 views

### Cox's Theorem: the necessity of (un)countably additivity

I've been trying to understand Cox's Theorem and the problems surrounding it. There's so much information on this topic that I've become confused as to the exact state of the theorem. I've gathered ...
66 views

### How do we call a more extreme case of fat tails than a power law?

According to Wikipedia the most extreme case of a fat tail follows a power law: The most extreme case of a fat tail is given by a distribution whose tail decays like a power law. That is, if the ...
142 views

### Diferrencing vs Moving Average

Moving Average and differencing a series can both be used to remove seasonality. Does the difference of these two lie in the model they are used? Moving Average used in classical decomposition and ...
26 views

### Do variable-selection methods (e.g. Elastic Net; Lasso) invalidate theory-based models in fields where little is known?

I'm caught in a bind about the relationship between theoretical models about how the world works and statistical methods for accurately predicting an outcome in fields where little is known. I ...
70 views

### Statistical Theory of Power Sampling (within R code)

I am curious about the statistical theory behind power.prop.test in R. I have dived into the code behind it and detailed it in Latex format. My question here is: ...
47 views

### Statistical theory proof intuition (UMVU estimators)

I've been working through this problem in Theoretical Statistics by Keener, but could not solve it. I looked up the answer and I do understand why it's correct, but I don't understand what intuition ...
390 views

### Isn't the Solomonoff Universal Prior Biased Like Any Other?

The Solomonoff universal prior is fixed relative to a specific choice of universal Turing machine (UTM). Now, I understand that a UTM can simulate any other UTM, so that they assign a complexity to ...
265 views

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### Operator Theoretic Perspectives on Bayesian Inference

On the Wikipedia page for conjugate prior there is a section "Analogy with Eigenfunctions", which describes a metaphor where observation of data is seen as a "linear operator" on the space of ...
25 views

### Correcting for sample overlap (loss of statistical independence) in two z-tests

Short form: How can I correct two p-values computed from normal distributions to account for the fact that part of the samples overlap? Long form: I have a sequence of i.i.d RVs of length $n$. The ...
75 views

### High-level time-series question: How does one study a series' trend?

I want to understand a series' trend, not the deviations from the trend. I would like to do analysis on the trend, such as run a multivariate regression, but every time-series source I read online ...
44 views

### Does it ever make sense to talk about the confidence (faith) in a probability value?

Let us suppose that we want to know what weather will be tomorrow. We ask two meteorologists and both give us an identical probabilistic answer: It will rain with probability of 30% It will snow ...
76 views

### Maximum likelihood estimator with atoms

MLE (maximum likelihood estimation) can be defined mathematically for discrete or continuous variables. But there is a technical specificity about variables being neither discrete nor continuous. ...
45 views

### Name of most general operator on probabilities whose output are also probabilities?

Not sure if the title is correct phrasing, I'll try to explain. Consider finite domain discrete probabilities for simplicity and illustration. The n-probabilities are contained on a (n-1)-simplex ...
47 views