# Questions tagged [algebraic-statistics]

Use for questions relating to algebraic statistics, the branch of statistical theory concerned with methods from abstract algebra, especially algebraic geometry and commutative algebra. This tag is not for questions about the applications of linear algebra to statistics, nor for questions about grade school algebra in statistical problems.

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### How to incorporate the uncertainty of the model coefficients in the prediction interval of a multiple linear regression

The question is a bit similar to question 147242 . I'm dealing with a multiple linear regression model, say: $$y = \beta_0 + \beta_1 x_1 + \beta_2 x_2$$ and I'm looking for an algebraic equation to ...
16 views

### covariance in 2 dimensional field

I want to know is the covariance equation which is shown below is how valid when we are in 2-dimensional fields (not 2-dimensional data)? $$Cov(x,y)=\frac{\sum_{i=1}^{n}(x_i-\bar{x})(y_i-y)}{N-1}$$ ...
192 views

### R: linear algebra representation of the prediction operator for a mixed effects model

(See edit at the bottom for the bounty) I am trying to learn how to simulate LMM data with matrix linear algebra. So far I've managed to simulate a simple model with a random intercept: ...
39 views

### Determinants of the sum of two matrices and their eigenvalues

I know some basic property of determinant. I read an article and see this formula: \begin{equation} |(\delta-p-1)D+S|=\bigg(\prod_{i=1}^{p}\lambda_{i}(D)\bigg) \bigg(\prod_{i=1}^{p}(\delta-p-1)\...
93 views

### Given two related ratios within a population, derive a third ratio (eg. redheads, non-redheads, and skin cancer)

If People X are N times more likely to have attribute A than non-X People X are P percent of the population then What percentage of A's are X? Example (the numbers are just for illustration). If ...
158 views

### Independence vs. conditional mean independence

Independence, i. e. cov(g(e),f(x))=0, can be considered as a stronger assumption than conditional mean independence, i. e. cov(e,f(x))=0. Does independence, i. e. E{f(x)g(e)}=E{f(x)}E{g(e)} imply ...
18 views

### index and base year

I am creating a league table of a group of people with the aim to track their performance on 5 KPIs using indices. Base month value is set to 100. Out of 5 KPIs, an increase in 3 indices means good ...
51 views

### How do I check the validity of a set of inequality constraints? [closed]

I have a table of inequality constraints, each with an "x < y" relation. How can I check this table for contradictory logic such as a < b, b < c, c < a? For example ...
816 views

170 views

### Calculating Formula with logs and Weighted Average

I am trying to figure out an equation from the following paper by Cadena and Kovak (2016): http://pubs.aeaweb.org/doi/pdfplus/10.1257/app.20140095 on pages 264 and 265. I don't think the context is ...
266 views

### Cases where TDA outperforms public benchmarks?

Precise Question What are some specific examples where topological data analysis (TDA) outperforms other models on publicly available data? Context When new ML algorithms are developed, it seems ...