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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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35 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)\...
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1answer
90 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 ...
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0answers
102 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 ...
0
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1answer
12 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 ...
3
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2answers
38 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 ...
2
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1answer
460 views

LASSO: Deriving the smallest lambda at which all coefficient are zero

I'am trying to derive mathematically the lowest $\lambda$ at which all coefficients are zero, reffering to the Exercise 2.1 of the book Sparsity with Statistical Learning. The result should be $\...
2
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0answers
21 views

Design of Experiments through Algebraic Statistics [closed]

I would like to ask you about how to compute a circuit basis of a design matrix in software R. Let me explain you. I have found a software, named Macaulay2, that calculates some algebraic tools, and ...
0
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1answer
35 views

Annualized Excess Return [closed]

I have been given the following formula to calculated Annualized excess return: Annualized excess return = (1+Monthly excess return)^12-1 The answer is provided ...
1
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0answers
15 views

How To Find The Right Formula [duplicate]

First off, I'm kind of out of my element when it comes to formulas and figuring out how to come up with a formula for what I need. If you need any other information, let me know and I'll add it. ...
0
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1answer
53 views

MLE Estimate - final step

The image below is the final steps taken from the MLE for the Pr. of success (parameter $\pi$) to a Negative Binomial. Source: SE thread. Here are the final steps from that: $ \frac{d\ell(\pi;x_i)}{...
4
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0answers
164 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 ...
6
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1answer
244 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 ...
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2answers
2k views

Algebraic Geometry for Statistics

I have heard about uses of Algebraic Geometry in Statistics and Machine Learning. I wanted to try to learn a bit about this topics. I don't know nearly anything about Algebraic Geometry, but I have ...
9
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4answers
2k views

What are important pure mathematics courses for a prospective statistics PhD student?

I know that linear algebra and analysis (especially measure theory) are important. Is it helpful to take graduate level courses in real and complex analysis? Should I take courses in abstract algebra ...