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.

Filter by
Sorted by
Tagged with
0 votes
1 answer
21 views

About ideal data and its distribution

I was just thinking about what would be the properties of an ideal data set $X \in R^{n,d}$ where n is sample size, d represents features. I think (or at least I understood from reading text books) ...
user avatar
0 votes
1 answer
22 views

PRML - Bishop: Order of Addition - Variance calculation

My question is related to section 3.2: Bias-Variance decomposition. My doubt is specific to formula for variance (3.47, below), on pg 150 - 151. Background: General formula for variance is: $\begin{...
user avatar
0 votes
0 answers
30 views

Kernel trick in feature space

I am working on KPCA based fault detection. I have question concerning the kernel trick in the feature space. We all know that the dot product in the feature space is computed using kernel function. I ...
user avatar
1 vote
0 answers
39 views

Matrix Covariance Algebra

In the structural equation modeling (SEM) context, one of the modeling frameworks is called the reticular action model (RAM). In RAM, the observed variables (y) and latent variables (η) are combined ...
user avatar
2 votes
1 answer
62 views

Are permutation groups used in statistics?

I was told that there may be a connection between concepts in abstract algebra and applications in statistics (also confirmed by the 'algebraic statistics' tag on this website). I had no idea, so I'm ...
user avatar
0 votes
0 answers
45 views

Algebra: When calculating the variance of Zero-inflated Poisson dist

I am deriving the variance of zero-inflated Poisson distribution, whose PMF is $$ P(X=k) = \begin{cases} \pi + (1-\pi)e^{-\lambda} \; , \; if \; k=0 \\ (1- \pi) e^{-\lambda} \frac{\lambda^k}{k!} \; , \...
user avatar
1 vote
0 answers
256 views

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 ...
user avatar
0 votes
0 answers
32 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)? $$Cov(x,y)=\frac{\sum_{i=1}^{n}(x_i-\bar{x})(y_i-y)}{N-1}$$ ...
user avatar
  • 1
4 votes
2 answers
423 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: ...
user avatar
  • 639
1 vote
1 answer
50 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)\...
user avatar
  • 35
1 vote
1 answer
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 ...
user avatar
0 votes
0 answers
285 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 ...
user avatar
  • 1
0 votes
1 answer
20 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 ...
user avatar
3 votes
2 answers
144 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 ...
user avatar
  • 1,712
3 votes
1 answer
2k 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 $\...
user avatar
  • 455
2 votes
0 answers
33 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 ...
user avatar
0 votes
1 answer
65 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 ...
user avatar
  • 105
1 vote
0 answers
21 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. ...
user avatar
  • 111
0 votes
1 answer
65 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)}{...
user avatar
  • 103
5 votes
0 answers
369 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 ...
user avatar
  • 267
6 votes
1 answer
317 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 ...
user avatar
10 votes
2 answers
3k 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 votes
4 answers
3k 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 ...