"References" is our generic tag for questions seeking information about books, papers, presentations, videos of lectures, on-line tutorials, etc., regarding any subject matter that is on-topic for Cross Validated.

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Gamma distribution and applications

I'm looking for references to read about gamma distribution and applications in industry or in quality control. I had a look at statistical methods for reliability data (Meeker and Escobar). It has ...
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5 views

Questionnaire Analysis Resources

Looking for resources (online resource, book, etc) that details how to analyze questionnaire data. I would like the resource to specifically deal with multiple choice questions, differences in sample ...
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23 views

Cheap, available in used market AP Statistics textbook [on hold]

I am teaching an Advanced Placement (AP) Statistics class and the high school currently has no textbooks for it. What is a cheap, available-in-the-used-market Statistics textbook that people actually ...
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0answers
40 views

Detailed reference to facilitate manual implementation of ARIMAX

ARIMAX is implemented in SAS and R (function arimax in "TSA" package). I want to implement ARIMAX in an open source library in Scala and Python. Is there any ...
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20 views

Estimating the Parameters of Multivariate Gaussian from Conditioned Distributions

My goal is estimating the distribution parameters of a multivariate Gaussian $\mathcal{N}(\mu,\Sigma)$ in $\mathbb{R}^n$ from observations that were generated from different conditioned variants of ...
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23 views

Entropy of independent draws of balls from a bin

Problem Setting Consider a bin containing $B$ balls, each ball is red or blue with equal probability ($0.5$). Let $R$ denote the number of red balls. It is easy to see that $R \sim Binomial(B,0.5)$ ...
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1answer
2k views

Statistical tables in old books purposefully wrong?

I remember having read a while ago that in old (pre-computer days) books, the last digits of the theoretical quantiles shown in the appendices were inaccurate in order to discourage plagiarism (the ...
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1answer
38 views

Regularized linear model: adding special constraints to the coefficient

I understand we can add $L_1$ or $L_2$ regularization to linear regression (Lasso and Ridge regression). In addition, it is possible to restrict the coefficient to be integers (see this post). ...
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17 views

Differences between Mutual Information

Let $X_1, X_2$ be $\{0,1\}$ identical random variables with the following joint distribution. $$ p(X_1=1,X_2=1) = 0.25 + \epsilon \\ p(X_1=0,X_2=0) = 0.25 + \epsilon \\ p(X_1=0,X_2=1) = 0.25 - \...
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39 views

Book about generalized linear models [duplicate]

Does anyone know a good book about generalized linear models. I am a practitioner and need to master the concepts of generalized linear model, but also my experience tells me that knowing about the ...
24
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1answer
796 views

Cross-validation misuse (reporting performance for the best hyperparameter value)

Recently I have come across a paper that proposes using a k-NN classifier on an specific dataset. The authors used all the data samples available to perform k-fold cross validation for different k ...
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1answer
23 views

How to embed prior distribution of datasets into the classification model

Given 3 training sets : $(X_1,y_1),(X_2,y_2)$ and $(X_3,y_3)$. These three datasets are separated as it is being manually tagged in the preprocessing. Based on the datasets, three classifiers can be ...
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1answer
26 views

Quantify compatibility between posterior estimates

I performed two distinct, independent experiment $E_1$ and $E_2$ to ideally measure the same quantity $X \in \mathbb{R}$ of interest. For each experiment, I computed the posterior pdf of $X$ via MCMC, ...
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29 views

How can I understand: “The Elements of Statistical Learning: Data Mining, Inference, and Prediction” [duplicate]

I just started to read the book: "The Elements of Statistical Learning: Data Mining, Inference, and Prediction", recommended as one of the best books about ML in a statistician perspective. I already ...
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1answer
53 views

Time series prediction using ARIMA vs LSTM

The problem that I am dealing with is predicting time series values. I am looking at one time series at a time and based on for example 15% of the input data, I would like to predict its future values....
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17 views

Academic Reference Request on Multivariate Mixed Model

The problem at hand was to predict two values, $Y^1$ and $Y^2$, from another one, $X$. We decided that a mixed model would be apropriate considering the clustered nature of data. After visual ...
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2answers
40 views

Very specific kind of textbook needed

I will (if I can find a good text) be teaching very basic stats to prisoners at a local med/high security prison. Because of the conditions imposed I will have only fifteen 1.5 hours classes and I ...
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0answers
19 views

Regression or fit with an homographic or a linear fractional relation

This question is motivated by exploratory data analysis. I have a number of variables, related to a chemical reaction. Each variable is the quantity of a chemical species produced in different ...
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1answer
43 views

Video Lectures on Regression Modeling and Analysis

I am hoping to build a collection of free video lectures that teach how to: Model regression problems. Interpret regression coefficients and the overall fit. Happy to make this CW if helpful. ...
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Changing the basis of random variables

Let $X_1$ and $X_2$ be two independent (1-dimensional) random variables and let $Y_1 = f^1(X_1, X_2)$ ($f^1$ is a deterministic function) be a (1-dimensional) random variable too. Question Does ...
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0answers
8 views

Resources for Determining Value-Added by Parameter Sweeps

I am working on a project that aims to use Design of Experiments to improve our testing process. We are performing tests using a parameter sweeps of numerous input variables (40+). Each input variable ...
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2answers
77 views

Meaning of (and proof of) “RNN can approximate any algorithm”

Recently I read that a recurrent neural network can approximate any algorithm. So my question is: what does this exactly mean and can you give me a reference where this is proved?
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2answers
63 views

Variance of the modulus of a random variable

Let $X$ be a random variable with mean $\mu$ and variance $\sigma^2$. What is the upper-bound on the variance of $Y=\left|X\right|$? My gut feeling says that $\operatorname{Var}(Y) \leq \operatorname{...
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Unable to recreate the sine function in Figure 5.3 - Pattern recognition and machine learning (Bishop)

I'm trying to recreate the sine function according to Figure 5.3. Of course since in the range [-1;1] this function won't look like the one in the figure (because the closest minima and maxima are x = ...
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Pattern recognition and machine learning (Bishop) - Figure 5.3: Something is wrong with the sine function

In Figure 5.3, Pattern recognition and machine learning (Bishop), the author says he fitted 4 function: f(x) = x^2; f(x) = sin(x) ; f(x) = abs(x); f(x) = Heaviside(x), using 50 points chosen uniformly ...
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1answer
89 views

What are multi-variable calculus pre-requisite for Machine Learning

I wanted to complete calculus pre-requisites for machine learning class. I am doing an online course of multi-variable calculus. Can someone please suggest what lectures after Lecture 15 are relevant. ...
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1answer
37 views

Pattern recognition and machine learning (Bishop) - Derivation of Evidence approximation

I'm reading section 3.5 of the PRML book, entitled Evidence approximation, and is having difficulty understanding this part: . I don't understand how to derive (3.75) from (3.74). The author says it ...
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9 views

Citation of a particular paper discussing the phrase “representative” sample

Some time ago (like decades?) I read a paper that gently explained why the phrase "representative sample" is an unfortunate and misleading usage, and why one should speak of random samples, perhaps in ...
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Reference request about feature maps in ML

Can someone kindly link to some recent papers on understanding feature maps in ML? It would help to get an idea of what are the recent issues there that people have been working on with regards to ...
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7answers
2k views

What are some examples of anachronistic practices in statistics?

I am referring to practices that still maintain their presence, even though the problems (usually computational) they were designed to cope with have been mostly solved. For example, Yates' ...
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1answer
43 views

Good text on nonlinear regression (M.S. graduate-level)?

I've covered a linear models sequence where the classes discussed linear models using matrices, covering various experimental designs (split-plot, for example), ANOVA using matrices, and ending with ...
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9 views

How much variance is captured by the RFF maps?

The RFF maps here are possibly the most used feature maps. I was wondering if there are cases where anyone has theoretically estimated the total variance captured by these maps? Is any simplification ...
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2answers
90 views

Seeking a Recommendation on Machine Learning Books for Biological Research

I am an undergraduate student studying mathematics and microbiology. I recently got a research project to study the evolution of viruses from the computational perspective, particularly from machine ...
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24 views

Normalized term frequency comparisons across documents of differing length & language

I aim to infer on the prevalence of terms across and within corpora of different languages (where document length varies within and across corpora). Given Zipf’s and Heap’s laws a simple tf/n seems ...
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2answers
78 views

Good examples/books/resources to learn about applied machine learning (not just ML itself)

I've taken an ML course previously, but now that I am working with ML related projects at my job, I am struggling quite a bit to actually apply it. I'm sure the stuff I'm doing has been researched/...
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1answer
36 views

Book about time series analysis in Stata

Does somebody know a good book which outlines the time series analysis in Stata, that is, the various commands explained. I am aware of the Stata manuals; however, they are not that user friendly for ...
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1answer
23 views

Reference for incremental sandwich covariance from biglm?

I am working on some similar methods to Lumley's biglm wrapper around Miller's AS274 algorithm, and I can't seem to find a reference for his incremental Huber/White ...
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0answers
13 views

Literature (guidelines) on unbalancedness in two-way within-subject ANOVA

I am looking for literature (guidelines) which discuss the consequences of unbalanced designs on running a (two-way) within-subject ANOVA and pros/cons of various counter-measures. I came up with ...
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1answer
34 views

Reference Books on Asymptotic theory of Statistics and Probability

Can anyone suggest me some good reference books on Asymptotic Theory of Statistics and Probability for students pursuing a post-graduate degree in Statistics ? It would be very much helpful if the ...
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4answers
153 views

Which book should I read to get started with machine learning, Elements of statistical learning or Pattern recognition in machine learning?

I want to learn machine learning. I found tons of material on the internet but couldn't decide which book to get started with.
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1answer
78 views

Logistic Regression Problem

The following table gives data on income in thousand dollars (x), the number of families (N) at income x and the number of families owning a house (n). ...
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What does “complete i” subscript mean in Gelman's model of incumbency in congressional elections?

I'm having a look at section 14.3, "Regression for causal inference: incumbency in congressional elections" in Gelman et al's Bayesian Data Analysis, third edition, pages 358-362. I'm looking for the ...
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0answers
14 views

Posterior pointwise uncertainty of multivariate normal-Wishart (variational GMM)

Given a variational mixture of Gaussians (as per, e.g., Chapter 10 of Bishop, 2006), we can compute the posterior predictive pdf: $$ \left\langle p(x|\alpha,\beta,\nu,\mu,V) \right\rangle $$ where $\...
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0answers
9 views

Reference for forecasting nonstationary variables

My goal is to extrapolate / forecast data up to 10, 20, 100 years depending on certain independent variables. Is there like a publication or a book that I could follow that specifically pertains to ...
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1answer
61 views

Intraclass correlation coefficient in Bayesian statistics

I need some references about intraclass correlation coefficient in Bayesian statistics and hypothesis testing. I already take a look in A. Gelman, J.B. Carlin, H.S. Stern and D.B. Rubin, Bayesian ...
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0answers
47 views

Bayesian inference via approximate data likelihood

Suppose that we have a very large i.i.d. sample $x_1,...,x_n$ and a data likelihood defined by $$p(x | \theta,\beta) = \prod_ip(x_i | \theta,\beta)$$. Further suppose that $\theta$ is the parameter ...
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16 views

Validating regression - common and best practice

Is there a reference setting out a best practice way to validate a regression (such as Lasso, but in general any automated regression), and what is done in practice? My motivation for the question is ...
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0answers
13 views

Factor Analysis with low sample size

Does anyone know of references to support conducting EFA with a low sample size?
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1answer
27 views

convergence of geometric mean/harmonic mean

Does any one know papers regarding the convergence of geometric mean or harmonic mean in probability, parallel to central limit theorem?
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“*usefulness*” is a bivariate property used in Regression and Anova. Has a generalization (trivariate) analogon been discussed?

Just for selfstudy/exercising of algorithms I looked at the computation of the "usefulness"-measure in multiple regression, which means the part of variance which one independent item contributes to ...