Questions tagged [references]

Questions seeking external references (books, papers, etc.) about a particular subject. Always use a more specific tag in addition.

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5
votes
1answer
69 views

Name and interpretation of “$h(x)$” in exponential family

The exponential family is defined (in many sources) as: $$p(x | \theta) = h(x) \exp\{\theta^TT(x) - A(\theta)\}$$ where: $T(x)$ is a sufficient statistic, $\theta$ is a canonical parameter, and $A(...
4
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1answer
70 views

Distribution Reference $\gamma x^{\gamma-1}$

I have been unable to find resources regarding the family of distributions with pdf $$ f_\gamma(x) = \begin{cases} \gamma x^{\gamma-1}, & \text{if } 0 \leq x \leq 1 \\ 0, & \text{...
1
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1answer
39 views

Generalizing Bayesian methods by assuming a “distribution of distributions” instead of a prior

Bayesian methods assume a prior distribution with several hyperparameters. Unfortunately, this is asymptotically incorrect, because distributions in the real world are never exact. For example, the ...
1
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0answers
26 views

A book-chapter long nontechnical introduction / overview of neural networks

I will be teaching an introductory course in machine learning for students in management who have minimal quantitative skills. I am looking for a brief and gentle introduction to neural networks that ...
0
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1answer
24 views

applied papers on probabilistic generative models and inference engines

I am looking for applications papers where people choose some task on which they will do Bayesian inferencing and graphical modeling, and then build an inference engine to infer latent parameters. And ...
3
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0answers
53 views

What are the main approaches to the foundation of statistics without probability

The frequentist, likelihood and, to an even greater extent, Bayesian approaches to statistics are all based on probability. Without probability, it seems difficult to use a data sample ("seen" cases), ...
2
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0answers
20 views

Probability of sparse spectrum

Consider a vector $v$ such that $v \sim \mathrm{Unif}(\mathbb{S}^{d-1})$, the uniform distribution on the unit sphere in $d$ dimensions. Question: is there an upper bound on the probability that $v$ ...
3
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0answers
37 views

Convergence rate of the inverse covariance matrix [closed]

I am trying to find results regarding the convergence rate of the inverse covariance matrix in the case where the number of observations $n$ is larger than the number of dimensions $p$. Assume that $...
0
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2answers
83 views

Alternatives to The Statistical Sleuth?

I am looking for a simple and concise book on statistics (t-test, ANOVA and all its variants, linear regression, etc.), centered on data analysis. I am not interested in theory or proofs, but just ...
0
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0answers
22 views

Dimension of a probability distribution function

Consider the following statement We want to sample from a complex high dimensional distribution which is intractable. What is meant by a dimension of distribution here? Does each random variable ...
1
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1answer
27 views

How much matrix differentiation background for Seber and Lee's Linear Regression Analysis

How self-contained is Seber & Lee's textbook 'Linear Regression Analysis'? It seems to assume knowledge of matrix differentiation.
1
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1answer
26 views

Does a more powerful test mechanically lead to more type III errors then?

"Type III error occurs when you correctly conclude that the two groups are statistically different, but you are wrong about the direction of the difference. Say that a treatment increases some ...
1
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0answers
39 views

Literature on conceptual understanding of beta regression

I am researching beta regression models to decide if they are appropriate for my data. My very first search yielded this basic introduction, that also describes the zero-one inflated beta regression. ...
0
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0answers
17 views

Literature recommendation for convolutional neural nets

I am looking for a good book or an article concearning convolutional neural nets, especially their architecture. I like the http://deeplearningbook.org but it does not provide any information on the ...
2
votes
1answer
65 views

Targeted Maximum Likelihood Estimation for dummies?

I have tried to get my head around the concept of TMLE, but most references seem to be written by people who despise being understood (or maybe I am just hebetudinous). I have tried to read the paper ...
0
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0answers
19 views

References for this ARMA two step method estimation

I was doing some survey on ARMA parameters estimation methods. While on that, I found these lecture notes: http://www.phdeconomics.sssup.it/documents/Lesson12.pdf There, the author describes a two ...
1
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1answer
20 views

Gradually increasing reinforcement learning environment complexity

The problem of robotic arm control has different levels of complexity ranging from simulation to real-world application. For example, a simulation may not model friction of the joints, which becomes ...
0
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1answer
29 views

When kernels are not useful in SVM?

In SVM using kernels we map the original features to the higher, transformer space (feature mapping) and then perform linear SVM in this higher space. But when kernels are not useful? I could not find ...
0
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0answers
38 views

Mysteries of the Normal Distribution [duplicate]

I have been studying ML for over a year and am actually a Bachelors of Statistics myself and am sick of not knowing the beauty of the Gaussian distribution and why it is so prevalent in nature. I've ...
1
vote
1answer
84 views

Why is using keras ImageDataGenerator for data augmentation relevent?

I have used keras ImageDataGenerator to generate more data in my neural networks as I have had really small datasets and it has proven itself. As far as I ...
2
votes
1answer
192 views

Analysis of count data with percentages

for my master thesis I count and identify sediment grains. In total I have 82 samples from 3 different gravity cores. I divided the sediment components in 11 groups (Quarz, Mica, Opaque, Aggregate, ...
4
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0answers
29 views

How to combine noisy and noise-free datasets to train a model

Overview Suppose I have two datasets, both of which consist of rows of features and their matching labels. One of these datasets is noise-free and its labels correspond to the ground truth, but the ...
4
votes
2answers
127 views

Are GLMs just glorified WLS regressions?

When performing weighted least squares $L = \frac{1}{2} \sum_i w_i r_i^2$, Aitken showed that one ought to weight each sample by the inverse of its variance $w_i=1/\sigma_i^2$. This leads to gradients ...
0
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2answers
39 views

Dealing with extreme outliers in administrative data (in R)

I work with some data that includes some "extreme outliers". E.g. timestamps that are totally unreasonable (surgery took 20 days when most take 1 hour). Is there a set of principles one can use to ...
0
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0answers
6 views

Risk of Spurious Relationships As a Function of 3 Magnitudes: # Times Sampled, # Individuals Sampled and # Variables Measured

I've seen some literature that quantifies the risk of spurious relationships in terms of sample size vs number of variables but I've not seen literature that quantifies the risk based on all 3 ...
3
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0answers
33 views

Fisher information matrix and gradients

I'm a math Ph.D. without formal training in statistics. Quite a few papers on normalization methods in deep learning mention the Fisher information matrix and how it's related to the Riemannian metric ...
0
votes
1answer
33 views

Suggested books to study statistics [closed]

I am doing a research that requires me collecting and analyzing data samples in order to identify if there is correlation or no with respect to some parameter. I am looking for the best resources to ...
4
votes
2answers
51 views

Best resources on imputation in R [duplicate]

This is my first question at stats. I need to impute some factors and numbers in my data set in R. What are my best options regarding packages and also a source to read more about the theory.
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0answers
41 views

Where to learn the theory behind common statistical techniques [duplicate]

I'm a college student and pursuing (in part, at least) a statistics and data science track. Much of my coursework beyond the introductory statistics sequence has involved topics like multiple ...
0
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0answers
26 views

Wilks' lambda's exact distribution when one of the parameters is 1 or 2

Citing Wikipedia, From the relations between a beta and an F-distribution, Wilks' lambda can be related to the F-distribution when one of the parameters of the Wilks lambda distribution is either 1 ...
5
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1answer
274 views

Statistical analysis applied to methods coming out of Machine Learning [closed]

Most of the recent famous methods coming out of the machine learning, are supervised learning methods like Decision Trees, Random Forests, Deep Learning, SVMs. The more traditional supervised ...
3
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0answers
42 views

Looking to identify a book by a top statistician with a chapter on Simpson's Paradox

It was more than 20 years ago. I had just gotten acquainted with Simpson's paradox. I was browsing in a bookstore and saw a book by an eminent statistician -- eminent in the sense that I had come ...
1
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1answer
45 views

marchenko pastur for Correlation

It has been suggested to me that if I construct a covariance or correlation matrix using factor model then I can use the Marchenko-Pastur distribution to highlight significant correlations (or ...
0
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0answers
20 views

Phase marginal for a multivariate complex Gaussian density

Suppose $z$ is a random variable taking values in $\mathbb{C}^n$ and admitting the complex Gaussian density $p(z;W) \propto \exp{(-\frac{1}{2}z^*Wz)}$, where $W$ is Hermitian. Let $r$ be the vector of ...
1
vote
2answers
884 views

Finding the MLE of Poisson in R [closed]

I'm trying to determine the MLE of $\lambda$ in a Poisson distribution using R. I'm aware that the MLE is $\hat{\lambda}=\bar{x}$ but I want to demonstrate this using Rmarkdown. My experience with R ...
0
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0answers
13 views

(Existence part of) Neyman-Pearson via weak-* convergence

I would like a ask whether there is any statistical reference containing the following functional analytic argument for the existence part of Neyman-Pearson: Let $(R, \mathcal{F}, \mu)$ be a measure ...
1
vote
0answers
36 views

Correspondence between time series models in continuous vs. discrete time

I am interested in an overview over the connection and correspondence between time series models in continuous vs. discrete time in finance. E.g. take ARMA(p,q) or GARCH(s,r) or ARMA(p,q)-GARCH(s,r) ...
2
votes
1answer
71 views

Best Course of Study for Data-Science/Statistician Interviews [closed]

This is my first question here, so please pardon my gaffes. I am currently working as a Data-Scientist, a position which I worked up from Junior Analyst position.My bachelors is in Computer Science ...
2
votes
1answer
181 views

Poisson Binomial Distribution - confidence intervals

I'm working on a project which involves multiple trials for which the probability of success is not the same across trials. Given the unequal probabilities per trial, I'm using the Poisson Binomial ...
1
vote
1answer
46 views

Scientific papers using “entry” level Econometric procedures

I am studying Econometrics on a Masters' level. I have a pretty good grasp of the theoretical aspect of different processes, from dummy variables to time series, stationarity or simultaneous models (...
1
vote
1answer
49 views

Books for self-learning about statistic Simulation?

Preferably an introductory book, i.e. for undergrad (or notes or something like that) that explains concepts with detail and with lots of examples, without losing the formality. That covers the ...
0
votes
1answer
82 views

Best book for statistical inference (Self-study) [duplicate]

I want to develop some skills in statistical inference for a career in data science or machine learning. I purchased the book "All of Statistics" which is a good book, but there are not answer keys ...
3
votes
1answer
24 views

Reference request: initializing big neural networks with small neural networks

I am currently trying some meta-algorithms on training neural networks. Start with a small but expressive enough network for training and after several epochs, initialize a larger neural network with ...
3
votes
0answers
24 views

Are there extant deep learning analogs to random coefficient (aka mixed) models?

Random coef models, applied to longitudinal data, capture response heterogeneity by cross-sectional unit. I've got a longitudinal prediction problem, in which I know that some "features" (or ...
3
votes
1answer
41 views

Seminal works in deep learning [closed]

I'm compiling a list of 7 seminal works in deep learning to work on during 14 week semester course. I'd appreciate if you suggested papers for the list. I'm looking for the papers that impacted the ...
0
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0answers
10 views

SEM resources from a linear model prospective

I'm starting a new project at work that requires theory and application of structural equation models, but my background is quite low in this area. I have a very good background in regression, linear ...
0
votes
1answer
31 views

Kolmogorov Distribution D statistics

As far as I have searched the cumulative distribution function of 𝐾, asymptotically (kolmogorov distribution) is given by Pr(𝐾≤𝑥)=1−2∑∞𝑘=1(−1)𝑘−1𝑒−2𝑘2𝑥2=2𝜋√𝑥∑∞𝑘=1𝑒−(2𝑘−1)2𝜋2/(8𝑥2). But ...
0
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0answers
147 views

Does High Dimensional Data effects SVM?

As we move into higher dimensions, we will find even more corners. This will make an ever increasing percentage of the total space available. Now imagine we have data spread across some ...
0
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0answers
86 views

What are some introductions to classical statistics that emphasize unifying principles? [duplicate]

I'd like to know an introduction to classical statistics, that: Emphasizes connections and unifying principles (I checked this question and the links posted therein, but didn't find an introduction ...
1
vote
1answer
51 views

Variable Importance for Logistic regression with categorical data?

If I run the logistic regression with X variables containing categorical data. (I do one-hot encoding on categorical data) How do I evaluate the variable importance? Is there any methods or literature ...