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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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What are some applications of machine learning and any associated career opportunities in engineering domain? [closed]

I'm a university student currently enrolled in a Statistics Bsc. As of lately I've taken an interest into how statistics/machine learning can be applied to engineering disciplines, but haven't found ...
sonictiger's user avatar
1 vote
0 answers
13 views

What do we call a Poisson point process with an instantaneous log-rate being a Wiener process?

I have implemented a stochastic process for simulating demand of service that wanders in its average rate. This is a useful scenario for evaluating a controller that tries to optimize availability and ...
Galen's user avatar
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7 votes
2 answers
498 views

Markov Chains with Changing Number of States

I have seen these kinds of Discrete State Markov Chains before (Continuous Time or Discrete Time): Homogeneous (Probability Transition Matrix is constant) Non-Homogeneous (Probability Transition ...
udon762's user avatar
  • 71
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0 answers
20 views

Data generation processes that "vary slowly enough"

I am considering some abstract data generation processes producing data by first drawing features $x_{1:n}\sim p(x)$ iid, and then drawing the responses $y_i\sim p(y\mid x_i)$ iid, where $p(y\mid x)$ ...
Daniel Robert-Nicoud's user avatar
1 vote
0 answers
26 views

Literature for a supervised task on time series

I was introduced to the following project at my company. We have $n$ time series coming from $n$ sensors. Each sensor has monitored a physical signal at a specific location. For each time series, a ...
brised by Linear Algebra's user avatar
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0 answers
15 views

Model parameter averaging in Bagging

I wonder if the following bagging method is used in practice, or at least any reference for this. Assume that we sample (sub)-datasets from the original training set, and train $n$ many logistic ...
Seewoo Lee's user avatar
2 votes
0 answers
37 views

Mathematical Introduction to Theory of Time Series Analysis

Assume that the reader has strong background in stochastic calculus (including and beyond continuous time stochastic processes like martingales and Markov chains and others, the construction of Levy ...
4 votes
2 answers
234 views

References to learn « Real and Functional Analysis for Statisticians »

I’m looking for a kind of book which gives the elements of Real Analysis for Mathematical Statistics and Econometric Theory, etc. I’m planning to work with the 3 following textbooks on advanced ...
Hiba__Nouhoum__Djeneba's user avatar
2 votes
2 answers
63 views

Nice real datasets for visually illustrating concepts

I am looking for relatively small (< 1000 sample) real datasets for use in teaching. I would like regression examples with a non-linear relationship between a single input and output ...
0 votes
1 answer
85 views

Normal approximation for posterior distribution

I am reading the example 4.3.3 of "The Bayesian Choice" by Christian P. Robert and I was wondering if it is possible to obtain a normal approximation in this case to estimate the posterior. ...
daniel's user avatar
  • 155
2 votes
0 answers
38 views

Reference request for the existence of minimal sufficient statistics

I'd like a recent paper or book that shows in what conditions we can guarantee the existence of a minimal sufficient statistic. I know the paper "Sufficiency and Statistical Decision Functions&...
rfloc's user avatar
  • 121
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0 answers
36 views

GLM Reference and Introudction to study my self [duplicate]

I am a third-year statistics student. I have a course in Generalized Linear Models. Unfortunately, the course is taught in French, which is not my primary language, and I am facing some difficulties ...
Nizar's user avatar
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1 vote
1 answer
25 views

What statistical methods are used for estimating the effect of political policies?

I've started to become interested in the statistical analysis of the efficacy of political policies on, say, health or economical outcomes. I have a background in epidemiology. Here, estimating the ...
Stijn's user avatar
  • 1,892
1 vote
0 answers
49 views

References on when to choose Bayesian vs. frequentist analysis

I'm looking for references discussing and comparing the advantages and drawbacks of Bayesian vs. frequentist analysis in various contexts. If it makes sense, I'd be particularly interested in learning ...
Coris's user avatar
  • 11
1 vote
0 answers
62 views

Is this the CDF of a known probability distribution?

Consider the following cumulative distribution function over $\mathbb{R}^{+}$ $F\left(x\right)\;=\;1+\mathcal{W}\left(-e^{-1-x}\right)$ where $\mathcal{W}\left(\cdot\right)$ is the Lambert W function. ...
bbecon's user avatar
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0 answers
7 views

Looking for terminology to describe a certain partial independence condition on conditional probability

I find myself in a position where for events $X,Y$ and $Z$, I might have $$ P(X|Y,Z) = P(X|Y)P(X|Z) $$ I don't know what to call this, and it's difficult to search for potential phrases, since all ...
David Roberts's user avatar
0 votes
0 answers
11 views

Analyze the variance of one adaptive process?

I'm currently interested in analyzing the variance of one adaptive process. To be more specific, suppose I have done some, let's say $n$ times, experiments where the results depend on some unknown ...
narip's user avatar
  • 187
1 vote
0 answers
46 views

Hypothesis testing upper bound involving $\chi^2$ distance

In this [note]https://www.stat.cmu.edu/~larry/=stat705/Lecture27.pdf, the author provides some upper bounds for hypothesis testing involving total variation distance and Hellinger distance in section ...
efsdfmo12's user avatar
  • 123
1 vote
0 answers
29 views

Extended Hidden Markov Models (HMM) parameter estimation

For simpler HMMs, we can use algorithms like Viterbi training (not decoding) or Baum Welch to estimate the parameters that best describe the observed data. How do we do the same when using a more ...
AlexS123's user avatar
1 vote
1 answer
43 views

Earliest paper on stratified log rank test

What is the earliest paper that proposed the stratified version of the log-rank test? Unfortunately, finding citations/references in textbooks for established statistics procedures is difficult.
user1916067's user avatar
0 votes
0 answers
16 views

How can we compare the "performance" of different Markov chain Monte Carlo algorithms?

How can we judge the performance a Markov chain Monte Carlo (MCMC) algorithm? I guess we could consider one of the following: The variance of $X_t$ for a given $t\in I$; The asymptotic variance of $(...
0xbadf00d's user avatar
  • 293
2 votes
0 answers
27 views

Example orthonormal basis of Word Embedding Space?

Models such as Word2Vec supposedly provide a bijection between language tokens and some "latent-space" that is in fact a high-dimensional vector space. If this is a vector space, it should ...
Vector's user avatar
  • 21
3 votes
0 answers
43 views

References for Generation of Synthetic Data

What are some of the introductory textbooks/references specifically on the task of generating synthetic data (from real data)? If possible, such a text is expected to cover a range of methods, be it ...
2 votes
0 answers
46 views

Finding a specific reference on the construction of a confidence interval where by inspection we can see it does contain the parameter

I realise this is a long shot but I am trying to find a reference to a specific example of a construction of a confidence interval which I came across in the past. My memory on this is hazy and I may ...
8e9yQBKVlIDwoIVegfkJ's user avatar
1 vote
0 answers
29 views

Statistical Modelling Research Papers

My task was to make a logistic regression model for a dataset to predict a binary variable (0/1). During this process I went through all of the stages of model building, from scratch given unprocessed ...
Alex Smirnov's user avatar
2 votes
0 answers
31 views

Translation of Stange's (1971) approach to tolerance limits in simple linear regression

In Stange (1971), Angewandte Statistik, Vol. II. Springer Verlag, Berlin, Heidelberg, New York, 141-143, the author derives a tolerance limit for simple linear regression which is widely used in ...
Aleph's user avatar
  • 31
4 votes
1 answer
124 views

Insights in a more complex multilevel model

I'm looking to understand how to build a multilevel model using Stan. The structure I'm looking at is y ~ x + (x|z) + (x|w) By following the "Data Analysis ...
Lefty's user avatar
  • 479
0 votes
0 answers
92 views

Is Federer Formula of sample size in experimentation study (t-1)(n-1) ≥ 15 legit?

I've seen this formula for sample size determination in experimental studies, which was claimed by Walter Federer, is well-known among Indonesian bio researchers. The formula is: $$ (t-1)(n-1) \geq 15$...
isaid-hi's user avatar
0 votes
0 answers
45 views

Mathematical rigorous approach to linear regression [duplicate]

I'd like a book or any PDF that teaches about linear regression in a complete way. That is, I want something that, for instance, doesn't use any random variable without stating its domain or the $\...
rfloc's user avatar
  • 121
0 votes
0 answers
26 views

On the asymptotic joint distribution of two weighted Bernoulli sums

Let $\theta_i$ be a Bernoulli random variable of success probability $p$. Given two fixed sets $A = \{a_1, a_2, ..., a_N\}$ and $B = \{b_1, b_2, ..., b_N\}$ where $a_i$ and $b_i$ are constants. For ...
Kevin B.'s user avatar
1 vote
0 answers
22 views

Reference request for Bayesian problem formulation [closed]

In Bayesian inference, there are two parts: the problem formulation, where the structure of the problem with parameters is built, and the solution of Bayesian inference, through MCMC, grid or normal ...
0 votes
0 answers
27 views

Conjugate or VB update for normal likelihood with shifted variance

Consider following model with normal likelihood at time $t$. \begin{align*} y_t | \mu_t, \sigma_t^2 \sim \mathcal{N}(\mu_t, \sigma_t^2 + P_t) \end{align*} we would like to find some priors $\mathcal{F}...
StatsyBanksy's user avatar
0 votes
0 answers
51 views

How much statistics knowledge is enough for studying time series?

I am interested in studying time series (both theoretical and applied), my background is in mathematics and my probability knowledge is well enough but I haven't studied stats deeply (only one course ...
Pat's user avatar
  • 1
1 vote
0 answers
35 views

Reference for autocorrelation formula for vectors

This post on Stack Overflow says that the autocorrelation, or self correlation, of vectors is defined as $$C(t, \{v\}_n) = \frac {1}{n-t}\sum_{i=0}^{n-1-t}\vec v_i\cdot\vec v_{i+t}$$ What is the ...
user366312's user avatar
  • 2,140
19 votes
4 answers
2k views

Are there situations where a vertical bar chart is preferable to a horizontal one?

I hardly see what kind of advantage a vertical bar chart could have over a horizontal one (edit: by "horizontal bar chart", I mean a chart with bars oriented horizontally). On the other hand,...
Coris's user avatar
  • 347
8 votes
0 answers
166 views

What are some good books on how to avoid, as a statistician, being used to lend false credibility to a dishonest project?

I mean for example companies or organizations who are not really interested in decision making driven by serious data analysis, but who employ or hire statisticians to try to give false credibility to ...
5 votes
3 answers
178 views

Reading tips on longitudinal mixed models and mediation

I'm a Swedish PhD student in psychology looking for advice on what to read to understand linear mixed models in a longitudinal context better. We're running a RCT with two active groups and weekly ...
3 votes
1 answer
49 views

Proof of lower bound of Cohen's kappa

Can anyone refer me to a paper or book showing that Cohen's kappa is bounded below by $-1$? I've read various papers stating this, but I have never found a complete proof. This question was asked here,...
nahp's user avatar
  • 151
0 votes
0 answers
12 views

"Time stratified" regression model?

I'm sure this type of model has a name but I can't for the life of me find the correct keyword to look it up. For each $t \in \{0, 1, \ldots, T \}$, suppose I have $n$ data tuples $\{ (X_{0,t}, Y_{0, ...
Anthony's user avatar
  • 530
1 vote
0 answers
53 views

Is there a good review on complete class theorems?

I'm trying to get an overview of the various results called "complete class theorems" and their relatives, especially the ones that say things along the lines of "every admissible ...
N. Virgo's user avatar
  • 425
5 votes
1 answer
132 views

What is a good real-life example of using correctly the Neyman-Pearson hypothesis testing framework?

I've read a couple of theoretical explanations of what it is (in particular this thread: When to use Fisher versus Neyman-Pearson framework?), but so far I didn't find real-life examples of people ...
Coris's user avatar
  • 347
5 votes
0 answers
90 views

Is there an English translation of Ladislaus Bortkiewicz’s book “The Law of Small Numbers" (1898)?

I finished reading Deaths by horsekick in the Prussian army – and other ‘Never Events’ in large organisations. It led me down a rabbit hole of thinking about Poisson point processes modelling demand ...
Galen's user avatar
  • 9,229
0 votes
1 answer
13 views

Literature on discriminatory model VS discriminatory feature

I have a dataset with 200 individuals, 50 features and an outcome variable with 2 levels. The majority of features are not (statistically) significantly different (T-test, Kolmogorov-Smirnov test). I ...
amr95's user avatar
  • 13
0 votes
1 answer
51 views

what book should I read to learn inferential statistics? [closed]

I am not a statistics student so I have no clue about inferential statistics. All I learned was descriptive stats. I am currently conducting research to find if two groups are similar/not. I have ...
Zel's user avatar
  • 9
0 votes
1 answer
33 views

Clustering of large text datasets with unknown number of clusters

I have a list of hotel names which may or may not be correct, and with different spellings (such as '&' instead of 'and'). I want to use clustering in order to group the hotels with different ...
user480840's user avatar
8 votes
3 answers
1k views

Median of a set with even number of elements

Consider the following sample of numbers: 9,18,11,14,15,17,10,69,11,13 Since there are 10 elements, the median of the set would be (13+14)/2 = 13.5 However, is it wrong to say that median is one of 13 ...
user avatar
1 vote
2 answers
94 views

Why do information criteria provide consistent estimation of the lag order?

Consider the following $AR(p)$ model $$Y_{t}=\sum_{j=1}^{p}\phi_{j}Y_{t-j}+\epsilon_{t},$$ where $\epsilon_{t}\sim i.i.d\ \mathcal{N}(0,\sigma^{2}).$ Say we have samples $t=1,\dots, T$. The true lag ...
JacobsonRadical's user avatar
1 vote
0 answers
51 views

What is the connection between permutation tests and rank tests?

I was trying to understand the null hypothesis of the Wilcoxon rank sum test and thought that the null distribution of the rank sum could be obtained by a permutation test/Monte Carlo test. If this ...
Ggjj11's user avatar
  • 1,373
4 votes
2 answers
95 views

Universal approximation theorem for neural networks reference

On Wikipedia, a nice theorem is given: However, I can not find the stated theorem in the given references. So where is the stated theorem from?
tamtam_'s user avatar
  • 158
1 vote
0 answers
79 views

Datasets with multiple maximum likelihood estimators

There is a sizeable body of literature on the issue of multiple maximizers in maximum likelihood estimation, such as https://projecteuclid.org/journals/statistical-science/volume-15/issue-4/...
Tom Solberg's user avatar

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