Skip to main content

Questions tagged [definition]

This tag indicates questions about definitions of statistical terms. Use a more general tag [terminology] for questions on statistical parlance that are not specifically about definitions.

Filter by
Sorted by
Tagged with
0 votes
0 answers
10 views

Can manual feature extraction be considered a part of a learning algorithm?

We can view a learning algorithm as a tuple $(\mathcal{H}, \mathcal{O}, \mathcal{L})$ where $\mathcal{H}$, $\mathcal{O}$ and $\mathcal{L}$ are the hypothesis class, optimizer and loss function ...
ado sar's user avatar
  • 477
1 vote
0 answers
45 views

Can you arbitrarily define your sample space?

Let's say you flip a fair coin. A sample space is a set of possible outcomes of an experiment. So, intuitively, the sample space will be {Head, Tail}. However, I have seen that it is also possible to ...
Sherlock_Hound's user avatar
1 vote
1 answer
107 views

Formal definition of sufficient statistic

Let $(\Omega_X,\mathcal{F}_X)$ and $(\Omega _T,\mathcal{F}_T)$ be measurable spaces. Let $\mathfrak{M}$ be a family of probability measures on $(\Omega_X,\mathcal{F}_X)$. Let $X:\Omega\to \Omega _X$ ...
rfloc's user avatar
  • 133
13 votes
11 answers
2k views

When is it important for a practitioner to understand CIs?

I have a physician friend who asks me questions about stats. He gets confused about stuff, e.g., the definition of a confidence interval (CI) and its intricacies. For example, he finds the following ...
Yair Daon's user avatar
  • 2,634
2 votes
2 answers
94 views

Fixed vs random: how can a fixed effect be constant across individuals?

For years, I have been trying to find a definition for fixed and random effects. I often see statements like this: Fixed effects are constant across individuals. - almost universal We define effects (...
opiczak's user avatar
  • 23
1 vote
1 answer
51 views

Motivation behind definition of PMF of function of $2$ variables

I am really curious to understand what motivates the definition $$p_{g(X,Y)} (g(X,Y)=z) = \sum_{(x,y)\in g^{-1}(\{z\})} p_{X,Y} (x,y)$$ where $g$ is a two variable function, and $X,Y$ are random ...
niobium's user avatar
  • 189
6 votes
4 answers
365 views

Frequentist probability: Can we prove mathematically what we are setting probabilities equal to, or are they just assumptions/definitions?

Just as an example, let's say I am modeling the rolling of a die. We can use the frequentist definition of probability to define a probability of an event, say rolling a 6, as the $\lim_{n\to\infty}$$\...
0 votes
1 answer
60 views

Unbiased estimator for mean

The question: Given a random sample $X_1,...,X_n$ show that $\frac{1}{n}\sum_{i=1}^n X_i$ is an unbiased estimator for $E(X_1)$. My confusion: Given a statistical model $(\Omega,\Sigma,p_{\theta})$, ...
user124910's user avatar
0 votes
0 answers
24 views

Kendall's Notation for Kelly Networks?

Background Kendall's notation (also see Ciw docs') is a convenience when you work with queues a lot. It not only provides an abbreviation, but its wide use helps make literature searches more specific....
Galen's user avatar
  • 9,412
1 vote
1 answer
71 views

Finding a source for the definition of "clustering accuracy"

In papers about unsupervised clustering I see a lot of references to a metric "clustering accuracy" or "unsupervised clustering accuracy" (ACC) which is usually defined as ...
Cyo's user avatar
  • 11
0 votes
0 answers
20 views

Example of statistical experiment in which the statistical unit is time

Could you give me some examples of statistical experiment/analysis in which the statistical unit is the time? If I conduct a study on the number of people who have attended a bachelor degree over time,...
Elia's user avatar
  • 1
3 votes
1 answer
83 views

Definition of $\text{“}R^2\text{”}$

I have always taken $\text{“}R^2\text{”}$ to mean the proportion of a sum of squares explained by a model. The context in which this idea is first encountered is when one explains part of the total ...
Michael Hardy's user avatar
1 vote
2 answers
163 views

Definition of Uncertainity

I have some confusion regarding Measurement Uncertainty. In some books/articles it is defined wrt true value as "Uncertainty in the average of measurements is the range in which true value is ...
Govind Prajapat's user avatar
16 votes
4 answers
1k views

Do testability and falsifiability have statistical definitions?

Psychology: the Core Concepts says Psychology differs from the pseudosciences in that it employs the scientific method to test its ideas empirically. The scientific method relies on ...
Tim's user avatar
  • 19.6k
1 vote
0 answers
115 views

Definition of exponent measure (extreme value theory)

Let $F$ be a distribution function on $\mathbb{R}^2$, and let $U_i$ be the left continuous inverse of $\frac{1}{1-F_i}$, where $F_i$ is the marginal distribution of $F$. In my textbook, there is the ...
Phil's user avatar
  • 636
10 votes
3 answers
917 views

For a confusion matrix, is there a name for FP / (FP + FN)?

For a confusion matrix, there are a variety of useful rates, ratios and indices. But I cannot find the one I care about: FP / (FP + FN) Of course this measure is ...
David Bridgeland's user avatar
1 vote
2 answers
235 views

What is a formal and authoritative definition of an 'assumption' in a statistical model?

The description of the tag in this website states that it Refers to the conditions under which a statistics procedure yields valid estimates and/or inference. E.g., many statistical techniques ...
Kuku's user avatar
  • 1,482
11 votes
2 answers
292 views

Definition of "unpredictable"

How do we rigorously define the term "unpredictable" in cases of point and density prediction? The term "unpredictable" is employed in various contexts, e.g. "the outcome of ...
Richard Hardy's user avatar
0 votes
0 answers
36 views

Clarification: confidence interval of the (slope of the) regression line

When confidence intervals are referenced in the regression context, I often see them mentioned (generally speaking) as "of the slope of the regression line," or as "of the regression ...
anumberofthem's user avatar
10 votes
7 answers
2k views

Data vs. Information. What’s the difference between these two terms?

Following are the definitions "representative" of the countless articles I have read about data vs information and yet have nothing to say about them. Can anyone just put some accent upon ...
Vinay Sharma's user avatar
1 vote
0 answers
36 views

Definition of Statistics by Sheldon M. Ross [closed]

Sheldon M. Ross in his book, "Introductory Statistics" states the definition of statistics to be: "Statistics is the art of learning from data. It is concerned with the collection of ...
TankFishToad's user avatar
1 vote
2 answers
175 views

meaning of independent samples

I am getting confused about the concept of independent samples, which is related to the concept of pseudoreplications. This question is related to this topic. But reading it does not make it clear for ...
quibble's user avatar
  • 1,694
1 vote
1 answer
1k views

The link between AQL, RQL and the reliability of a process

The problem is to distinguish between the definitions of AQL, RQL and reliability in the field of quality control. Let us just pose the context. We wish to calculate the reliability of a manufacturing ...
lulufofo's user avatar
  • 472
1 vote
1 answer
65 views

Questions on what it means when we talk about "overfit"

"Overfit" is a commonly discussed concept in ML community. However, I tend to feel that there might be abuse of using this terminology. I wonder what it means when we talk about overfit, ...
mw19930312's user avatar
12 votes
3 answers
1k views

What's the relationship between these two definitions of martingales?

On wikipedia, the definition of a martingale is given as follows: A basic definition of a discrete-time martingale is a discrete-time stochastic process (i.e., a sequence of random variables) $X_1, ...
ExcitedSnail's user avatar
  • 2,966
5 votes
1 answer
243 views

How to demonstrate amount of virus required to lyse all cells using Poisson distribution?

In a seminal article in virology ('Sur l’unité lytique du bactériophage' Comptes rendus des séances de la Societé de biologie et de ses filiales, 1939, 130, pp. 904-907) the Nobel prize winner ...
Gigiux's user avatar
  • 211
1 vote
0 answers
56 views

Definition p-value and find p-value in practice

I have a problem that I can't solution. Let $\mathbf{X}=\{X_1,X_2,\ldots,X_n\}\sim\mathrm{Uniform}(0,\theta)$ and we have $H_0:\theta=\theta_0$ and $H_1:\theta>\theta_0$. We reject the $H_0$ when $...
Samvel Safaryan's user avatar
0 votes
0 answers
34 views

marginal cdf and cdf of marginals

given a joint distribution of 2 variables $P(X,Y)$, is the cdf of the Y-marginal distribution equals to the Y-marginal of the cdf of $P(X,Y)$?
Alucard's user avatar
  • 325
2 votes
0 answers
75 views

Why are Square Integrable Functions important in Statistics?

I'm reading a paper by Giles Hooker on Functional Decomposition through the use of Functional ANOVA. In the paper he defines a function: $$ F(x) : \mathbb{R}^k \rightarrow \mathbb{R} $$ and explicitly ...
Connor's user avatar
  • 655
1 vote
0 answers
146 views

Is there a connection between the Kernels in Statistics and Linear Algebra?

According to this question, the etymology of the terms is related, and Kernel is used to mean the "core" of something. In general it seems to refer to an unchanging transformation at the ...
Connor's user avatar
  • 655
3 votes
1 answer
978 views

What are balanced and orthogonal designed experiments?

I have recently started studying Designed Experiments and have have come across non-rigorous definitions of "balanced" and "orthogonal" experiments and would be interested in ...
FD_bfa's user avatar
  • 243
2 votes
1 answer
486 views

Relationship between blocks, factors and treatments

I have recently began studying a course on Designed Experiments and am having some trouble understanding some of the terminology. I've looked at some other answers on the site and I think that I am ...
FD_bfa's user avatar
  • 243
4 votes
0 answers
459 views

Is there a difference between out-of-domain and out-of-distribution?

When I research papers on the generalisability of ML models, both terms "Out of Distribution" and "Out of Domain" pop up. Are these essentially the same? In my understanding, yes. ...
amsulic's user avatar
  • 61
7 votes
1 answer
200 views

Can we consider the loadings as a proxy for correlation, in a Principal Component Analysis (PCA)?

In a PCA, the loadings can be understood as the weights for each original variable when calculating the principal component, or "how much each variable influence a principal component". Thus,...
Idervas's user avatar
  • 107
1 vote
1 answer
89 views

Questions regarding power of test and type II error

I´m preparing for a lecture in decision theory and I´m a little bit confused by the notation used by my prof. On the first slide under remark 3.2 point v) its written, that $\beta(\varphi)$ is equal ...
this_is_not_easy's user avatar
3 votes
2 answers
722 views

What is independent censoring and what are its assumptions?

I'm reading the Introduction to Statistical Learning book. In chapter 11 (Survival Analysis, page 463), the authors state: In general, we need to assume that the censoring mechanism is independent: ...
Juan's user avatar
  • 57
4 votes
1 answer
1k views

Bounded density function: definition?

What is the correct definition of bounded probability density function: $\sup_{x} f(x)<\infty$. If this is the correct definition of bounded probability density function, can you give the example ...
Star's user avatar
  • 891
0 votes
0 answers
49 views

Understanding likelihood vs conditional joint pdf

My course notes (3rd-year module in Bayesian Statistics, unpublished) have a paragraph, Gaussian data with known variance Suppose we have $\textbf{x}=\{x_1,\dots,x_n\}$ iid given $\theta$ and $\...
mjc's user avatar
  • 599
12 votes
3 answers
1k views

Rationale behind defining distribution function with strict inequality

A friend from Italy pointed me to a nice Probability Theory book written in Italian by G. Dall'Aglio, a well-known Italian probabilist; Original title: Calcolo delle Probabilità, terza edizione, ...
utobi's user avatar
  • 12k
2 votes
1 answer
135 views

Are random variables mathematical functions when dealing with continuous sample spaces?

I'm struggling with some basic concepts regarding the definitions of random variables. If I'm not mistaken, random variables are functions which aim to "translate" outcomes of a sample space ...
Idervas's user avatar
  • 107
0 votes
0 answers
70 views

Definition of Hypothesis Testing in All of Statistics

In the book All of Statistics by Larry Wesserman, the author says "Let $X$ be a random variable and let $\mathcal{X}$ be the range of $X$. We test a hypothesis by finding an appropriate subset of ...
user159566's user avatar
7 votes
7 answers
2k views

Regression vs. Classification: Is there a clear, generally accepted definition?

As a mathematician/economist, I am not trained to think in classification and regression tasks. This is why I wonder: is there a clear, widely accepted definition of regression and classification ...
Arne Jonas Warnke's user avatar
1 vote
0 answers
38 views

Provide an example of a dataset where maximum likelihood is inapplicable as third moments and fourth moments "assumptions" do not apply

An additional complication arises with estimation, since maximum likelihood estimation may not be feasible without making unrealistically strong ?????"assumptions"????? about third‐ and ...
user avatar
31 votes
5 answers
5k views

What is the difference between something being "true" and 'true with probability 1"?

In the beginning of chapter 2 of Information Theory, Inference and Algorithms, the author says that he will refrain from being unnecessarily rigorous and provides the example of saying that something ...
stochasticmrfox's user avatar
1 vote
1 answer
334 views

What is the definition of a non-linear estimator? I heard that ratio of estimators is non-linear

Why don't we consider nonlinear estimators for the parameters of linear regression models? says that LASSO is a non-linear estimator. I think LASSO has a solution via matrix multiplication. I don'...
user avatar
5 votes
2 answers
2k views

When is a statistic not a statistic?

I have a fairly involved ``statistic'' that involves transformation of a set of samples $\mathbf{x}$ by a massive machine-learned matrix and subsequent nonlinear processing into said statistic $\...
David McKnight's user avatar
2 votes
2 answers
370 views

Define plateau of sigmoid function

I have a sigmoid function ...
Saraha's user avatar
  • 21
1 vote
0 answers
222 views

Definition of correlation between events?

I often hear people talk about correlation between events, e.g. event A and event B are positively correlated. However, unlike correlation between random variables (i.e. $\frac{Cov(X,Y)}{\sigma_X \...
iluvmath's user avatar
  • 205
3 votes
2 answers
319 views

A Rigorous Definition of Data Generating Process (DGP)

I am trying to find a rigorous mathematical definition of a data generating process (DGP) under a well-defined probability space. The closest source I have found on Cross Validated is this one, and it ...
Frank Swanton's user avatar
2 votes
1 answer
2k views

What does 'Parent Distribution' mean in statistics?

I am studying some articles related to statistics and some of them mention the term 'Parent Distribution'. What does that mean? Is it a distribution model that the authors decide to use as a basis of ...
Vicky's user avatar
  • 21

1
2 3 4 5
12