All Questions
Tagged with terminology bayesian
53 questions
6
votes
4
answers
1k
views
Is it incorrect terminology to say "confidence interval of a random variable"?
I have seen claims that "population paramter is not a random variable" when discussing confidence intervals.
eg here
Be sure to note that the population parameter is not a random variable.
...
- 284
10
votes
5
answers
2k
views
How would a Bayesian define a fair coin?
In the frequentist worldview, probabilities are long-run relative frequencies. Hence, a fair coin can be defined as a coin, for which the long run relative frequency of each of the sides approaches 0....
- 777
7
votes
1
answer
159
views
Terminology for distribution of posterior mean before seeing data
Imagine we are performing Bayesian inference with normal-normal conjugate priors. We have some prior:
$$
\mu \sim N(\mu_0, \sigma_0^2).
$$
We know we will collect some normally distributed data $x$ ...
- 71
2
votes
1
answer
75
views
Terminology question regarding a certain "partial maximum likelihood" which approximates the marginal likelihood
Suppose that we have a model with many parameters, which we'll partition into two subvectors called $\theta$ and $\lambda$. In this situation, $\lambda$ corresponds to those parameters that are really ...
- 475
0
votes
0
answers
31
views
Name for assuming a 50-50 split
is there a term or principle for assuming a 50-50 split for complementary events (they can’t both be true but one has to be true) when you have no data for the actual split/proportion?
3
votes
1
answer
2k
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Can we talk about statistical significance using Bayesian Inference?
In short: can we use the words statistical significance when interpreting the hypothesis testing results in the bayesian inference field ? Or is it only correct to use it in the frequentist approach ?
...
- 31
5
votes
0
answers
145
views
Using the terminology "Bayesian confidence interval" in place of "Bayesian credible interval."
In Peter Hoff's "A first course in Bayesian statistical methods," he states:
"Most authors refer to intervals of high probability as 'credible intervals' as opposed to confidence ...
- 73
3
votes
1
answer
431
views
Why maximum a posterior, not maximum posterior?
Is the additional "a" mean that different priors may lead to different posterior, MAP is a result of many possible results? And similar to MLE, why the abbreviation of maximum a posterior ...
- 93
6
votes
1
answer
93
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Does ( P(B|A) - P(B|~A) ) / P(B|A) have a name?
Without going into the details, which are unnecessary here, this morning I found uses for the quantity
$$ S = \dfrac{P(B|A) - P(B|\overline A)}{P(B|A)} , $$
something like the amount of "...
- 163
39
votes
6
answers
6k
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Is there a name for the opposite of the gambler's fallacy?
The gambler's fallacy is a fallacy because of the assumed probability and the independence of the events. However, if, after flipping a coin 100 times and obtaining heads each time, I still believe ...
- 9,688
11
votes
3
answers
2k
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What does it mean that a Gaussian process is 'infinite dimensional?'
I have glossed over this phrase many times without really understanding what it means. According to Wikipedia - Gaussian process
Gaussian processes can be seen as an infinite-dimensional ...
- 962
2
votes
2
answers
5k
views
What is Type II maximum likelihood?
It might be some straight forward thing.. But I referred to some threads already over internet to understand what exact does it mean when we use terms "evidence maximization" "type II ...
- 31
1
vote
1
answer
59
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How do I estimate survival probabilities using datasets that cover different amounts of time?
I'm looking for help classifying a problem that I don't yet have the statistical terminology for, and for help thinking about possible approaches to work on the problem. Below, I give an analogous ...
- 111
4
votes
1
answer
104
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What is the origin of the term 'inverse probability'?
Inverse probability relates strongly, or is synonymous to, Bayesian probability.
Thomas Bayes applied the idea in 'An Essay towards solving a Problem in the Doctrine of Chances' (published in 1763).
...
- 86.5k
30
votes
4
answers
10k
views
What exactly does the term "inverse probability" mean?
I keep seeing the term "inverse probability" mentioned in passing albeit without any explanation.
I know it has to do with Bayesian inference, but what exactly do we mean by inverting a ...
- 1,617
3
votes
1
answer
173
views
Coin flipping: Relationship between Bayesian and Frequentist's point estimates
I have a (biased) coin that has an unknown Head probability $p\in(0,1)$. To point estimate $p$, say that I'm going to use two approaches.
Approach 1. I can use the Bayesian inference technique. ...
- 423
0
votes
0
answers
19
views
How to describe a methodology that infers objects' unobserved properties from their similarity to simulations
I am trying to succinctly describe a technique I've developed for inferring some unobserved properties of galaxies based on their observed similarity to simulations.
I have a bunch of simulated ...
- 213
2
votes
1
answer
53
views
multi-level models and hierarchical models
I am wondering what are the differences between multi-level modeling and hierarchical models? Are the in fact the same thing?
- 5,282
17
votes
2
answers
556
views
What is the origin of the name "conjugate prior"?
I know what a conjugate prior is. But I'm confused by the name itself. Why is it called "conjugate"? A complex conjugate $z^\ast$ has a reciprocal relationship with $z$, i.e., ${z^\ast}^\ast ...
- 684
1
vote
3
answers
375
views
Why is inference different in logic and statistics?
In Bayesian Inference, the term "inference" means learning parameters. In logic, inference means deducing something. Why are these two terms different?
1
vote
1
answer
222
views
Subscript in expected value notation [duplicate]
I am a bit confused about the terminology when using subscripts in expectations and probabilities. I was reading about the reparameterization trick from the following link:
"gregorygundersen - ...
- 65
16
votes
1
answer
477
views
What is the "direct likelihood" point of view in statistics?
I am reading a Springer title from 1997 called Applied Generalized Linear Models by James K. Lindsey. In the preface, Lindsey writes
For this text, the reader is assumed to have knowledge of basic ...
- 263
2
votes
0
answers
37
views
What does it mean when a distribution is "INDEXED" by something? [duplicate]
I am doing some reading and am seeing phrases such as the following. For context, I am learning about Bayes Inference and prior/posterior distributions so theta is the parameter:
In such problems, ...
- 3,263
1
vote
2
answers
220
views
Why do we call the set of latent variables a "family" in variational inference?
we posit a family of approximate densities Q. This is a set of densities over the latent
variables. Then, we try to find the member of that family that minimizes the Kullback-Leibler(KL) divergence ...
- 1,382
13
votes
3
answers
318
views
Terminology for Bayesian Posterior Mean of Probability with Uniform Prior
If $p \sim$ Uniform$(0,1)$, and $X \sim$ Bin$(n, p)$, then the posterior mean of $p$ is given by $\frac{X+1}{n+2}$.
Is there a common name for this estimator? I've found it solves lots of people's ...
- 21.6k
14
votes
5
answers
4k
views
What precisely does it mean to borrow information?
I often people them talk about information borrowing or information sharing in Bayesian hierarchical models. I can't seem to get a straight answer about what this actually means and if it is unique to ...
- 2,692
5
votes
1
answer
814
views
bayesian terminology for fixed and random effects
What is the Bayesian terminology for
- fixed effect
- random effect
- least squares mean ?
Or is it OK to use the frequentist terminology?
- 2,237
7
votes
3
answers
540
views
Can "cross-validation" be used to choose a prior?
To be clear, I doubt I am using the term "cross-validation" correctly here; what I am suggesting also seems similar to "boot-strapping" and "hyperparameter tuning". ...
- 6,479
8
votes
0
answers
1k
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Are Log Predictive Likelihood, Log Predictive Probability, Log Marginal Likelihood and Log Predictive Density same?
I have seen different papers use different terms to express the scoring rules that they used to compare Bayesian models. Some of those terms are,
Log Predictive Density (Bayesian Data Analysis - by ...
- 153
5
votes
2
answers
257
views
Term for "extent to which a test throws away information"?
A statistical test $T$ is a mapping from the space $\Delta$ of possible data $D$ to $\{R,A \}$, (meaning: Reject, Accept).
If we have a null hypothesis $H_0:\theta \in \Theta_0$ for which $T$ is a ...
- 2,987
7
votes
3
answers
552
views
Is the posterior distribution $P(\theta|\mathbf{X})$ a statistic?
The textbook definition of a statistic is any function of the data, $g(\mathbf{X})$. Much of frequentist inference is concerned with deriving sampling distributions for various statistics under some ...
- 3,387
12
votes
3
answers
987
views
What does it mean for something to have good frequentist properties?
I've often heard this phrase, but have never entirely understood what it means. The phrase "good frequentist properties" has ~2750 hits on google at present, 536 on scholar.google.com, and 4 on stats....
2
votes
0
answers
54
views
On the definition of the Bayes Classifier
Let $(X,Y): \Omega \to (\mathbb{R}^d, F)$, with $F = \left\{ 1, \dots, n \right\}$ be a random variable. According to Wikipedia the Bayes classifier is $$C_B(x) = \arg\, \max \mathbb{P}(Y= i \,|\, X=x)...
- 151
7
votes
2
answers
7k
views
In Bayesian terminology, what does evidence refer to?
In Bayes theorem of a parameter $\theta$ with data $D$, we have:
$$P(\theta|D) = \frac{P(D|\theta)P(\theta)}{P(D)}$$
where I know $P(D)$ as the marginal likelihood. Is it true that the marginal ...
- 6,724
3
votes
2
answers
314
views
The usage of word "prior" in logistic regression with intercept only
Suppose I am fitting a logistic regression with intercept only, which is equivalent tho using the count to estimate the outcome probability and make prediction.
Can I say following?
We are using ...
- 37.3k
2
votes
0
answers
50
views
How should I call the complement of a credible region?
Incredible interval/region?
More explicitly, if I have a unimodal distribution with a 95% credible interval in [A,B], what would I call the complementary region ]A,B[? It is 100% credible region ...
- 121
5
votes
2
answers
2k
views
Does "improper" posterior or prior refer to a density function that does not integrate to 1 or to one that does not integrate to a finite value?
I am a bit confused about improper priors and posteriors.
I have seen references that classify a prior or posterior probability density function as "improper" if the integral over infinite support ...
- 2,425
5
votes
1
answer
843
views
Relation between Bayesian analysis and Bayesian hierarchical analysis?
I have been studying a Bayesian hierarchical model. In that model all I am dealing is with the estimation of parameters. In Bayesian analysis, loosely speaking, we update our prior knowledge (in light ...
- 569
19
votes
1
answer
2k
views
Antonym of variance
Is there a word that means the 'inverse of variance'? That is, if $X$ has high variance, then $X$ has low $\dots$? Not interested in a near antonym (like 'agreement' or 'similarity') but specifically ...
- 609
6
votes
2
answers
75
views
Prior distribution on/of a parameter
Is it correct to write the prior distribution on $\mu$ ?
I think it is correct because it refers to the fact that "we put a distribution on (the state space of) $\mu$".
However, I would not say the ...
- 19.7k
13
votes
1
answer
4k
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What do we mean by hyperparameters? [duplicate]
Can anyone give me full details about what we mean by hyperparameters, and what in the Dirichlet distribution are called hyperparameters? A practice example for the estimation of those parameters ...
- 131
-1
votes
1
answer
761
views
What does posterior "over" parameters $\alpha$ exactly mean? [closed]
From my understanding the posterior "over" parameters $\alpha$ is
$$p(D|\alpha)$$
and not
$$p(\alpha|D),$$
is it correct?
- 358
1
vote
1
answer
276
views
Terminology Numerator Baye's Rule?
I am considering this formulation of Baye's Rule
$\mathrm{Pr}(\theta | D) = \frac {\mathrm{Pr}(\theta)\mathrm{Pr}(D|\theta)}{\int \mathrm{Pr}(D|\theta)\mathrm{Pr}(\theta)\mathrm{d}\theta}$
Is there ...
- 595
3
votes
1
answer
642
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Bayesian linear regression with continuous and binary covariates
I am interested in learning more about applying Bayesian linear models for covariates some of which are continuous and some are binary.
What is the appropriate terminology for such models so that I ...
4
votes
2
answers
2k
views
What makes a GLM Hierarchical?
Wikipedia defines a Hierarchical GLM as:
Hierarchical linear models (or multilevel regression) organizes the
data into a hierarchy of regressions, for example where A is regressed
on B, and B ...
- 19.7k
3
votes
3
answers
282
views
Bayes in English
I am not a statistician or mathematician but am trying to learn.
My question: In Bayes Theorem, $p(C|X)=p(X|C)p(C)/p(X)$, what are the English terms for $p(X|C)$ and $p(C)/p(X)$?
In other words, is ...
- 81
2
votes
0
answers
85
views
What do you call $p(Y|X_1)$?
Given random vectors $Y= [Y_1, \dots, Y_m]$ and $X = [X_1, \dots, X_n]$, $p(y|x)$ is the conditional distribution of $Y$ given $X$.
We can call $p(y_1|x)$ the marginal conditional distribution of $...
- 19.8k
10
votes
1
answer
3k
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What is a loss function in decision theory?
My notes define a loss function as the 'cost' incurred when the true value of $\theta$ is estimated by $\hat\theta$. What kind of cost is it talking about? monetary cost? or is it something related to ...
- 969
2
votes
1
answer
178
views
Statistical error in Bayesian framework
Residuals and errors are related but not exchangeable. In Wikipedia I read:
In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of ...
- 430
25
votes
3
answers
3k
views
What does "fiducial" mean (in the context of statistics)?
When I Google for
"fisher" "fiducial"
...I sure get a lot of hits, but all the ones I've followed are utterly beyond my comprehension.
All these hits do seem to ...
- 1,977