All Questions
Tagged with sufficient-statistics intuition
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Help developing intuition behind sufficient statistics (Casella & Berger) [duplicate]
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I am trying to understand the following intuition for sufficient statistics in Casella & Berger (2nd edition, pg. 272):
A sufficient statistic captures all of the information ...
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Sufficient statistic as iso-surfaces in the distribution density. Is it possible to generalise to multiple parameters?
For continuous distributions, there is a geometric intuition behind sufficient statistics that regards a multivariate probability density as several iso-surfaces.
This works at least for cases where a ...
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Concrete example of what Sufficient Statistics is [closed]
Having read articles to try to understand Sufficient Statistics.
Sufficient statistics for layman
A sufficient statistic summarizes all the information contained in a sample so that you would make ...
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What is the space that a class of probability distributions spans when T is a complete sufficient statistic?
There are a few good posts/notes (see here, and here) giving high level geometric intuition of a complete statistic ($E_{T}[g(T); \theta] = 0 \Rightarrow P(g(T)=0; \theta) = 1 \text{ almost everywhere}...
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Understanding the Importance of "Sufficiency" within Statistics
I am trying to better understand what it means to be a "sufficient statistic".
"In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown ...
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Understanding sufficient statistics geometrically
Consider the distribution $\mathcal{P} = \mathcal{N}(\mu, 1)$, where the variance is known but the mean is unknown. Let $X_1,X_2\sim P$ i.i.d. In this case $T = X_1+X_2$ is a sufficient statistic.
I ...
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Sufficient Statistics - Relating the Intuition with the Mathematical Definition
I believe the heuristic definition of a Sufficient Statistic makes sense to me - when you take a sample in order to make an inference about the parameter related to the probability distribution, and ...
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What is the intuition behind the factorization theorem? (Sufficient statistics)
By the Fisher's factorization theorem, a statistics is a sufficient statistic if (and only if) the joint density,
$$ f(x_1, x_2, x_3, \dots x_n; \theta) $$
can be factorized into two functions, $ g(s; ...
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Intutitive meaning behind the formal definition of sufficient statistic?
According to the definition of sufficiency, a statistic is sufficient for a parameter if the conditional distribution of $X$ given a value of statistic does not depend upon the parameter.
What I am ...
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Intuitive understanding of the Halmos-Savage theorem
The Halmos-Savage theorem says that for a dominated statistical model $(\Omega, \mathscr A, \mathscr P)$ a statistic $T: (\Omega, \mathscr A, \mathscr P)\to(\Omega', \mathscr A')$ is sufficient if (...
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Sufficient Statistic and Maximum likelihood
This is more a conceptual question, but it seems to me that a sufficient statistic for a parameter is a concepts that applies only if we want to estimate the parameter via maximum likelihood. Is this ...
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If $T(\bf{X})$ is a sufficient statistic for $\theta$, why does the conditional distribution of $\bf{X}$ given $T(\bf{X})$ doesn't depend on $\theta$? [duplicate]
I know that if $T(\bf{X})$ is a sufficient statistic for $\theta$, then the conditional distribution of $\bf{X}$ given $T(\bf{X})$ doesn't depend on $\theta$. However, I am not sure why this makes ...
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Fisher-Neyman factorization theorem, role of $g$
The theorem states that $\tilde Y=T(Y)$ is a sufficient statistic for $X$ iff $p(y|x) = h(y)g(\tilde y | x)$ where $p(y|x)$ is the conditional pdf of $Y$ and $h$ and $g$ are some positive functions.
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Basic intuition about minimal sufficient statistic
As stated by Wikipedia:
A sufficient statistic is minimal sufficient if it can be represented as a function of any other sufficient statistic. In other words, $S(X)$ is minimal sufficient if and ...
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Why does a sufficient statistic contain all the information needed to compute any estimate of the parameter?
I've just started studying statistics and I can't get an intuitive understanding of sufficiency. To be more precise I can't understand how to show that the following two paragraphs are equivalent:
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