All Questions
Tagged with sufficient-statistics bayesian
15
questions
0
votes
1
answer
31
views
When are Bayes estimators injective as a function of sufficient statistics?
I know that Bayes estimators can be written only as a function of sufficient statistics. When are those functions injectives? That is, when can I say that, given a bayes estimator $\delta (\cdot)$ and ...
5
votes
1
answer
377
views
Is the Sufficiency Principle an axiom?
Sufficiency Principle as defined in Casella:
Where Sufficient Statistic is defined as:
Question: Is the Sufficiency Principle an axiom?
My thoughts and research so far:
I'm uncertain if the ...
- 284
2
votes
0
answers
149
views
Bayesian definition of sufficient statistics [duplicate]
Some time ago I wrote a question about what I think/thought (up to my understanding) is an ambiguity of the common definition of sufficient statistics :
Conditioning in the definition of sufficient ...
- 910
12
votes
1
answer
2k
views
What is "Likelihood Principle"?
While I was studying "Bayesian Inference", I happen to encounter the term, "Likelihood Principle" but I don't really get the meaning of it. I assume it is connected to "...
- 3,525
4
votes
1
answer
796
views
Conjugate priors outside exponential family
The usual exception I have come across regarding non-existence of conjugate prior outside the exponential family is the uniform distribution on $(0,\theta)$ (i.e. $U(0,\theta)$) where $\theta$ has a ...
- 11.5k
0
votes
0
answers
551
views
Bayesian Linear Regression and the Exponential Family
In a straight forward linear regression model, assuming a fixed input $\mathbf{x}$, and additive noise with unit variance we can write:
\begin{equation}
p(y\mid \mathbf{x,w})=\frac{1}{\sqrt{2\pi}\...
- 545
8
votes
2
answers
647
views
Is there a difference between Bayesian and Classical sufficiency?
The title pretty much says it all. I wonder whether there is any difference in the way Bayesians understand sufficiency vs. the way orthodox statistics understands sufficiency, or are they equivalent? ...
- 3,104
2
votes
1
answer
68
views
Question about sufficiency
I learned in my (classical) statistics class that (if we have densities) $T(X)$ is sufficient iff $$f(x)= g(T(x))h(x)$$
I am reading "the Bayesian Choice" and there the factorization-lemma is quoted ...
- 3,104
5
votes
2
answers
320
views
MCMC combined with numerical integration towards more efficient Bayesian inference
I am quite new to Bayesian statistics so the question can be a bit naive.
My question is on how to deal with a model with individual coefficients. Simple versions of a task and a model I deal with is ...
13
votes
2
answers
1k
views
How does Bayesian Sufficiency relate to Frequentist Sufficiency?
The simplest definition of a sufficient statistics in the frequentist perspective is given here in Wikipedia. However, I recently came across in a Bayesian book, with the definition $P(\theta|x,t)=P(\...
- 5,822
1
vote
1
answer
1k
views
Showing sufficiency using the Fisher-Neyman factorization theorem
I have derived a likelihood function for $\theta$ as follows:
$$L(\theta)=(2\pi\theta)^{-n/2} \exp\left(\frac{ns}{2\theta}\right)$$
Where $\theta$ is an unknown parameter, $n$ is the sample size, ...
- 1,627
1
vote
0
answers
116
views
Updating sufficient statistics parameter sets in Bayesian Inference (Changepoint Detection) [closed]
I am trying to implement and customize a changepoint detection method based on Bayesian Inference (referring to https://arxiv.org/pdf/0710.3742v1.pdf). Now I struggle understanding the conjugate prior ...
- 35
1
vote
0
answers
718
views
Are sufficient statistics for regression equivalent in the frequentist and Bayesian cases? [duplicate]
If I have a Poisson regression such that $\lambda = \alpha + \beta t$, $\alpha + \beta t \geq 0$ $\forall t, \alpha, \beta$ and $Y_t \sim \textrm{Poisson}(\lambda_t)$ for which I have 10 observations ...
- 163
4
votes
0
answers
166
views
Sufficient statistics of posterior (with Poisson data)
Suppose that, for year $t$, the data $y$ is Poisson with mean $a + bt$. Assume also a uniform prior on $(a,b)$. If we have $n$ years of data then I think the posterior for $(a,b)$ will be
\begin{...
- 41
3
votes
0
answers
146
views
Kolmogorov's paper defining Bayesian sufficiency
I'm looking for a translation to either English, French or German of Kolmogorov's Russian paper
Kolmogorov, A. (1942). Sur l’estimation statistique des paramètres de la loi de Gauss. Bull. Acad. Sci. ...
- 1,443