All Questions
Tagged with mathematical-statistics bayesian
354
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Mapping two Dirichlet Distributions into a comparative Dirichlet
Assume I observe some draws from 2 choice options, and want to infer the probabilities of various outcomes, e.g. non-negative integers up to a limit L. I could simply use 2 Dirichlet distributions to ...
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43
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Help with completing a derivation of usefulness of cross-validation
This question is raised as a result of my attempt to answer this other question of mine.
Let's refer to all our prior knowledge, both explicit and implicit, as $X_\text{true}$. Almost always, we are ...
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Conjugate prior for a beta distribution [duplicate]
What is the conjugate prior of the beta distribution? All I can find is the wikipedia page on conjugate prior. Is this correct? And does anyone know where it came from? Like a specific paper? Thanks
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How the randomisation probability is updated for each new patient entering adaptive clinical trial?
Disclaimer: You may need to read the entire paper to answer this question :)
I am reading this paper to learn about adaptive clinical trials. Here in page 1723 under "Statistical methods" ...
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Can an outcome variable be used twice in the same model?
When is it appropriate to use the same outcome variable in two likelihoods in the same model framework?
Here is a specific example:
...
4
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1
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368
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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 ...
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What is the terminology for the Log Ratio of Beta Distributions in a Bayesian Update?
Consider a prior distribution $\text{Beta}(\alpha, \beta)$ and $N$ observed Bernoulli($p$) coin tosses with $k$ heads. The quantity I'm interested in is:
\begin{align}
\log \left(\frac{\text{Beta}(p; \...
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1
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54
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When a credible interval coincides with a confidence interval, can one interpret confidence interval as credible interval and vice versa?
Let's say I have a frequentist model with $n$ data points to derive a confidence interval for a parameter. I also have a Bayesian model with $n$ data points to derive posterior for the parameter. In ...
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76
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Sample mean of Bernoulli trials is admissible under squared loss
Let $X_1,\ldots,X_n$ be i.i.d. Bernoulli trials with probability $\theta\in(0,1)$, and let $L:(0,1)\times[0,1]\to\mathbb{R}$ be the squared loss function, i.e. $L(\theta,a)=(\theta-a)^2$. I am trying ...
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Help with Posterior Distribution for a Poisson-Gaussian Process Model [closed]
I'm working on a regression model where variable Y is regressed on x, expressed as
$$y_i | f(x_i) \sim \text{Poisson}(\exp(f(x_i)))$$
for i.i.d observations (i = 1, ..., n). Here, (f) is modeled as a ...
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394
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Bayesian Justification of Cross-validation
If I understand correctly, K-fold cross-validation is supposed to approximate expected log predictive density (ELPD), which is defined as $\mathop{\mathbb{E}}_{D_{new}\sim P(.|M_{true})}\log P(D_{new}|...
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24
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The concept and notation about MLE(Likelihood) and MAP
In generally, we say that X1, X2, ..., Xi are from a certain distribution, which can be represented by f(x;θ), where θ is an unknown parameter.
When I read content related to MLE or the Likelihood ...
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4
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Do we believe in existence of true prior distribution in Bayesian Statistics?
Let $X$ be an $\mathcal{X}$ valued random variable. Suppose that we have observed $X = x$ .
We use a parametric model with $\theta \in \Theta$ being the parameter .
In frequentist approach, we believe ...
- 435
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57
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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 ...
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How to interpret a noninformative joint prior?
I am currently working on a homework assignment and have the following question:
$\theta_1$ and $\theta_2$ are parameters of interest and $y_1$ and $y_2$ are the likelihood functions which are $\text{...
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