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Normalising likelihood for BIC/AIC calculation

Lower BIC scores are better, so the normalised value you're supposed to use is $\Delta BIC = BIC - BIC_{\text{min}}$, not max (see this paper, which shows the calculations for AIC, but the BIC ...
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1 vote

Normalising likelihood for BIC/AIC calculation

I would advise against normalizing the likelihood by the number of observations, since this would make the definitions of the BIC and the AIC irrelevant. AIC/BIC are not arbitrary combinations of a ...
1 vote

How to determine if the log likelihood of logistic regression is too large or not?

The fact that you are referring to "good fit", "not good fit", and "excellent fit", is already an indication that such statements aren't objective; good, not good, and ...
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1 vote

Is it practical to derive the prior distribution by dividing the posterior by the likelihood and multiplying by the "evidence"?

Mathematically, starting from given densities $\pi(\theta|x)$ and $f(x|\theta)$, there is no reason for these two functions to be compatible, namely for$$\dfrac{\pi(\theta|x)}{f(x|\theta)}$$to ...
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1 vote
Accepted

What is the "direct likelihood" point of view in statistics?

Hugo, I have seen the term "Direct-Likelihood" used as a method with respect to handling missing data (aka missingness, e.g. clinical trial) via using likelihood-based mixed-effects models, ...
2 votes
Accepted

Is it practical to derive the prior distribution by dividing the posterior by the likelihood and multiplying by the "evidence"?

It is generally regarded as bad practice to decide the prior on the basis of the evidence. It would often be possible to do as you suggest: take a desired posterior distribution, divide it by the ...
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0 votes

Distribution check using R

Much useful information in the comments here, but I must add a point overseen by the commenters: You are trying to compare the fits by looking at their log-likelihood values. In R this is simply ...
1 vote
Accepted

Derivation of Box-Cox and Yeo-Johnson Log-Likelihood Functions

Box-Cox Transformation: Parametric family of transformations $y\mapsto y^{(\lambda) }$ defined by \begin{align}y^{(\lambda)} &:=\begin{cases}\frac{y^\lambda-1}{\lambda}~~&\lambda \ne 0\\ \ln y~...
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1 vote
Accepted

Coding the likelihood function for logistic regression

You need to do probability computations like this in log-space Your computation is using a naïve method that is not how we code likelihood functions (or other probability functions) in practice. When ...
  • 102k
1 vote

Where information comes for Binomial Likelihood?

I don't think your conclusion that the second factor in the likelihood (the binomial distribution) does not contain information on $N$ is true. First, we know for sure that $N\ge \max_r n_r$. Second, ...
2 votes
Accepted

$L(\theta;x)=f(x;\theta)$ vs. $L(\theta;x)\propto f(x|\theta)$

What's the significance of the order of parameters separated by a semicolon, e.g. $(\theta;x)$ vs. $(x;\theta)$? Do $f(x;\theta)$ and $f(x|\theta)$ refer to the same function? The function $f(\theta;...
1 vote

$L(\theta;x)=f(x;\theta)$ vs. $L(\theta;x)\propto f(x|\theta)$

& 2. $;$ means $|$, i.e., conditional dependence: $p(x|\theta) = p(x;\theta)$ and $f(x|\theta) = f(x;\theta)$. Also, because $\theta$ is not a random variable per se, it's the model's $f$ ...
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0 votes

Akaike Information criterion for k-means

It doesn't matter anyway because you typically compare which AIC is better, in which case the constant doesn't matter (if $A > B$, $cA > cB$ for positive $c$).
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0 votes

Nested sampling: What does "uniform sampling over the prior" mean?

Why does sampling from π(x) correspond to uniform sampling in ξ∈[0,1]? When you sample from the prior, and evaluate the likelihood, you are sampling also a distribution of likelihoods. In the ...
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