# Tag Info

### Why is everything based on likelihoods even though likelihoods are so small?

The key lies not in the absolute size of the likelihood values but in their relative comparison and the mathematical principles underlying likelihood-based methods. The smallness of the likelihood is ...
• 601

### Why is everything based on likelihoods even though likelihoods are so small?

First, as others have mentioned, we usually work with the logarithm of the likelihood function, for various mathematical and computational reasons. Second, since the likelihood function depends on the ...
• 1,255

### Why is everything based on likelihoods even though likelihoods are so small?

I can think of two things that might help you. First, likelihoods are defined only to a proportionality factor and their utility comes from their use in a ratio and while they are proportional to the ...
• 14.8k
Accepted

### Finding the MLE for a piecewise function

$\require{cancel}$ $$L(\theta) = f(x\mid\theta) = \xcancel{ \prod_{i=1}^n \frac{x_i^\alpha} {\beta^{n\alpha}}I\{0<x<\beta\} \cdot \prod_{i=1}^n 1 I\{x>\beta\}}.$$ First you have the density ...
• 9,400

### Why is everything based on likelihoods even though likelihoods are so small?

If you flip a coin which is known to be weighted $100$ times and it comes up heads $80$ times, then you probably have a guess as to what the weight might be. One way to formalize this intuition is to ...

• 74.9k
1 vote

### SEM: Multivariate normality of the residuals?

Most SEM experts probably agree that violations of multivariate normality are not as problematic nowadays given that appropriate correction methods for the standard errors and test statistics (which ...
• 3,036
1 vote

### How to select the "best" distribution of the errors in linear data?

The first thing to understand about issues like this one is that statistical models live in the land of mathematics rather than in real life, and in real life no statistical model is ever fulfilled (...
• 22.7k
1 vote

### How to select the "best" distribution of the errors in linear data?

You can always try different distributions and compare (penalized) likelihoods to get a measure of what fits best. This provides a solution, but can be criticized for being purely data-based as ...
• 5,706
1 vote

### Bayesian estimates for Deming regression coinciding with least-squares estimates

I have a running version of Bayesian Deming regression. I used a fixed variance ratio approach starting from Linnet's work on Weighted Deming, 1988. Thus, sampling a single error term. I also added a ...
• 11
1 vote

### MLE for triangle distribution?

MLE's for triangle distributions are now implemented in R's triangle package. There is also a short discussion of the methodology here in the vignette. The ...
• 5,093

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