# Questions tagged [likelihood-principle]

According to the likelihood principle, all the evidence that a sample provides about parameters of a given statistical model is contained in the likelihood function.

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### Likelihood principle and inference

I've been reading Casella and Berger's Statistical Inference. In section 6.3 the author stated the likelihood principle: if the likelihood functions from two samples are proportional, then the ...
467 views

### Why is the weak likelihood principle not a theorem?

The weak likelihood principle (WLP) has been summarized as: If a sufficient statistic computed on two different samples has the same value on each sample, then the two samples contain the same ...
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### Does approximating the likelihood function violate the likelihood principle in Bayesian Inference?

Suppose we have a prior $p(\theta)$ and a likelihood function $L(\theta|x)$, and that the likelihood $L(\theta|x)$ is intractable somehow (difficult or impossible to compute) and we instead replace it ...
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### Does Bayesian statistics bypass the need for the sampling distribution?

Let's take the classic case where the population follows a normal distribution, observations are iid, and we want to estimate the mean of the population. In Frequentist stats, we calculate the ...
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### Does Approximate Bayesian Computation (ABC) follow the Likelihood Principle?

I know that ABC is commonly used when the likelihood is intractable, so likelihood principle is not an interest in that case. But, I am curious whether the ABC satisfies the likelihood principle when ...
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### Did Deborah Mayo refute Birnbaum's proof of the likelihood principle?

This is somewhat related to my previous question here: An example where the likelihood principle *really* matters? Apparently, Deborah Mayo published a paper in Statistical Science refuting Birnbaum'...
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### An example where the likelihood principle *really* matters?

Is there an example where two different defensible tests with proportional likelihoods would lead one to markedly different (and equally defensible) inferences, for instance, where the p-values are ...
657 views

### Can the maximum-likelihood method be derived from something else?

I am an author of a paper, in which we show that the maximum-likelihood (ML) method can be derived a limiting case of an iterated weighted least-squares fit. https://arxiv.org/abs/1807.07911 We, the ...
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### P-values and likelihood principle

This question came up in class: If we use p-values to evaluate hypotheses on an experiment, which part of the Likelihood Principle are we not obeying: Sufficiency or Conditionality? My intuition ...
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1k views

### Do you have to adhere to the likelihood principle to be a Bayesian?

This question is spurred from the question: When (if ever) is a frequentist approach substantively better than a Bayesian? As I posted in my solution to that question, in my opinion, if you are a ...
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### Why is a Bayesian not allowed to look at the residuals?

In the article "Discussion: Should Ecologists Become Bayesians?" Brian Dennis gives a surprisingly balanced and positive view of Bayesian statistics when his aim seems to be to warn people about it. ...
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### Likelihood principle: difference between weak and strong version

Does anyone understand the difference between weak likelihood principle and strong likelihood principle?
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I currently try to understand Likelihood Principle and I frankly don't get it at all. So, I will write all my question as a list, even if those might be pretty basic questions. What exactly does "all ...
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