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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 ...
INvisibLE's user avatar
2 votes
2 answers

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 ...
virtuolie's user avatar
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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 ...
user356974's user avatar
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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 ...
confused's user avatar
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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 ...
Minsuk Shin's user avatar
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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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6 answers

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 ...
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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. We, the ...
olq_plo's user avatar
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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 ...
rrrrr's user avatar
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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 ...
RustyStatistician's user avatar
53 votes
2 answers

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. ...
Mankka's user avatar
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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?
user114618's user avatar
17 votes
1 answer

Questions about Likelihood Principle

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 ...
Karel Bílek's user avatar
22 votes
2 answers

If the likelihood principle clashes with frequentist probability then do we discard one of them?

In a comment recently posted here one commenter pointed to a blog by Larry Wasserman who points out (without any sources) that frequentist inference clashes with the likelihood principle. The ...
Michael Lew's user avatar
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Difference between likelihood principle and repeated sampling principle

In statistical inference, there are many fundamental statistical principles, such as likelihood principle and repeated sampling principle. I am wondering whether there are any other principles? And ...
Honglang Wang's user avatar