Questions tagged [likelihood-ratio]
The likelihood ratio is the ratio of the likelihoods of two models (or a null and alternative parameter value within a single model), which may be used to compare or test the models. If either model is not fully specified then its maximum likelihood over all free parameters is used - this is sometimes called a generalized likelihood ratio.
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Monte Carlo method for likelihoods ratio density estimation
I recently started reading Stephen Kay's Fundamentals of Statistical Signal Processing - Detection Theory (Volume II) and there is something I do not fully understand about likelihoods and hypothesis ...
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Comparing Models with Unequal Sample Sizes
I have performed an association analysis where I have associatiated several different perdictor variables to a dependent variable. For each predictor, I run two models and compare them via the ...
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is the likelihood ratio test "best" for finite samples?
Wikipedia says
The Neyman–Pearson lemma states that this likelihood-ratio (lr) test is the most powerful among all level α alpha tests for this case.
Is this only true for infinite sample sizes? Is ...
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Rejection region in LRT test
Let's say I have $X_i \sim Bi(1, \theta$) and want to test $H_0: \theta \geq \theta_0$ vs $H_1: \theta < \theta_0$.
I've found that $\lambda = \frac{\sup_{\theta \in \Theta_0}L(\theta)}{\sup_{\...
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Comparison of two test metrics
I'm trying to compare two test metrics (Metric A and Metric B) to determine which one better predicts a delta value, which represents a Euclidean difference. I am unsure how to determining which ...
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Hypothesis Test Finite Sample Spatial Gaussian Mixture Model
I have $n$ observations of pairs $(x, y)$ and three different models I would like to compare. Model0 is nested within Model1. Model0 is also nested within Model2. I would like to do hypothesis ...
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Likelihood ratios not distributed as a chi2 distribution with the correct dof (Wilks' theorem)
I perform Bayesian inference on a mixture model such that $\mu$ is the mixture weight for a feature in the mixture
$p(x | \mu, \theta) = \mu p_{f}(x|\theta) + (1-\mu)p_{nf}(x|\theta)$
I have prior $p(\...
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Likelihood-ratio and score tests of a (non)linear combination of coefficients
The likelihood-ratio and score test are typically used for simple scalar hypotheses such as $\beta_1 = 0$ or $\beta_1 = \beta_2 = 0$. How can we test a linear combination of coefficients using the ...
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likelihood ratio tests on bounded parameters
I am confused by the likelihood ratio test's boundary condition limitation. A commonly stated is that it causes problem for variance parameter because it is bounded below by 0. Can these models ...
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One sided likelihood ratio test for a logistic regression model?
I need to run a one-sided test on one parameter of a logistic regression model:
$H_0$: $\beta = 0$
$H_1$: $\beta \geq 0$
I want to avoid Wald-equivalent methods as these are known to have problems ...
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Lower threshold for Sequential Probability Ratio Test on Contingency Table testing
For testing whether a die is fair, we have the log likelihood ratio:
$$
\Lambda = \frac{1}{2} \sum_{i} \mathrm{observed}_i \log\left(\frac{\mathrm{observed}_i}{\mathrm{expected}_i}\right).
$$
Suppose ...
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LR statistics add up for nested models. What about the Wald test?
Consider models M0, M1, M2.
Let M0 $\subset$ M1 $\subset$ M2, i.e. let the models nest each other.
I test the following pairs of models using the likelihood-ratio (LR) test: M0 vs. M2, M0 vs. M1, M1 ...
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Am I using the correct test statistic for a binomial glm using the type III Anova function in the package car?
I am trying to look at how the likelihood of event Y is influenced by two factors A (5 levels) and B (2 levels) and my model is as follows:
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Why do I get a negative chi-squared value in my type III ANOVA output for my binomial GLM?
I am trying to look at how the likelihood of event X occurring is affected by three factors A (5 levels), B (2 levels) and C (3 levels). To do this I have run a binomial glm followed by a type 3 ANOVA ...
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equivalence between the likelihood ratio test and t-tests
The linked sites (link1, link2) demonstrate that the likelihood ratio tests and the corresponding one- and two-sample t-tests are equivalent. However, based on my understanding, the null distribution ...
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