# Tagged Questions

Given a random variable $X$ which arise from a parameterized distribution $F(X;θ)$, the likelihood is defined as the probability of observed data as a function of $θ: \text{L}(θ)=\text{P}(θ;X=x)$

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### Are we frequentists really just implicit/unwitting Bayesians?

For a given inference problem, we know that a Bayesian approach usually differ in both form and results from a fequentist approach. Frequentists (usually includes me) often point out that their ...
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### Information matrix for a Student's T distribution

I'm reading a paper from Creal, Koopman, Lucas "Univariate Generalized Autoregressive Score Volatility Models" and I'm stuck with this computation. After considering the log likelihood, the score ...
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### Is likelihood ratio test a nonparametric test?

I have a few doubts about the Likelihood ratio test. I understand that we compute a p-value based on the ratio of likelihoods between two models. I am wondering: Is the likelihood ratio test, a ...
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### Likelihood based on sample mean from Gaussian

If we know that mean of sample is 4, and that sample size is 3, and that samples are taken from Gaussian distribution with variance 1, i.e. $N(\mu, 1)$, what can we tell about distribution's mean?
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### Is it safe to assume that $\ln{L} = -\frac{\chi^2}{2}$?

I have written a code that fits a 2D model image to some observed 2D image. One of the optimization libraries I use (MultiNest) in order to do that requires to be ...
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### Which one is more robust ? CI with maximum likelihood method or by bootstrap?

I have a question about confidence interval calculation. I am wondering is calculatin the CI with the function confint is more robust with the likelihood method or the boostrap method ? thanks !
Given a statistical model $$\{p_\theta(y) : \theta \in \Theta \}$$ and same data $y$. The log likelihood function is then $l(\theta)=\log(p_\theta(y))$. For a one parameter hypothesis $\theta_j=\beta$ ...