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1 vote

How to get most likely value with confidence interval or expected value from a set of observations

A key comment above is @Bernhard's statement that you may need to make additional assumptions for a good answer. One reasonable assumption is that the data are normal. Descriptive statistics (fron R) ...
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Is the profile likelihood (dependent on one parameter) always a concave function?

As a profile likelihood is a very general concept, there can be no reason why this should be true in general. Maybe something can be proved within limited model families? For a non-convex example on ...
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3 votes

Estimating Mixture Models with Maximum Likelihood

While the observed likelihood is a well-defined function $$L(\theta|\mathbf x)=\prod_{i=1}^n \{\pi_1\varphi(x_i;\mu_1,\sigma_1)+ (1-\pi_1)\varphi(x_i;\mu_2,\sigma_2)\}$$ it does not offer enough ...
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Does approximating the likelihood function violate the likelihood principle in Bayesian Inference?

The likelihood principle states that two experiments with the same likelihood functions (up to a multiplicative constant) of the same parameter $\theta$, provide the same evidence on the parameter $\...
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5 votes
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Expected Fisher information isn't positive definite for truncated normal with heteroskedasticity

The expected Fisher information is positive-definite by definition, so there must be some mistake in your code. Here is exactly the same calculation using MATLAB's symbolic math toolbox, which ...
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