New answers tagged maximum-likelihood
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Likelihood of Bayes' theorem
Your question makes me believe that you are starting to learn statistics:
Welcome aboard, good luck and bon courage! It's a tricky field but there many interesting problems in there.
A key ...
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Question about likelhood function of discriminative models
Three points:
Your $p(x, y)$ and $p(y \mid x)$ each depend on $\theta$, and you are looking for the value of $\theta$ which maximises the products, so it might be worth including $\theta$ somewhere ...
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Maximum Likelihood Estimation for Poisson Mean with Given Observations
Defining $n_3=n - n_1 - n_2$, the log-likelihood function can be written as
$$ \ell(\lambda) = -(n_2+n_3)\lambda + n_2 \log \lambda + n_1 \log\left(1 - e^{-\lambda} - \lambda e^{-\lambda}\right). $$
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Accepted
Maximum Likelihood Estimation for Poisson Mean with Given Observations
The critical point $\hat \lambda$ satisfies
$$n - n_1 = \frac{n_2}{\lambda} + \frac{n_1 \lambda}{e^\lambda - (1 + \lambda)}$$
or equivalently,
$$e^\lambda = \frac{n_2 - (n - n_1 - n_2)\lambda - n \...
- 141k
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Maximum Likelihood Estimation for Poisson Mean with Given Observations
You have a univariate function which is bounded in its valid range.
For $\lambda \to 0$ it goes to infinity.
For $\lambda \to \infty$ the function goes to $-n + {n}_{1}$ which is negative.
Show it ...
- 8,984
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Accepted
Rejection region in hypothesis test using LRT
The rejection region should be $\{U > c\}$ where $c$ is the $1-\alpha$ quantile of the chi-squared distribution. The intuition is that larger $U$ values correspond to larger values of $\sup_{\theta ...
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