# Questions tagged [log-likelihood]

For questions that use the natural logarithm of a likelihood function.

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### Multinomial Logistic Regression likelihood

Suppose we have the following parametric model for logistic regression: $$\phi_{i} = \frac{\exp{(a^{T}x_{[i]}})}{\sum_{k = 1} ^{M} \exp{(a^{T}x_{[k]})}}$$for $i = 1, \dots, M$ and that the parameter ...
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### Likelihood-function : How to simplify it?

The fracture strength of hard bricks satisfies an Erlang distribution of order $2$. There are $n \in \mathbb{N}$ fracture strength tests that are carried out. We consider the statistical product model ...
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### Differentiating log likelihood with respect to data

I'm working with the probabilistic model derived from the KL NMF, in which we sample each entry of a data matrix X from the distribution \$\forall_{i,j},X_{ij}\sim\text{Poisson}\left(\left[WH\right]_{...
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