All Questions
Tagged with logarithm likelihood
16
questions
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Deriving log-likelihood contribution involving fixed effects (panel model)
I would appreciate some help with the following problem:
We have the following panel model: $y_{it} = h(x_{it}\beta + c_i) + \epsilon_{it}, \quad t=1,\ldots,T, \quad i=1,\ldots,N $ where
\begin{align*}...
9
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4
answers
915
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An interesting observation regarding the log transformation of data
I stumbled upon something interesting while attempting to do a log transformation for some data (with zeros) today. It seems that there must be a good reason for this that I'm just not seeing. I'm ...
- 8,392
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1
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218
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Numerically stable transformation of log-likelihoods to probability [closed]
I have the following problem: I have log-likelihoods that need to be transformed to probabilities. One thing I have attempted is the following. Define $\kappa_{s} := \log \int p (\theta | X_s) \text{d}...
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26
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nakagami distribution
How can i do the parameter's estimation with nakagami distribution with fisher scoring ? i've problem with derive the log likelihood for the variabel of m.(i attach the picture with screenshot file)
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59
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How do I find log likelihood function based on observations
Assuming the regression model Yi = BiXi + E is appropriate.
And I have observations : X1...X10, Y1...Y10
How do i find the log likelihood function based on the observed values?
Any help is much ...
2
votes
1
answer
532
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Is negative log likelihood calculated in log space or exponential space?
I have a question about calculating negative log likelihood in a machine learning model over a dataset which seems simple but I cannot find a solid answer/explanation online.
Is the NLL calculated as ...
- 942
3
votes
3
answers
1k
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Prove that the likelihood function L(θ|x) is equivalent to maximizing log L(θ|x) where log is the natural logarithm
In other words, why
$\text{argmax} \text{ } L(\theta) = \text{argmax} \text{ } \text{log} \text{ } L(\theta)$
?
- 31
5
votes
2
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591
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Why is the expected gradient of a density not parallel to the expected gradient of the log density?
I'm confused by a seemingly counter-intuitive property of the interaction between distributions, log transforms, expectations and gradients.
Suppose I have some distribution over random variable $x$ ...
- 1,047
1
vote
1
answer
860
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Behaviour of likelihood ratio test as sample size increases
I know that the log likelihood statistic, i.e. $X^2=-2(LL_1 - LL_2)$ where $LL_1$ and $LL_2$ are the maximum log likelihoods of two models, one nested in the other, is asymptotically distributed as a ...
- 131
15
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1
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What is the log of the PDF for a Normal Distribution?
I am learning Maximum Likelihood Estimation.
Per this post, the log of the PDF for a normal distribution looks like this:
$$
\log{\left(f\left(x_i;\,\mu,\sigma^2\right)\right)}
=
- \frac{n}{2} \log{\...
- 1,995
2
votes
1
answer
6k
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Computing the Hessian of maximum log likelihood function
I am trying to find the Hessian matrix for the maximum log likelihood function given training data ${(xi, yi)}$ for $i=1:N$ with $yi ∈ \left\{+1, −1\right\}$ for each $i = 1,\dots, N$ for the function:...
- 23
3
votes
1
answer
48
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Is it ever convenient to maximize different functions of the likelihood than the logarithm?
We all know that it's often much more convenient to maximize the log-likelihood rather than the likelihood to get a parameter estimate, since it amounts to the same thing by the fact that the ...
- 375
1
vote
1
answer
8k
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How to normalize log-likelihoods? [closed]
I have referred to this post here. In my case, I am trying to normalize the log-likelihoods I obtained from the same data set. However, the approach in the top answer did not work out for me. Below ...
- 2,909
2
votes
1
answer
529
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logarithm in loglikelihood
I think I understand likelihood, and also log-likelihood as well. After reading about log-likelihood in various sources, I thought that the purpose of taking the logarithm of likelihood was all about ...
- 163
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1
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4k
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Why don't log-likelihoods lead to log(0)?
How do log likelihoods function in practice? I seem to oscillate between understanding this and not understanding this (which most likely means I've never understood it).
When you take log( P( X | Y )...
- 215