Why log likelihood is negative

The likelihood is the product of the density evaluated at the observations. Usually, the density takes values that are smaller than one, so its logarithm will be negative. However, this is not true for every distribution. This density will concentrate a large area around zero, and therefore will take large values around this point.

Naturally, the logarithm of this value will be positive. In model estimation, the situation is a bit more complex. When you fit a model to a dataset, the log likelihood will be evaluated at every observation. Add a comment. Active Oldest Votes. Improve this answer. Nick Cox I am working on a project and I would like to clearly understand it.

Could you advise me on some peer-review paper or a book about this, please? In principle also saying that the likelihood is zero amounts to saying that some observed data are impossible and that surely means a misspecified model.

Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. In such case,. We can then interpret the output of the softmax as the probabilities that a certain set of features belongs to a certain class.

We then take the softmax and obtain the probabilities as shown:. Figure: Softmax Computation for three classes. The output of the softmax describes the probability or if you may, the confidence of the neural network that a particular sample belongs to a certain class. Thus, for the first example above, the neural network assigns a confidence of 0. The same goes for each of the samples above. The fact is that likelihood can be in range 0 to 1. The Log likelihood values are then in range -Inf to 0.

What happens when the number is positive? Thank you!!! Answers 1. Wayne King on 9 Dec Cancel Copy to Clipboard. I think your problem is that this statement is not true: "The fact is that likelihood can be in range 0 to 1.

There's nothing wrong with a positive log likelihood. The likelihood is the product of the density evaluated at the observed values. Probability densities can take "large" positive values depending on how concentrated they are. Remember, PDFs integrate to 1, they are not bound by values in the interval [0,1].