Why Likelihood
نویسندگان
چکیده
The Likelihood Principle has been defended on Bayesian grounds, on the grounds that it coincides with and systematizes intuitive judgments about example problems, and by appeal to the fact that it generalizes what is true when hypotheses have deductive consequences about observations. Here we divide the Principle into two parts -one qualitative, the other quantitative -and evaluate each in the light of the Akaike information criterion. Both turn out to be correct in a special case (when the competing hypotheses have the same number of adjustable parameters), but not otherwise.
منابع مشابه
Algorithms in Computational Biology Lecture #10: The Baum-Welch EM Algorithm
Where L(θ : D) is the likelihood of D given θ. Why is this difficult? Why can’t we use standard optimization techniques such as Gradient Ascent? • The likelihood is not necessarily convex, therefore we might converge to a local optimum. • The likelihood is not easy to work with, and it is cumbersome to recalculate during each iteration of Gradient Ascent. In addition, it may not be differentiable.
متن کاملFast and Accurate Inference of Plackett–Luce Models Supplementary Material
1 Stationary Points of the Log-Likelihood In this section, we briefly explain why the log-likelihood in Luce's model has a unique stationary point, that at the ML estimate. Recall that we assume that the comparison graph G D is strongly connected. The log-likelihood is given by
متن کاملLikelihood for random - effect models
For inferences from random-effect models Lee and Nelder (1996) proposed to use hierarchical likelihood (h-likelihood). It allows inference from models that may include both fixed and random parameters. Because of the presence of unobserved random variables h-likelihood is not a likelihood in the Fisherian sense. The Fisher likelihood framework has advantages such as generality of application, s...
متن کاملA Universally Consistent Modification of Maximum Likelihood
In some models, both parametric and not, maximum likelihood estimation fails to be consistent. We investigate why the maximum likelihood method breaks down with some examples and notice the paradox that, in those same models, maximum likelihood estimation would have been consistent if the data had been measured with error. With this motivation we define doubly-smoothed maximum likelihood as a n...
متن کاملOlympic Medals, Economy, Geography and Politics from Sydney to Rio
T he paper uses Heckman model to examine the statistical importance of over 140 independent variables on the Olympic performance of all countries participating in the Summer Olympic Games from Sydney 2000 to Rio 2016. We find that countries which export more products have a higher likelihood of winning an Olympic medal than their counterparts exporting fewer products, and explain why...
متن کاملOn Estimation in Binary Autologistic Spatial Models
There is a large and increasing literature in methods of estimation for spatial data with binary responses. The goal of this article is to describe some of these methods for the autologistic spatial model, and to discuss computational issues associated with them. The main way we do this is via illustration using a spatial epidemiology data set involving liver cancer. We first demonstrate why Ma...
متن کامل