5. Likelihood¶
In statistical inference, our task is to make statements about the underlying parameter(s) of our proposed model given the observed data. In particular, we typically wish to obtain the best estimate of the unknown parameters. We also wish to know how well we have estimated the unknown parameter(s). The concept of likelihood provides the best single framework for this task. We will see that the likelihood function, often simply called the likelihood, plays a fundamental role in both frequentist and Bayesian inference.
By the end of this session you will be able to:
explain the concepts of likelihood and maximum likelihood estimation
derive a likelihood in a simple situation
explain the connection between maximising the likelihood and maximising the log-likelihood
describe and apply the process of obtaining a maximum likelihood estimator
The next sub-sections introduce the idea of maximum likelihood estimation, define the likelihood and log-likelihood functions and illustrate the process of obtaining the maximum likelihood estimator.