5. Maximum Likelihood Estimation (cont.)  Summary and Q&A
TL;DR
Maximum Likelihood Estimation is a statistical method that involves maximizing the likelihood function, often represented by the loglikelihood, to estimate the parameters of a statistical model.
Key Insights
 🧑💻 Maximizing the likelihood function is equivalent to minimizing the negative loglikelihood function.
 🧑💻 The loglikelihood function is often used instead of the likelihood function because it simplifies the optimization process.
Transcript
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Questions & Answers
Q: What is the likelihood function?
The likelihood function is a function that measures how likely a set of observed data is given certain model parameters.
Q: Why is the loglikelihood often used instead of the likelihood?
The loglikelihood function is often used because it simplifies the optimization process and has the same maximum as the likelihood function.
Q: What is the Fisher information?
The Fisher information is a measure of the curvature of the likelihood function and can be used to quantify the amount of information that the data contains about the model parameters.
Summary & Key Takeaways

Maximum Likelihood Estimation (MLE) involves maximizing the likelihood function, which is a function of the observed data and the model parameters.

MLE can be used to estimate parameters for various statistical models, such as Bernoulli trials, Poisson distribution, and Gaussian distribution.

The loglikelihood function is often used instead of the likelihood function because it simplifies the optimization process.