Professional Certificate in Parameter Estimation with Likelihood

This course is designed for professionals in statistics, data science, and related fields who need to estimate parameters from data using likelihood methods. Participants will gain proficiency in applying likelihood techniques to model fitting, hypothesis testing, and prediction. The course covers essential concepts and practical skills in likelihood-based inference, including maximum likelihood estimation, likelihood ratio tests, and confidence intervals.

Upon completion, learners will be able to select appropriate likelihood methods for their datasets, implement these methods using statistical software, and interpret the results effectively in their professional practice.

1. 1. Introduction to Parameter Estimation: Learners will understand the basic concepts of statistical estimation and explore the principles of parameter estimation, including point estimation and interval estimation. They will gain foundational skills in assessing the accuracy and precision of estimated parameters.
2. 2. Likelihood Fundamentals: This module introduces the concept of likelihood and its role in parameter estimation. Learners will study the likelihood function and how it relates to the probability density or mass function of the observed data given the parameters.
3. 3. Maximum Likelihood Estimation (MLE): Learners will delve into the method of maximum likelihood estimation, learning how to find the parameter values that maximize the likelihood function. Practical skills include implementing MLE in real-world scenarios and interpreting the results.
4. 4. Properties of Estimators: This module covers the properties of estimators, such as bias, consistency, and efficiency. Learners will explore how these properties affect the reliability of parameter estimates and learn how to assess them.
5. 5. Bayesian Parameter Estimation: Learners will be introduced to Bayesian methods for parameter estimation, including prior and posterior distributions. They will learn how to use Bayes' theorem to update parameter estimates based on new data.
6. 6. Likelihood Ratio Tests: This module focuses on likelihood ratio tests, a method for comparing the goodness of fit of two statistical models. Learners will understand how to construct and interpret likelihood ratio tests and apply them in hypothesis testing.
7. 7. Advanced Topics in Likelihood: Learners will explore advanced topics such as profile likelihoods, likelihood-based confidence intervals, and the use of likelihood in complex models. Practical skills include applying these techniques to solve real-world problems.
8. 8. Computational Methods in Likelihood: This module covers computational techniques for likelihood-based inference, including numerical optimization and simulation methods. Learners will gain hands-on experience using software tools for likelihood-based analyses.
9. 9. Model Selection and Validation: Learners will learn how to select among competing models using criteria such as AIC and BIC. They will also study methods for validating model assumptions and assessing model fit.
10. 10. Case Studies in Parameter Estimation: In this final module, learners will apply the knowledge and skills gained throughout the programme to real-world case studies. They will work on projects that involve data analysis, model fitting, and interpretation of results in various fields such as biology, economics, and engineering.