### Workshop Topics

This workshop begins with the fundamental question "why use statistics?" and step by step introduces the ideas and statistical concepts that underpin pharmacometric modelling and simulation today. The following list gives an idea of the breadth of the workshop;

- Probability and statistical inference.
- Laws of probability and Bayes theorem.
- Univariate probability distributions – Expected value and variance.
- Multivariate probability distributions – joint, marginal and conditional distributions. The covariance matrix. Independence and conditional independence.
- Modelling, estimation, estimators, sampling distributions, bias, efficiency, standard error and mean squared error.
- Point and interval estimators. Confidence intervals.
- Hypothesis testing, null and alternative hypotheses. P-value, Type I and type II errors and power.
- Likelihood inference, maximum likelihood estimator (MLE), likelihood ratio. BQL and censored data.
- Minimal sufficiency and invariance of the likelihood ratio and the MLE.
- The score function, hessian, Fisher information, quadratic approximation and standard error.
- Wald confidence intervals and hypothesis tests.
- Likelihood ratio tests.
- Profile likelihood, nested models.
- Model selection, Akaike and Bayesian Information Criteria (AIC & BIC).
- Maximising the likelihood, Newton’s method.
- Mixed effects models, the hierarchical and marginal likelihoods.
- Estimation of the fixed effects, conditional independence, prior and posterior distributions.
- Approximating the integrals, First order (FO & FOCE) and Laplace approximations, numerical quadrature.
- The Expectation Maximisation (EM) algorithm.
- MU-modelling,Iterative Two Stage (ITS).
- Monte Carlo EM (MCEM), Importance sampling, Direct sampling, SAEM, Markov Chain Monte Carlo
- Estimating the random effects, empirical bayes estimates (EBE) and shrinkage.
- Asymptotic properties of the MLE, efficiency, the Cramer-Rao Lower Bound (CRLB), normality.
- Robustness of the MLE, the Kullback-Liebler distance. Quasi likelihood and the robust or sandwich variance estimator.