### Workshop Topics

This workshop begins with the fundamental question "why use statistics?" and, in a step by step fashion, it 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.
- 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.
- Minimal sufficiency, asymptotic properties of the MLE, efficiency, the Cramer-Rao Lower Bound (CRLB), normality.
- Robustness of the MLE, the Kullback-Liebler distance. The robust or sandwich variance estimator.