Question

All the above calculations have simple analytic solutions. For most real life problems reuqireing more complex statistical models, we will need to search for solutions using more advanced numerical methods and simulations. However, the types of problems that we will be addressing are largely similar to those asked of the toy coin toss problem. These include

• point estimation (e.g. summary statistics)
• interval estimation (e.g. confidence intervals or Bayesian credible intervals)
• function estimation (e.g. density estimation, posteriro distributions)

and most will require some knowledge of numerical methods for

• optimization (e.g. least squares minimizaiton, maximum likelihood)
• Monte Carlo simulations (e.g. Monte Carlo integration, MCMC, bootstrap, permutation-resampling)

The next section of the course will focus on the ideas behiind these numerical methods.