Classical inference treats parameters as fixed unknowns. A desk updating a default probability or a mean-return view often starts with a prior and wants a posterior; a risk system needs simulated scenarios and intervals for statistics with no closed-form sampling law; and every empirical claim about markets must confront how returns actually look — skewed, heavy-tailed, and volatility-clustered. This topic supplies those three tools after Statistical inference, without modelling GARCH or teaching a parallel econometrics programme.
By the end of this note you should be able to:
- update a conjugate prior through a likelihood to a posterior for a default probability or a mean return;
- simulate from a distribution, quantify Monte Carlo error via the CLT, and build a bootstrap confidence interval;
- distinguish simple and log returns, diagnose non-normality, name volatility clustering as a fact, and state what the CLT does and does not license for daily returns.
In this lesson
- Contents
- The big picture
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