MAS-II study plan

Map the full MAS-II syllabus into a one-page topic inventory and rate your current confidence on each item from 1 to 5

Derive the likelihood, score, and observed/expected Fisher information for exponential-family models from first principles, working three examples by hand

Set up a spaced-repetition deck covering core distributions (Poisson, binomial, gamma, normal, inverse Gaussian) with mean, variance, and canonical link noted

Build a formula sheet template in a spreadsheet with columns for model, assumption, estimator, and asymptotic variance

Derive maximum likelihood estimators for frequency and severity models and verify each with a simulated dataset in R or Python

Distinguish maximum likelihood, method of moments, and Bayesian estimation and state when each fails or is preferred

Compute standard errors from the Hessian and from the inverse Fisher information, then compare the two numerically on one simulated sample

Write out the Cramer-Rao lower bound argument and identify where regularity conditions matter

State the asymptotic normality result for MLEs and apply the delta method to transform a parameter estimate and its variance

Derive confidence intervals and Wald, score, and likelihood-ratio test statistics for a single parameter and a vector of parameters

Run a likelihood-ratio test on nested models and interpret the chi-square reference distribution

Tabulate the three test statistics side by side with their formulas and small-sample caveats

Derive the profile likelihood and construct a profile-likelihood confidence interval for one parameter of interest

Explain the construction of bootstrap confidence intervals (percentile and basic) and implement one by resampling

Compare profile-likelihood and bootstrap intervals on the same dataset and explain any disagreement

Review weeks 1-3 notes and rewrite every derivation from memory

Specify a generalized linear model with a non-canonical link and derive the score and information equations

Fit a log-link Poisson frequency model and a log-link gamma severity model, then interpret every coefficient on the response scale

Diagnose overdispersion and zero-inflation and state the corrective modeling options

Derive the deviance and compare it with the Pearson chi-square statistic

Derive the credibility premium under the Bühlmann and Bühlmann-Straub frameworks and connect it to the linear mixed model formulation

Compute the credibility factor and structural parameters from a small multi-group dataset by hand

Explain how Bayesian conjugate updating yields the same credibility formula and identify the prior-to-structural-parameter correspondence

Set up the hierarchical likelihood for a random-effects model and state what the random effect represents

Derive the empirical Bayes estimator and distinguish it from the fully Bayesian and pure random-effects estimators

Explain shrinkage, and plot how the credibility weight changes as between-group variance and within-group variance vary

Fit a random-effects frequency model and extract the predicted group effects

Identify the assumptions that break the credibility framework and describe a diagnostic for each

Assemble a single condensed review sheet covering every derivation from weeks 1-7

Timed practice: complete a set of mixed estimation and inference problems under exam time pressure and score yourself

Re-derive from memory the three items you scored lowest on and log the corrections

Write a final self-assessment listing weak topics with a specific remediation action for each