Fitting a zeta distribution | Using the fitted distribution to estimate P terms | Fitting a zero-inflated zeta distribution | Confidence intervals for the parameter estimates | Profile-likelihood and bootstrap confidence regions for the zero-inflated zeta | Comparing two surveys | References

Two kinds of uncertainty | Four approaches available in fitPS | Fit the ZIZ model | Confidence and credible regions for the parameters | Comparing parameter uncertainty across the four methods | From parameter uncertainty to probability uncertainty | Comparing the probability estimates | What does the inflation parameter mean? | Which method should I use? | References

When to add a new model | What a model must provide | Why MCMC needs unconstrained parameters | [\log p(z\mid x) | P and S surveys shift the probability sequence | Example 1: an external Poisson model | Construct the model | Supply the observation mapping | Supply probabilities | Supply the log likelihood | Add the Bayesian mathematics | Register the external S3 methods | Fit and use the model | Example 2: a Poisson-normal model with mu and sigma | [P(Y = y \mid \mu, \sigma) | [g(k; \mu, \sigma) | [\ell(\mu,\sigma) | Construct the two-parameter descriptor | Map the data and choose starting values | [\operatorname{Var}(Y) | Evaluate the marginal probability by numerical integration | Add Bayesian methods for the Poisson-normal model | Register the Poisson-normal methods | Fit the two-parameter model | Bayesian fitting of the external two-parameter model | Serialization and retained model objects | What an extension package should contain | Practical lessons from the two examples

Why compare models? | Maximum-likelihood comparison | Bayesian fits and DIC | Look at the fitted probabilities | Parameter uncertainty and predictive probabilities | What should be concluded? | References

Introduction | Simulation | More advanced options