## Bayesian analysis: pros and cons

- Address most data analysis issues (missing data, non-standard data types, non-iid, weird loss functions, adding expert knowledge, …)
- Bayesian analysis: address those in a (semi) automated fashion / principled framework (“reductionist”)
- Reductionism can be bad or good (main con of reductionism is computational)

- Frequentist statistics: every problem is a new problem

- Implementation complexity
- Efficient in analyst’s time (thanks to PPLs)
- Harder to scale computationally
- \(\Longrightarrow\) shines on small data problems (there a much more of those than the “big data” hype would like you to think)

- Statistical properties
- Optimal if the model is
**well-specified**
- Sub-optimal in certain cases when the model is
**mis-specified**
- Thankfully the modelling flexibility makes it easier to build better models
- Important to make model checks

## Week 2 example

*Would you rather get strapped to…*
- “shiny rocket”: 1 success, 0 failures
- “rugged rocket”: 98 successes, 2 failures

## Paradox?

- Maximum likelihood
*point estimates*:
- “shiny rocket”: 100% success rate (1 success, 0 failures)
- “rugged rocket”: 98% success rate (98 successes, 2 failures)

- What is missing?

## Uncertainty estimates

- Take-home message:
- Point estimates are often insufficient, and can be very dangerous
- We want some
**measure of uncertainty**

- Bayesian inference provides one way to build uncertainty measures
- Bayesian measures of uncertainty we will describe:
**credible intervals**

- Alternatives exist:
**Confidence intervals**, from frequentist statistics
- “End product” looks similar, but very different in interpretation and construction

## Uncertainty will not go away

- Just collect more data??
- Just launch more rockets and wait? Collecting more data might be too costly/dangerous/unethical.
- In some cases the data is just “gone”, i.e. we will never be able to collect more after a point (e.g.: phylogenetic tree inference)