| 1 | Role of probability theory in science | 1 |
| 2 | Probability theory as extended logic | 21 |
| 3 | The how-to of Bayesian inference | 41 |
| 4 | Assigning probabilities | 72 |
| 5 | Frequentist statistical inference | 96 |
| 6 | What is a statistic? | 139 |
| 7 | Frequentist hypothesis testing | 162 |
| 8 | Maximum entropy probabilities | 184 |
| 9 | Bayesian inference with Gaussian errors | 212 |
| 10 | Linear model fitting (Gaussian errors) | 243 |
| 11 | Nonlinear model fitting | 287 |
| 12 | Markov chain Monte Carlo | 312 |
| 13 | Bayesian revolution in spectral analysis | 352 |
| 14 | Bayesian inference with Poisson sampling | 376 |
| App. A | Singular value decomposition | 389 |
| App. B | Discrete Fourier transforms | 392 |
| App. C | Difference in two samples | 434 |
| App. D | Poisson ON/OFF details | 445 |
| App. E | Multivariate Gaussian from maximum entropy | 450 |