Evaluating ecological models with data

**hemlock growth**

```
hemlock <- readr::read_delim(
"https://raw.githubusercontent.com/bios2/biodiversity_modelling_2021/master/data/hemlock.txt",
delim = " ",
col_names = c("x","light", "growth"), skip = 1)
knitr::kable(head(hemlock, n = 3))
```

x | light | growth |
---|---|---|

1 | 32.34929 | 118.2052 |

2 | 58.84066 | 138.0278 |

3 | 75.05452 | 185.7844 |

```
sutton <- readr::read_csv2("https://raw.githubusercontent.com/bios2/biodiversity_modelling_2021/master/data/sutton.csv")
knitr::kable(head(sutton, n = 3))
```

x | y | abba | acpe | acsa | beal | bepa | fagr | piru |
---|---|---|---|---|---|---|---|---|

0 | 0 | 1 | 55 | 11 | 7 | 0 | 92 | 0 |

0 | 100 | 0 | 5 | 4 | 3 | 0 | 6 | 0 |

0 | 120 | 2 | 7 | 12 | 4 | 1 | 7 | 0 |

```
states <- readr::read_delim("https://raw.githubusercontent.com/bios2/biodiversity_modelling_2021/master/data/transitions.txt",
delim = " ",
col_names = c("x","ID", "temp", "state1",
"state2", "interval"),
skip = 1)
knitr::kable(head(states, n = 2))
```

x | ID | temp | state1 | state2 | interval |
---|---|---|---|---|---|

1 | 685303 | 3.609000 | B | B | 9 |

2 | 685016 | 4.701333 | M | M | 7 |

- Gibbs Sampler Example: guided step-by-step approach for programming a gibbs sampler
- Cumulative exercise in “collecting” a statistical distribution for use in practice.
- Simulated annealing code, presented in 2 styles.
- Metropolis hastings code
- Grid search demo
- Excercise problems

Probabilities and distributions

**16 August**

know your data, define your problem.

distribution | positive or negative? | Quick description |
---|---|---|

Normal | positive or negative values | Can result from many small effects added together |

Lornormal | positive values only | results from many things multiplied together |

Gamma | positive values only | can be the time to wait for a given number of things to happen |

Exponential | Positive only | Lengths of time between random events |

Beta | Positive only | Between 0 and 1. Can be any proportion. |

distribution | positive or negative? | Quick description |
---|---|---|

Poisson | Positive | Counting things that occur randomly over time |

Negative Binomial | Positive | Counts of things as in the Poisson, but more variable. Also: the number of trials till a certain number of successes. |

Binomial | Positive | Number of “successes” out of a number of trials, when probability of success is always the same |

Maximum likelihood methods

**18 August**

write down equations for your model.

Optimization

Once we know how to calculate likelihood, we can apply this to a very general statistical practice: how do we find parameters that maximize the likelihood of the data? this is an optimization problem

Bayesian statistics

Sampling algorithms