index.Rmd

---
title: "Biodiversity Modelling Summer School"
author:
- name: Dominique Gravel, Ph.D.
  affiliation: Université de Sherbrooke
- name: Andrew MacDonald, Ph.D.
  affiliation: Université de Sherbrooke
- name: Willian Vieira, M. Sc.
  affiliation: Université de Sherbrooke
date: "2021-08-16"
description: |
  Evaluating ecological models with data
output:
  distill::distill_article:
    toc: true
    toc_float: true
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE)
xaringanExtra::use_panelset()

# Learn more about creating websites with Distill at:
# https://rstudio.github.io/distill/website.html

# Learn more about publishing to GitHub Pages at:
# https://rstudio.github.io/distill/publish_website.html#github-pages
```

## Resources and exercises

**hemlock growth**

<small>
```{r message=FALSE, echo=TRUE}
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))
```
</small>


**Sutton trees** 
```{r message=FALSE, echo=TRUE}
sutton <- readr::read_csv2("https://raw.githubusercontent.com/bios2/biodiversity_modelling_2021/master/data/sutton.csv")

knitr::kable(head(sutton, n = 3))
```


**States**
```{r, message=FALSE, echo=TRUE}
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))

```


* [Gibbs Sampler Example](gibbs_review.html): guided step-by-step approach for programming a gibbs sampler
* [Cumulative exercise](cumulative_exercise.html) in "collecting" a statistical distribution for use in practice.
* [Simulated annealing code](simulated_annealing.html), presented in 2 styles.
* [Metropolis hastings code](metropolis_example.html)
* [Grid search demo](grid_search.html)
* [Excercise problems](exercise_questions.html)

## Slides and lecture materials

::::: {.panelset}

::: {.panel}
[Probabilities and distributions]{.panel-name}

**16 August**  

know your data, define your problem.

```{r share-again, echo=FALSE}
xaringanExtra::use_share_again()
```

```{r slides-intro, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/01_introduction.html", ratio = "16:9")
```


```{r slides-definitions, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/02_definitions.html", ratio = "16:9")
```


```{r slides-rules, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/03_rules.html", ratio = "16:9")
```


```{r slides-problem, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/04_problem.html", ratio = "16:9")
```


```{r slides-solutions, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/05_solutions.html", ratio = "16:9")
```


#### Univariate probability distributions


```{r slides-distributions, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/06_distributions.html", ratio = "16:9")
```


##### Continuous distributions

| 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.                        |

#### Discrete distributions


| 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                       |

:::

:::{.panel}

[Maximum likelihood methods]{.panel-name}

**18 August**  

write down equations for your model.


```{r slides-likelihood, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/07_likelihood.html", ratio = "16:9")
```


```{r slides-likelihood-problem, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/08_likelihood_problem.html", ratio = "16:9")
```


```{r slides-likelihood-solution, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/09_likelihood_solution.html", ratio = "16:9")
```

:::

:::{.panel}

[Optimization]{.panel-name}

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 


```{r slides-optimization, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/10_optimization.html", ratio = "16:9")
```


```{r slides-optimization-problem, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/11_optimization_problem.html", ratio = "16:9")
```


:::


:::{.panel}

[Bayesian statistics]{.panel-name}


```{r slides-bayes, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/12_Bayes.html", ratio = "16:9")
```

```{r slides-generative, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/13_generative.html", ratio = "16:9")
```


```{r slides-tree-problem, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/14_tree_models.html", ratio = "16:9")
```

:::

:::{.panel}

[Sampling algorithms]{.panel-name}

```{r slides-mcmc, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/15_mcmc.html", ratio = "16:9")
```


```{r slides-hmc, echo=FALSE, fig.cap="[Slides](slides/index.html)"}
xaringanExtra::embed_xaringan(url = "slides/16_stan.html", ratio = "16:9")
```


:::

::::