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01_introduction.html
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<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title>Introduction</title>
<meta charset="utf-8" />
<meta name="author" content="Dominique Gravel" />
<script src="assets/header-attrs-2.8/header-attrs.js"></script>
<link href="assets/remark-css-0.0.1/default.css" rel="stylesheet" />
<link href="assets/remark-css-0.0.1/hygge.css" rel="stylesheet" />
<link rel="stylesheet" href="assets/ecl707.css" type="text/css" />
</head>
<body>
<textarea id="source">
class: title-slide, middle
<style type="text/css">
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# Model evaluation with ecological data
<hr width="65%" align="left" size="0.3" color="orange"></hr>
## Introduction
<hr width="65%" align="left" size="0.3" color="orange" style="margin-bottom:40px;" alt="@Martin Sanchez"></hr>
.instructors[
**ECL707/807** - Dominique Gravel
]
<img src="assets/img/logo.png" width="25%" style="margin-top:20px;"></img>
---
# Let's start with a simple problem
<div style='text-align:center;'>
<img src="assets/img/coates.png" width="300px"></img>
</div>
Coates and Burton (1999) studied the effect of light availability on the annual height increment as a function of an index of light availability, 5 years after they were planted.
---
# Let's start with a simple problem
<div style='text-align:center;'>
<img src="assets/img/coates.png" width="300px"></img>
</div>
What could you tell from the data ?
---
# Let's start with a simple problem
<div style='text-align:center;'>
<img src="assets/img/coates.png" width="300px"></img>
</div>
How would you fit a curve into this ?
---
# Let's start with a simple problem
<div style='text-align:center;'>
<img src="assets/img/coates.png" width="300px"></img>
</div>
What equation to pick ?
---
class: inverse, middle, center
# Now try it !
<hr width="65%" size="0.3" color="orange" style="margin-top:-20px;"></hr>
---
# Let's start with a simple problem
<div style='text-align:center;'>
<img src="assets/img/coates.png" width="300px"></img>
</div>
What are the uncertainties in your model ?
---
# Let's start with a simple problem
<div style='text-align:center;'>
<img src="assets/img/coates.png" width="300px"></img>
</div>
What will happen if we sample more ?
---
# Let's start with a simple problem
<div style='text-align:center;'>
<img src="assets/img/coates.png" width="300px"></img>
</div>
Can we reduce this uncertainty ?
---
class: inverse, middle, center
# Why to develop modelling skills ?
<hr width="65%" size="0.3" color="orange" style="margin-top:-20px;"></hr>
---
# Develop innovative methods
Objective : detect events of suppression and release of understory saplings using time series
<div style='text-align:center;'>
<img src="assets/img/canham.png" width="600px"></img>
</div>
*Gravel et al. 2010. Large-scale synchrony of gap dynamics and the distribution of understory tree species in maple-beech forests. Oecologia 162 : 153-161.*
---
# Complex probabilistic problems
Objective : evaluate a logistic model with presence only-data
<div style='text-align:center;'>
<img src="assets/img/bartomeus.png" width="850px"></img>
</div>
*Bartomeus et al. 2016. A common framework for identifying linkage rules across different types of interactions. Functional Ecology 30: 1894-1903*
---
# Complex probabilistic problems
Objective : evaluate non-stationary auto-regressive multivariate models
<div style='text-align:center;'>
<img src="assets/img/autoregression.png" width="800px"></img>
</div>
*Gravel et al. Evidence of critical slowing down of interaction networks before physiological meltdown. In prep.*
---
# Transfer of information across scales
Objective : make sure that a species distribution model evaluated at continental scale is coherent with experiments done at the micro scale
<div style='text-align:center;'>
<img src="assets/img/talluto.png" width="800px"></img>
</div>
*Talluto et al. 2016. Cross-scale integration of knowledge for predicting species ranges : a metamodelling framework. Global Ecology and Biogeography 25 : 238-249.*
---
# Use all information available
Objective : how to evaluate mortality rate of rare tropical trees with very few observations ?
<div style='text-align:center;'>
<img src="assets/img/soberania.jpg" width="250px"></img>
</div>
*Condit et al. 2006. The importance of dempraphic niches to tree diversity. Science 313: 98-101.*
---
# Other motivations
- Philosophical motivation
- Representation of uncertainty
- Adaptive modelling
- Better understand statistics
---
class: inverse, middle, center
# What about you ?
<hr width="65%" size="0.3" color="orange" style="margin-top:-20px;"></hr>
---
# Logistics
- On site and remote teaching
- Lectures are recorded
- Priority to exercises and problems
- Minimal interactive lectures
- Participation
Any other suggestion ?
---
# Content
1. Probabilities
2. Maximum likelihood estimation
3. Algorithms for optimization
4. Bayesian models
5. Algorithms for posterior distributions
---
# Expectations
- Write down an equation for likelihood and code it in R
- Develop an algorithm to find the maximum likelihood estimates
- Have some notions of the philosophies of satistical inferrence
- Develop the full equation for the posterior distribution
- Estimate posterior distribution by MCMC for a simple regression problem
---
# Evaluation
- Pass or fail based on participation and progress
- Auto-evaluation form at the end of the course
- Possibility of doing a supervised project as a side
</textarea>
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