reminders
LM
GLM
Some satistical notions needed for biological studies Vivien Rossi
CIRAD - UMR Ecologie des forêts de Guyane
[email protected]
Master 2 - Ecologie des Forêts Tropicale AgroParisTech - Université Antilles-Guyane Kourou, novembre 2010
Vivien Rossi
Stat for Biology
estimation
reminders
LM
GLM
estimation
objectives of the course
Give your own overview of statistical tools though Generalized Linear Model framework 1
reminders about some useful stuffs (usual probability distribution, data transformation . . . )
2
reminders about Linear Model
3
insights of the GLM formalism
4
Parameter estimation
Vivien Rossi
Stat for Biology
reminders
LM
GLM
outlines
1
some reminders
2
Linear Model
3
Generalized Linear Model
4
Parameter estimation
Vivien Rossi
Stat for Biology
estimation
reminders
LM
GLM
1
some reminders
2
Linear Model
3
Generalized Linear Model
4
Parameter estimation
Vivien Rossi
Stat for Biology
estimation
reminders
LM
GLM
the normal distribution names: normal, gaussian, Laplace-Gauss
Vivien Rossi
Stat for Biology
estimation
reminders
LM
GLM
the normal distribution names: normal, gaussian, Laplace-Gauss continuous probability distribution, with density 1 (x − µ)2 f (x) = √ exp − 2σ 2 2πσ 2 the corner stone of the statistic:
Vivien Rossi
Stat for Biology
estimation
reminders
LM
GLM
the normal distribution names: normal, gaussian, Laplace-Gauss continuous probability distribution, with density 1 (x − µ)2 f (x) = √ exp − 2σ 2 2πσ 2 the corner stone of the statistic: CLT Let (x1 , . . . , xn ) iid random variables, having mean µ and variance σ 2 then n √ 1X d n xi − µ − → N (0, σ 2 ) n i=1
Vivien Rossi
Stat for Biology
estimation
reminders
LM
GLM
the normal distribution
link with other distributions The binomial distribution B(n, p) ≈ N (np, np(1 − p)) for large n and for p not too close to zero or one. The Poisson distribution P(λ) ≈ N (λ, λ) for large values of λ. The chi-squared distribution χ2 (k ) ≈ N (k , 2k ) for large ks. The Student distribution T (ν) ≈ N (0, 1) when ν is large.
Vivien Rossi
Stat for Biology
estimation
reminders
LM
GLM
estimation
data transformation logarithm IR+ x
→ IR 7→ log x
sd proportional to the mean or the effects are multiplicatives usual for growth or multiplicative processes if some data are small (
