Foundations in Statistics for Ecology and Evolution.1 Introduction.pptx

Founda'ons in Sta's'cs Ecology and Evolu'onary Biology

Sara Calhim ([email protected] ) Andrés López-‐Sepulcre ([email protected])

Lecture

Discussion

Course Structure

Prac'cal Homework

Mostly Mondays 10-‐12

Mostly Wednesdays 10-‐12

Hand in by next lecture

Office Hours: (Mostly) Mondays 13-‐16h Sara: C410.2 Andrés: C423.1

1. Sta's'cs and the Scien'fic Process

What is Sta's'cs?

•  Study of uncertainty Lindley 2000 The philosophy of sta's'cs. Sta$s$cian 49: 293-‐337

•  Applied Philosophy of Science Kempthorne 1971 Probability, Sta's'cs, and the Knowledge Business. In Godambe and Spro3, pp 470-‐499

Realism vs. Pragma'sm

Regardless, what ma`ers is PREDICTION

What is Scien'fic Knowledge?

Models

Data

Data

Models

The Scien'fic Process

Charles S. Peirce

Abduc'on Data Model

Predic'ons

Deduc'on Induc'on

Hypothesis genera'on

Theory Inferen'al Sta's'cs

Sta's'cal Inference

Popula'on

Sample

STATISTIC PARAMETER

(Random) Selec'on

We want to know about these We have these to work with

Popula'on mean (μ) Popula'on standard devia'on(σ) Probability of survival Popula'on size

Sample mean (x) Sample standard devia'on (s) Propor'on survived? hmmm…

Es'mate

MODEL y = μ + N(0, σ)

Sta's'cal Models

weight = ! + ! ∙ length+ ! ∙ length! + ! ∙ length! + !(0,!)

weight = !(length!)+ !(0,!) Determinis'c Stochas'c

dependent variable

parameters

independent variable

Spherical cow

Sta's'cal Models weight = !(length!)+ !(0,!) weight = !(length!)+ !(0,!) weight = !(length)+ !(0,!)

Guppy males are lines and females are discs

…maybe except very pregnant females

Sta's'cal Models

•  Determinis'c component – Describes a central tendency or propensity

•  Stochas'c component –  Inherent random process –  Ignorance – Measurement error

Inferring Pa`erns or Processes?

Phenomenological Models

Mechanis'c Models

Phenomenological vs. Mechanis'c

Fryxell et al. 1994

Phenomenological Models ! = ! + !" + !

a = 0.34 b = 0.07

How high How steep

Phenomenological Models ! = ! + !" + !"! + !

How humped

a = 0.16 b = 0.22 c = -‐0.02

Phenomenological Models ! = ! ∙ !"# ! + 1 + !

a = 0.41

How steep and fast it saturates

Phenomenological Models

Mechanis'c Models

Mechanis'c Models ! = !"

1+ !ℎ! + !

a = 0.762 kg/day

h = 1.2 days/kg

Beavers found

and handled them for

PHENOMENOLOGICAL

•  Pa`erns •  No causality •  Parameters describe shape

•  Cannot predict beyond range of data

•  Underlying processes •  Model implies causality •  Parameters describe processes

•  Be`er for predic'on and extrapola'on

MECHANISTIC

Things to do with Sta's'cal Models

Integra'ng Models and Data

1.  Model fihng and parameter es'ma'on: •  Least squares, Maximum Likelihood, Bayesian •  Parameter uncertainty

! = !"1+ !ℎ! + !

a = 0.76 ± 0.29 h = 1.2 ± 0.18


1.  Model fihng and parameter es'ma'on:

2.  Model Selec'on •  Best Fit •  Parsimony •  Predic've power



2.  Model Selec'on

3.  Hypothesis tes'ng •  Sta's'cal significance



2.  Model Selec'on

3.  Hypothesis tes'ng

4.  Predic'on

Sta's'cal Models vs. Techniques

Models •  Linear models, GLMs •  GLMMs, repeated measures •  Logis'c model •  Phylo(gene'c) models •  Popula'on models •  Null hypothesis •  Normal distribu'on et al. •  … your own hypothesis!

Techniques •  Least squares regression •  ANOVA •  Maximum Likelihood •  Hypothesis tes'ng (p-‐value) •  Model selec'on, AIC, etc. •  Monte Carlo •  Bayesian inference •  …

THE BIOLOGY THE SCIENTIFIC METHOD

Course Emphasis

•  Construc'on and biological interpreta'on of models

•  Mechanis'c understanding of sta's'cal techniques (programming)

•  Cri'cal evalua'on of methods and their assump'ons

•  Think ‘out of the canned package’ •  Foster independent learning by teaching the fundamental building blocks

Literature

Review of Sta's'cs 101

Sta's'cal Inference

Popula'on

Sample

STATISTIC PARAMETER

(Random) Selec'on

We want to know about these We have these to work with

Popula'on mean (μ) Popula'on variance (σ2)

Sample mean (x) Sample variance (s2)

Es'mate

How wrong?

BIAS (Accuracy)

ERROR (Precision)

Describing Distribu'ons

Variance

Standard Devia'on

Variances are addi've!!

Standard Error

Popula'on

Sample

STATISTIC PARAMETER

(Random) Selec'on

We want to know about these

We have these to work with

Popula'on mean (μ) Popula'on variance (σ2)

Sample mean (x) Sample variance (s2)

Es'mate

Repeat infinite 'mes

What is the standard devia'on of my infinite es'mates?

e.g. for the mean

COVARIANCE

CORRELATION

Correla'ons only describe linear rela'onships

Correla'on does not imply causa'on (maybe …we’ll see)

Rela'onships among variables

What is a Probability?

•  Physical Probability – Frequen'st: long-‐run outcome – Propensity: property of the system

•  Eviden'al Probability (Bayesian) – Measure of statement (un)certainty

Probability Cheat Sheet

Foundations in Statistics for Ecology and Evolution.1 Introduction.pptx

Education

Transcript of Foundations in Statistics for Ecology and Evolution.1 Introduction.pptx