PHILOSOPHICAL FOUNDATIONS 1. The Nature Scientific Inference 2. Statistical Models -The mathematical beauty of nature -The messy part: what is a Probability? 3. Integrating Models and Data SAMPLING 1. The Nature of Induction 2. Statistical Inference - Describing the Data - Estimating the Truth 3. Error and Bias

1. FOUNDATIONS of STATISTICS
for ecology and evolution

2. what is
STATISTICS ?Statistics is the science of learning from data, and of
measuring, controlling, and communicating uncertainty
” {Marie Davidian}
Applied philosophy of science
” {OSCAR KEMPTHORNE}

3. PHILOSOPHICAL FOUNDATIONS

4. PHILOSOPHICAL FOUNDATIONS
1. The Nature Scientific Inference
2. Statistical Models
2.1. The mathematical beauty of nature
2.2. The messy part: what is a Probability?
3. Integrating Models and Data

5. the SCIENTIFIC PROCESS
THEORY OBSERVATION
DEDUCTION
HYPOTHETICO
DEDUCTIVE
ABDUCTIVE
INDUCTION

6. the SCIENTIFIC PROCESS
MODELS DATA
DEDUCTION
HYPOTHETICO
DEDUCTIVE
ABDUCTIVE
INDUCTION

7. PRAGMATISMREALISM
TRUTH is REAL and science
aims to discover it
TRUTH is in our minds but
it’s still USEFUL
PREDICTION
THEORIES describe
REALITY
THEORIES describe
OBSERVATIONS

8. Discovery of Neptune
1846
...a bit of HistoryA BIT OF HISTORY

9. Give me the positions and velocities of all the
particles of the universe and I will predict the
future
{ P. SIMON de LAPLACE }
”
CLOCKWORK UNIVERSE

10. DETERMINISTIC MODELS
Discovery of Neptune through
deterministic models…
(… sort of)
ERROR FUNCTION to account for observation errors

11. THE MESS OF LIFE

12. PROBABILISTIC MODELS
Evolutionary Biologists were interested in [co]VARIATION
PROBABILITY DISTRIBUTION

13. ● Physical Probability
- Frequency: long-run outcome
- Propensity: property of the system
● Evidential Probability (Bayesian)
- Measure of statement uncertainty
WHAT IS PROBABILITY?

14. + ℙ[y]
STATISTICAL MODELS
y = axb
deterministic probabilistic
Femur length
Femurwidth

15. How do we
contrast models
and data?
How much wood
could a beaver
chuck?
Do we ever get
satiated?

16. MODELS AND DATA
inspired by
Fryxell et al.1994. Oikos

17. How steep
MODELS AND DATA

18. MODELS AND DATA

19. How steep
How curved
MODELS AND DATA

20. How steep
How curved
MODELS AND DATA

21. PHENOMENOLOGICALMECHANISTIC
● Processes
● Parameters quantify
mechanisms
● Patterns (shape)
● Parameters describe
shape

22. MECHANISTIC MODELS
Attack rate
(a)
Handling time
(h)

23. WHITEBOARD TIME!

24. Attack rate
Handling
time
a = 0.76/day
h = 1.20days/kg
MODELS AND DATA

25. ● Model fitting and parameter estimation
- Least squares, Maximum Likelihood, Bayesian
- Parameter uncertainty
INTEGRATING MODELS and DATA

26. ● Model fitting and parameter estimation
● Model comparison
- Best fit
- Parsimony and information
- Predictive power
INTEGRATING MODELS and DATA

27. INTEGRATING MODELS and DATA
● Model fitting and parameter estimation
● Model comparison
● Hypothesis testing
- Statistical significance
- Power

28. ● Model fitting and parameter estimation
● Model comparison
● Hypothesis testing
● Prediction
- Repeatability
- Forecasting
INTEGRATING MODELS and DATA

29. ● Model fitting and parameter estimation
● Model comparison
● Hypothesis testing
● Prediction
INTEGRATING MODELS and DATA

30. Statistics is the grammar of Science
”
{ KARL PEARSON }

31. TECHNIQUESMODELS
● Linear models, GLMs
● Normal distribution
● Null hypothesis
● Hierarchical models, repeated
measures
● Phylogenetic models
● Population models
● ...your own hypothesis
● Least squares regression
● ANOVA
● Maximum Likelihood
● Hypothesis testing (p-value)
● Model selection (AIC, etc)
● Monte Carlo, Bootstrapping
● Goodness of fit (R2
,etc)
● Bayesian Inference
THE BIOLOGY THE SCIENTIFIC METHOD

32. ● Biological INTERPRETATION of models
● Mechanistic UNDERSTANDING of
statistical techniques
COURSE EMPHASIS

33. The most misleading assumptions are the
ones you don’t even know you’re making
{ DOUGLAS ADAMS }
”

34. ● Bolker B. 2005. Other people’s data. BioScience, 55:
550-551
FURTHER READING

35. SAMPLING

36. SAMPLING
1. The Nature of Induction
2. Statistical Inference
2.1. Describing the Data
2.2. Estimating the Truth
3. Error and Bias

37. the problem of
INDUCTION

38. { DAVID HUME }
”a wise [wo]man proportions his belief to
evidence

39. statistical inference
SAMPLE
[evidence]
POPULATION
[truth]

40. statistical inference
STATISTIC
[estimate]
PARAMETER
[unknown]

41. statistical inference
sample
mean
[x]
population
mean
[μ]

42. WHITEBOARD TIME!

43. population

44. SAMPLE
mean
i = 1
n
X = n
xi
2.47

45. SAMPLE
mean Variance
i = 1
n
X = n
xi
0.29
i = 1
n
(xi
-X)2
n
S2
=

46. SAMPLE
mean Variance
i = 1
n
X = n
i = 1
n
(xi
-X)2
n
xi
0.29
standard deviation
S2
=
SD = S2

47. SAMPLE
mean
i = 1
n
X = n
xi
= 2.47
How close is this to the
population mean?

48. PLAY
TIME!

49. ERROR and BIAS
● Standard Error: Standard Deviation of the
parameter estimates corresponding to different
samples
● Bias: Average difference between estimates and
true parameters among samples

50. ERROR
[¬
precision]
BIAS
[¬
accuracy]
HOW GOOD IS MY ESTIMATE?
Parameter
(TRUTH)Estimate

51. ERROR
BIAS
HOW GOOD IS MY ESTIMATE?
Parameter
(TRUTH)
Estimate

52. ERROR BIAS
HOW GOOD IS MY ESTIMATE?
Parameter
(TRUTH)
Estimate

53. MEASUREMENTSAMPLING
BIAS
How random is sampling
BIAS
Technique tends to over or
underestimate
ERROR
How consistent is the
measurement
ERROR
How variable are different
samples

54. What is a CONFIDENCE INTERVAL?
Find out the
definition for
tomorrow