Graduate Program

__Credit hours__

In-class work per week |
Practice per week |
Credits |
Duration |
Total |

5 |
2 |
8 |
15 weeks |
120 hours |

__Instructor__

João Luis Ferreira Batista

__Objective__

Present and discuss the main forms of statistical inferences and their application in forest research, given the emphasis on hypothesis testing techniques of Classical Inference and Likelihood Inference.

__Content__

1. Scientific Inference and Statistical Inference: Scientific knowledge; Practical knowledge; Articulation between theory and empirical; Hypotheses, Models and Data; Data: Surveys and Experiments; Strength of inference; Causes: fixed factors and random factors; Bases of Inference: Design and Model; Measurement, estimation and prediction; Interpolation and Extrapolation.

2. Fundamentals of Statistical Inference: The Concept of Stochastic Models; Discrete Families: Binomial, Poisson, Negative Binomial; Continuous Families: Exponential, Gaussian, Weibull; Properties of stochastic models; Relationship between distribution families.

3. Classic Inference: Hypothesis Test: Sample distributions: Z, t, Chi-square and F; Neyman-Pearson Paradigm; Statistical Hypotheses and Inference Errors; Fisher's Hypothesis Test; Student's Test t; Chi-Square Test; Test F and analysis of experiments;

4. Classical Inference: Regression: Simple Linear Model; Multiple Linear Model; Estimates by Minimum Squares; Inference with regression models;

5. Inference by Likelihood: Stochastic Scenario and Models; Operant model, approach model and discrepancies; Likelihood Axiom; Likelihood and Estimation Function; Hypothesis Testing by Model Comparison.

__Bibliography__

Anderson, D.; Burnham, K. & Thompson, W. Null hypothesis testing:

problems, prevalence, and an alternative.

Journal of Wildlife Management, 2000, 64, 921-923.

Anderson, D. R. & Burnham, K. P. Avoiding Pitfalls When Using

Information-Theoretic Methods.

The Journal of Wildlife Management, 2002, 66, 912-918.

Bolker, B. Integreating ecological models and data in R.

Princeton University Press, 2006.

Burnham, K. P. & Anderson, D. R. Model selection and multimodel inference:

a pratical information-theoretic approach.

Springer-Verlag, 2002.

Graeme D. Ruxton The unequal variance t-test is an underused alternative

to Student's t-test and the Mann–Whitney U test.

Behavioral Ecology, 2006, 17, 688–690.

Fischer, C. & Schonfelder, E. A modified growth function with

interpretable parameters applied to the age-height

relationship of individual trees.

Canadian Journal of Forest Research, 2017, 47, 166-173.

Hilborn, R. & Mangel, M. The ecological detective: confronting

models with data.

Princeton University Press, 1997.

Hobbs, N. & Hilborn, R. Alternatives to statistical hypothesis

testing in Ecology: a guide to self teaching.

Ecological Applications, 2006, 16, 5-19.

Johnson, J. B. & Omland, K. S. Model selection in ecology and evolution.

TRENDS in Ecology and Evolution, 2004, 19, 101-108.

Lai, J.; Coomes, D. A.; Du, X.; Hsieh, C.-f.; Sun, I.-F.;

Chao, W.-C.; Mi, X.; Ren, H.; Wang, X.; Hao, Z. & Ma, K.

A general combined model to describe tree-diameter distributions

within subtropical and temperate forest communities.

Oikos, 2013, 122, 1636-1642.

Lehmann, E. The Fisher, Neyman-Pearson theories of testing hypotheses:

one theory or two?

Journal of the American Statistical Asssociation, 1993, 88,

1242-1249.

Lehmann, E. L. Fisher, Neyman, and the Creation of Classical Statistics

Springer, 2011.

Lima, R.A.F. de; Batista, J.L.F. & Prado, P.I. Modeling Tree Diameter

Distributions in natural Forests: An Evaluation of 10 Statistical

Models.

Forest Science, 61, 320-327.

Royall, R. Statistical evidence: a likelihood paradigm.

Chapman & Hall, 1997

Sober, E. Likelihood, Model Selection, and the Duhem-Quine Problem.

The Journal of Philosophy, 2004, C1, 221-241.

Sober, E. Instrumentalism, Parsimony, and the Akaike Framework.

Philosophy of Science, 2002, 69, S112-S123.

Subedi, M. R. & Sharma, R. P. Allometric biomass models for bark

of Cinnamomum tamala in mid-hill of Nepal.

Biomass & BIoenergy, 2012, 47, 44-49.

Taubert, F.; Hartig, F.; Dobner, H.-J. & Huth, A. On the Challenge

of Fitting Tree Size Distributions in Ecology.

PLoS ONE, 2013, 8, e58036.