The application of maximum likelihood techniques to the estimation of evolutionary trees from nucleic acid sequence data is discussed. A computationally feasible method for finding such maximum likelihood estimates is developed, and a computer program is available. This method has advantages over the traditional parsimony algorithms, which can give misleading results if rates of evolution differ in different lineages. It also allows the testing of hypotheses about the constancy of evolutionary rates by likelihood ratio tests, and gives rough indication of the error of the estimate of the tree.

Evolutionary trees from DNA sequences: A maximum likelihood approach

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The understanding of the dynamics of animal populations and of related ecological and evolutionary issues frequently depends on a direct analysis of life history parameters. For instance, examination of trade-offs between reproduction and survival usually rely on individually marked animals, for which the exact time of death is most often unknown, because marked individuals cannot be followed closely through time. Thus, the quantitative analysis of survival studies and experiments must be based on capture- recapture (or resighting) models which consider, besides the parameters of primary interest, recapture or resighting rates that are nuisance parameters. Capture-recapture models oriented to estimation of survival rates are the result of a recent change in emphasis from earlier approaches in which population size was the most important parameter, survival rates having been first introduced as nuisance parameters. This emphasis on survival rates in capture-recapture models developed rapidly in the 1980s and used as a basic structure the Cormack-Jolly-Seber survival model applied to an homogeneous group of animals, with various kinds of constraints on the model parameters. These approaches are conditional on first captures; hence they do not attempt to model the initial capture of unmarked animals as functions of population abundance in addition to survival and capture probabilities. This paper synthesizes, using a common framework, these recent developments together with new ones, with an emphasis on flexibility in modeling, model selection, and the analysis of multiple data sets. The effects on survival and capture rates of time, age, and categorical variables characterizing the individuals (e.g., sex) can be considered, as well as interactions between such effects. This "analysis of variance" philosophy emphasizes the structure of the survival and capture process rather than the technical characteristics of any particular model. The flexible array of models encompassed in this synthesis uses a common notation. As a result of the great level of flexibility and relevance achieved, the focus is changed from fitting a particular model to model building and model selection. The following procedure is recommended: (1) start from a global model compatible with the biology of the species studied and with the design of the study, and assess its fit; (2) select a more parsimonious model using Akaike's Information Criterion to limit the number of formal tests; (3) test for the most important biological questions by comparing this model with neighboring ones using likelihood ratio tests; and (4) obtain maximum likelihood estimates of model parameters with estimates of precision. Computer software is critical, as few of the models now available have parameter estimators that are in closed form. A comprehensive table of existing computer software is provided. We used RELEASE for data summary and goodness-of-fit tests and SURGE for iterative model fitting and the computation of likelihood ratio tests. Five increasingly complex examples are given to illustrate the theory. The first, using two data sets on the European Dipper (Cinclus cinclus), tests for sex-specific parameters,

https://ag.arizona.edu/classes/wfsc578/Lebreton%20et%20al.%201992.%20Modeling%20Survival%20and%20Testing%20Biological%20Hypotheses%20Using%20Marked%20Animals.pdf

Modeling Survival and Testing Biological Hypotheses Using Marked Animals: A Unified Approach with Case Studies

Modeling Survival and Testing Biological Hypotheses Using Marked Animals: A Unified

Correlation and correlation-based measures (e.g., the coefficient of determination) have been widely used to evaluate the “goodness-of-fit” of hydrologic and hydroclimatic models. These measures are oversensitive to extreme values (outliers) and are insensitive to additive and proportional differences between model predictions and observations. Because of these limitations, correlation-based measures can indicate that a model is a good predictor, even when it is not. In this paper, useful alternative goodness-of-fit or relative error measures (including the coefficient of efficiency and the index of agreement) that overcome many of the limitations of correlation-based measures are discussed. Modifications to these statistics to aid in interpretation are presented. It is concluded that correlation and correlation-based measures should not be used to assess the goodness-of-fit of a hydrologic or hydroclimatic model and that additional evaluation measures (such as summary statistics and absolute error measures) should supplement model evaluation tools.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998WR900018

Evaluating the use of “goodness-of-fit” Measures in hydrologic and hydroclimatic model validation

PART I: LOOKING AT DATA Looking at Data-Distributions Looking at Data-Relationships Producing Data PART II: PROBABILITY AND INFERENCE Probability: The Study of Randomness Sampling Distributions Introduction to Inference Inference for Distributions Inference for Proportions PART III: TOPICS IN INFERENCE Analysis of Two-Way Tables Inference for Regression Multiple Regression One-Way Analysis of Variance Two-Way Analysis of Variance Additional chapters available on the CD-ROM and online: Logistic Regression Nonparametric Tests Bootstrap Methods and Permutation Tests Statistics for Quality: Control and Capability

Introduction to the practice of statistics

Summary Statistical education now takes place in a new social context. It is influenced by a movement to reform the teaching of the mathematical sciences in general. At the same time, the changing nature of our discipline demands revised content for introductory instruction, and technology strongly influences both what we teach and how we teach. The case for substantial change in statistics instruction is built on strong synergies between content, pedagogy, and technology. Statisticians who teach beginners should become more familiar with research on teaching and learning and with changes in educational technology. The spirit of contemporary introductions to statistics should be very different from the traditional emphasis on lectures and on probability and inference.

/pdf/new-pedagogy-and-new-content-the-case-of-statistics-kkdf00ty6l.pdf

New Pedagogy and New Content: The Case of Statistics

How does statistical thinking differ from mathematical thinking? What is the role of mathematics in statistics? If you purge statistics of its mathematical content, what intellectual substance rema...

https://local.disia.unifi.it/rampichini/corso_insegnanti/papers/cobb1997.pdf

David S. Moore

Papers

Introduction to the practice of statistics

New Pedagogy and New Content: The Case of Statistics

Mathematics, statistics, and teaching

Introduction to the Practice of Statistics.

Statistics: Concepts and Controversies.