Introduction to WinBUGS for Ecologists: Bayesian approach to regression, ANOVA, mixed models and related analyses

Bayesian statistics has exploded into biology and its sub-disciplines such as ecology over the past decade. The free software program WinBUGS and its open-source sister OpenBugs is currently the only flexible and general-purpose program available with which the average ecologist can conduct their own standard and non-standard Bayesian statistics. Introduction to WINBUGS for Ecologists goes right to the heart of the matter by providing ecologists with a comprehensive, yet concise, guide to applying WinBUGS to the types of models that they use most often: linear (LM), generalized linear (GLM), linear mixed (LMM) and generalized linear mixed models (GLMM).Introduction to WinBUGS for Ecologists combines the use of simulated data sets "paired" analyses using WinBUGS (in a Bayesian framework for analysis) and in R (in a frequentist mode of inference) and uses a very detailed step-by-step tutorial presentation style that really lets the reader repeat every step of the application of a given mode in their own research. - Introduction to the essential theories of key models used by ecologists - Complete juxtaposition of classical analyses in R and Bayesian Analysis of the same models in WinBUGS- Provides every detail of R and WinBUGS code required to conduct all analyses- Written with ecological language and ecological examples- Companion Web Appendix that contains all code contained in the book, additional material (including more code and solutions to exercises)- Tutorial approach shows ecologists how to implement Bayesian analysis in practical problems that they face

[1]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[2]  Andrew Thomas,et al.  The BUGS project: Evolution, critique and future directions , 2009, Statistics in medicine.

[3]  C. Krebs Ecology: The Experimental Analysis of Distribution and Abundance , 1973 .

[4]  J. Andrew Royle,et al.  Inference About Species Richness and Community Structure Using Species-Specific Occupancy Models in the National Swiss Breeding Bird Survey MHB , 2009 .

[5]  W. Link,et al.  HIERARCHICAL MODELING OF POPULATION STABILITY AND SPECIES GROUP ATTRIBUTES FROM SURVEY DATA , 2002 .

[6]  Marc Kéry,et al.  Estimating Abundance From Bird Counts: Binomial Mixture Models Uncover Complex Covariate Relationships , 2008 .

[7]  Perry de Valpine Shared challenges and common ground for Bayesian and classical analysis of hierarchical statistical models. , 2009 .

[8]  S. Lele,et al.  ESTIMATING DENSITY DEPENDENCE, PROCESS NOISE, AND OBSERVATION ERROR , 2006 .

[9]  J. Andrew Royle N‐Mixture Models for Estimating Population Size from Spatially Replicated Counts , 2004, Biometrics.

[10]  A. Zeileis,et al.  Regression Models for Count Data in R , 2008 .

[11]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Andrew Gelman,et al.  R2WinBUGS: A Package for Running WinBUGS from R , 2005 .

[13]  Brian R. Cullis,et al.  Prediction in linear mixed models , 2004 .

[14]  P. Wade Bayesian Methods in Conservation Biology , 2000 .

[15]  M. McCarthy Bayesian Methods for Ecology: Frontmatter , 2007 .

[16]  James S. Clark,et al.  Models for Ecological Data: An Introduction , 2007 .

[17]  M. Freeman,et al.  Estimating species occurrence, abundance, and detection probability using zero-inflated distributions. , 2008, Ecology.

[18]  Res Altwegg,et al.  Climate and the range dynamics of species with imperfect detection , 2008, Biology Letters.

[19]  Stephen P Brooks,et al.  Bayesian computation: a statistical revolution , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[20]  Brian Dennis,et al.  Discussion: Should Ecologists Become Bayesians? , 1996 .

[21]  Marc Kery,et al.  Inferring the absence of a species -- a case study of snakes , 2002 .

[22]  Jay M. Ver Hoef,et al.  Space—time zero‐inflated count models of Harbor seals , 2007 .

[23]  William A Link,et al.  Model weights and the foundations of multimodel inference. , 2006, Ecology.

[24]  Marc Kéry,et al.  Extinction Rate Estimates for Plant Populations in Revisitation Studies: Importance of Detectability , 2004 .

[25]  N. Lazar,et al.  Methods and Criteria for Model Selection , 2004 .

[26]  R. Little Calibrated Bayes , 2006 .

[27]  M. McCarthy,et al.  Profiting from prior information in Bayesian analyses of ecological data , 2005 .

[28]  I. Cock Encyclopedia of Life Support Systems (EOLSS) , 2011 .

[29]  S. R. Searle,et al.  Generalized, Linear, and Mixed Models , 2005 .

[30]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[31]  Peter Dalgaard,et al.  Introductory statistics with R , 2002, Statistics and computing.

[32]  Brian Dennis,et al.  Hierarchical models in ecology: confidence intervals, hypothesis testing, and model selection using data cloning. , 2009, Ecology.

[33]  B. Schmidt,et al.  Monitoring distributions using call surveys: estimating site occupancy, detection probabilities and inferring absence. , 2005 .

[34]  S. T. Buckland,et al.  Estimating Animal Abundance , 2002 .

[35]  Marc Kéry,et al.  Imperfect detection and its consequences for monitoring for conservation , 2008 .

[36]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[37]  J. Andrew Royle Generalized estimators of avian abundance from count survey data , 2004 .

[38]  Murray G Efford,et al.  Population density estimated from locations of individuals on a passive detector array. , 2009, Ecology.

[39]  Petros Dellaportas,et al.  On Bayesian model and variable selection using MCMC , 2002, Stat. Comput..

[40]  Andrew Gelman,et al.  Data Analysis Using Regression and Multilevel/Hierarchical Models , 2006 .

[41]  L. L. Cam,et al.  Maximum likelihood : an introduction , 1990 .

[42]  Ian D Jonsen,et al.  Assessing threats to species at risk using stage-structured state-space models: mortality trends in skate populations. , 2009, Ecological applications : a publication of the Ecological Society of America.

[43]  M. Karim Generalized Linear Models With Random Effects , 1991 .

[44]  J. Nichols,et al.  ESTIMATING SITE OCCUPANCY, COLONIZATION, AND LOCAL EXTINCTION WHEN A SPECIES IS DETECTED IMPERFECTLY , 2003 .

[45]  Alan E. Gelfand,et al.  Bayesian statistics without tears: A sampling-resampling perspective , 1992 .

[46]  C. Robert,et al.  Bayesian Modeling Using WinBUGS , 2009 .

[47]  David J. Spiegelhalter,et al.  WinBUGS user manual version 1.4 , 2003 .

[48]  D. MacKenzie Modeling the Probability of Resource Use: The Effect of, and Dealing with, Detecting a Species Imperfectly , 2006 .

[49]  Xiao-Li Meng,et al.  POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES , 1996 .

[50]  D. MacKenzie Occupancy Estimation and Modeling: Inferring Patterns and Dynamics of Species Occurrence , 2005 .

[51]  Joseph Hilbe,et al.  Bayesian Analysis for Population Ecology , 2009 .

[52]  B. Schmidt,et al.  Monitoring the distribution of pond‐breeding amphibians when species are detected imperfectly , 2005 .

[53]  Alan Hastings,et al.  FITTING POPULATION MODELS INCORPORATING PROCESS NOISE AND OBSERVATION ERROR , 2002 .

[54]  A. Gelman Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[55]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[56]  M. Degroot,et al.  Probability and Statistics , 2021, Examining an Operational Approach to Teaching Probability.

[57]  M. Kéry,et al.  Predicting species distributions from checklist data using site‐occupancy models , 2010 .

[58]  K. Burnham,et al.  Program MARK: survival estimation from populations of marked animals , 1999 .

[59]  J. Nichols,et al.  OF BUGS AND BIRDS: MARKOV CHAIN MONTE CARLO FOR HIERARCHICAL MODELING IN WILDLIFE RESEARCH , 2002 .

[60]  D. Bates,et al.  Mixed-Effects Models in S and S-PLUS , 2001 .

[61]  John Hinde,et al.  Statistical Modelling in R , 2009 .

[62]  M. Conroy,et al.  Analysis and Management of Animal Populations , 2002 .

[63]  J Andrew Royle,et al.  A hierarchical model for spatial capture-recapture data. , 2008, Ecology.

[64]  J. Andrew Royle,et al.  Hierarchical models of animal abundance and occurrence , 2006 .

[65]  Christopher K. Wikle,et al.  Hierarchical Bayesian Models for Predicting The Spread of Ecological Processes , 2003 .

[66]  H. G. Andrewartha,et al.  The distribution and abundance of animals. , 1954 .

[67]  M. Kéry,et al.  How biased are estimates of extinction probability in revisitation studies? , 2006 .

[68]  Stephen N Freeman,et al.  On smoothing trends in population index modeling. , 2007, Biometrics.

[69]  J. Andrew Royle,et al.  A Bayesian state-space formulation of dynamic occupancy models. , 2007, Ecology.

[70]  Kenneth H. Pollock,et al.  Bayesian spatial modeling of data from avian point count surveys , 2008 .

[71]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[72]  George G. Woodworth,et al.  Biostatistics: A Bayesian Introduction , 2004 .

[73]  Ché Elkin,et al.  Modeling abundance using N-mixture models: the importance of considering ecological mechanisms. , 2009, Ecological applications : a publication of the Ecological Society of America.

[74]  J. Andrew Royle,et al.  HIERARCHICAL SPATIAL MODELS OF ABUNDANCE AND OCCURRENCE FROM IMPERFECT SURVEY DATA , 2007 .

[75]  J Andrew Royle,et al.  Web-based Supplementary Materials for “ Modeling Individual Effects in the Cormack-Jolly-Seber Model : A State-space Formulation ” , 2010 .

[76]  David Lindley,et al.  Theory and Practice of Bayesian Statistics , 1983 .

[77]  Benjamin M. Bolker,et al.  Ecological Models and Data in R , 2008 .

[78]  W. Link,et al.  A HIERARCHICAL ANALYSIS OF POPULATION CHANGE WITH APPLICATION TO CERULEAN WARBLERS , 2002 .

[79]  H. Possingham,et al.  IMPROVING PRECISION AND REDUCING BIAS IN BIOLOGICAL SURVEYS: ESTIMATING FALSE‐NEGATIVE ERROR RATES , 2003 .

[80]  David R. Jones,et al.  How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS , 2005, Statistics in medicine.

[81]  D L Borchers,et al.  Spatially Explicit Maximum Likelihood Methods for Capture–Recapture Studies , 2008, Biometrics.

[82]  James D. Nichols,et al.  Monitoring of biological diversity in space and time , 2001 .

[83]  M. Efford Density estimation in live‐trapping studies , 2004 .

[84]  Brian Dennis,et al.  Bayesian methods for hierarchical models: are ecologists making a Faustian bargain? , 2009, Ecological applications : a publication of the Ecological Society of America.

[85]  J. Andrew Royle,et al.  MODELING AVIAN ABUNDANCE FROM REPLICATED COUNTS USING BINOMIAL MIXTURE MODELS , 2005 .

[86]  L. Powell APPROXIMATING VARIANCE OF DEMOGRAPHIC PARAMETERS USING THE DELTA METHOD: A REFERENCE FOR AVIAN BIOLOGISTS , 2007 .

[87]  William N. Venables,et al.  Modern Applied Statistics with S , 2010 .

[88]  K. Mengersen,et al.  The power of expert opinion in ecological models using Bayesian methods: impact of grazing on birds , 2005 .

[89]  J. Andrew Royle,et al.  Trend estimation in populations with imperfect detection , 2009 .