BayesBasics.bib

@article{lewandowski_generating_2009,
	title = {Generating random correlation matrices based on vines and extended onion method},
	volume = {100},
	issn = {0047-259X},
	url = {http://www.sciencedirect.com/science/article/pii/S0047259X09000876},
	doi = {10.1016/j.jmva.2009.04.008},
	abstract = {We extend and improve two existing methods of generating random correlation matrices, the onion method of Ghosh and Henderson [S. Ghosh, S.G. Henderson, Behavior of the norta method for correlated random vector generation as the dimension increases, ACM Transactions on Modeling and Computer Simulation (TOMACS) 13 (3) (2003) 276–294] and the recently proposed method of Joe [H. Joe, Generating random correlation matrices based on partial correlations, Journal of Multivariate Analysis 97 (2006) 2177–2189] based on partial correlations. The latter is based on the so-called D -vine. We extend the methodology to any regular vine and study the relationship between the multiple correlation and partial correlations on a regular vine. We explain the onion method in terms of elliptical distributions and extend it to allow generating random correlation matrices from the same joint distribution as the vine method. The methods are compared in terms of time necessary to generate 5000 random correlation matrices of given dimensions.},
	number = {9},
	urldate = {2015-05-27},
	journal = {Journal of Multivariate Analysis},
	author = {Lewandowski, Daniel and Kurowicka, Dorota and Joe, Harry},
	month = oct,
	year = {2009},
	keywords = {Correlation matrix, Dependence vines, Onion method, Partial correlation},
	pages = {1989--2001},
	file = {ScienceDirect Full Text PDF:/Users/micl/Zotero/storage/XF3GNGKP/Lewandowski et al. - 2009 - Generating random correlation matrices based on vi.pdf:application/pdf;ScienceDirect Snapshot:/Users/micl/Zotero/storage/4JKQZS4G/S0047259X09000876.html:text/html}
}

@article{hoffman_no-u-turn_2014,
	title = {The {No}-{U}-{Turn} {Sampler}: {Adaptively} {Setting} {Path} {Lengths} in {Hamiltonian} {Monte} {Carlo}},
	volume = {15},
	shorttitle = {The {No}-{U}-{Turn} {Sampler}},
	url = {http://jmlr.csail.mit.edu/papers/v15/hoffman14a.html},
	abstract = {Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo
(MCMC) algorithm that avoids the random walk behavior and
sensitivity to correlated parameters that plague many MCMC
methods by taking a series of steps informed by first-order
gradient information. These features allow it to converge to
high-dimensional target distributions much more quickly than
simpler methods such as random walk Metropolis or Gibbs
sampling. However, HMC's performance is highly sensitive to two
user-specified parameters: a step size ϵ{\textbackslash}epsilon and a desired
number of steps LL. In particular, if LL is too small then the
algorithm exhibits undesirable random walk behavior, while if
LL is too large the algorithm wastes computation. We introduce
the No-U-Turn Sampler (NUTS), an extension to HMC that
eliminates the need to set a number of steps LL. NUTS uses a
recursive algorithm to build a set of likely candidate points
that spans a wide swath of the target distribution, stopping
automatically when it starts to double back and retrace its
steps. Empirically, NUTS performs at least as efficiently as
(and sometimes more efficiently than) a well tuned standard HMC
method, without requiring user intervention or costly tuning
runs. We also derive a method for adapting the step size
parameter ϵ{\textbackslash}epsilon on the fly based on primal-dual averaging.
NUTS can thus be used with no hand-tuning at all, making it
suitable for applications such as BUGS-style automatic inference
engines that require efficient “turnkey” samplers.},
	urldate = {2014-09-23},
	journal = {Journal of Machine Learning Research},
	author = {Hoffman, Matthew D. and Gelman, Andrew},
	month = apr,
	year = {2014},
	pages = {1593−1623},
	file = {The No-U-Turn Sampler\: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo:/Users/micl/Zotero/storage/JU5ZU8GG/Hoffman and Gelman - 2014 - The No-U-Turn Sampler Adaptively Setting Path Len.pdf:application/pdf}
}

@book{albert_bayesian_2009,
	address = {New York},
	edition = {2nd ed. 2009 edition},
	title = {Bayesian {Computation} with {R}},
	isbn = {978-0-387-92297-3},
	abstract = {There has been a dramatic growth in the development and application of Bayesian inferential methods. Some of this growth is due to the availability of powerful simulation-based algorithms to summarize posterior distributions. There has been also a growing interest in the use of the system R for statistical analyses. R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry. Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. The early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model. The construction and implementation of Markov Chain Monte Carlo (MCMC) methods is introduced. These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling. Algorithms written in R are used to develop Bayesian tests and assess Bayesian models by use of the posterior predictive distribution. The use of R to interface with WinBUGS, a popular MCMC computing language, is described with several illustrative examples. This book is a suitable companion book for an introductory course on Bayesian methods and is valuable to the statistical practitioner who wishes to learn more about the R language and Bayesian methodology. The LearnBayes package, written by the author and available from the CRAN website, contains all of the R functions described in the book. The second edition contains several new topics such as the use of mixtures of conjugate priors and the use of Zellner’s g priors to choose between models in linear regression. There are more illustrations of the construction of informative prior distributions, such as the use of conditional means priors and multivariate normal priors in binary regressions. The new edition contains changes in the R code illustrations according to the latest edition of the LearnBayes package.},
	language = {English},
	publisher = {Springer},
	author = {Albert, Jim},
	month = jun,
	year = {2009}
}

@book{scott_m._lynch_[scott_michael_introduction_2007,
	address = {New York},
	title = {Introduction to applied {Bayesian} statistics and estimation for social scientists},
	isbn = {978-0-387-71264-2},
	abstract = {Lynch covers the complete process of Bayesian statistical analysis in great detail from the development of a model through the process of making statistical inference. The key feature of the book is that it covers models that are most commonly used on social science research.},
	language = {eng},
	publisher = {Springer},
	author = {{Scott M. Lynch [Scott Michael}},
	collaborator = {ebrary, Inc},
	year = {2007},
	keywords = {Bayes' solution, Bayesian analysis, Bayesian statistical decision theory., Social sciences Statistical methods.}
}

@book{simon_jackman_bayesian_2009,
	address = {Chichester, UK},
	title = {Bayesian analysis for the social sciences},
	isbn = {978-0-470-01154-6},
	language = {eng},
	publisher = {Wiley},
	author = {{Simon Jackman}},
	year = {2009},
	keywords = {Bayes' solution, Bayesian analysis, Bayesian statistical decision theory., Social sciences Statistical methods., Bayes-Verfahren.}
}

@book{jeff_gill_bayesian_2008,
	address = {Boca Raton},
	edition = {2nd ed..},
	title = {Bayesian methods : a social and behavioral sciences approach},
	isbn = {978-1-58488-562-7},
	shorttitle = {Bayesian methods},
	language = {eng},
	publisher = {Chapman \& Hall/CRC},
	author = {{Jeff Gill}},
	year = {2008},
	keywords = {Bayes' solution, Bayesian analysis, Bayesian statistical decision theory., Social sciences Statistical methods., Decisión estadística., Methode van Bayes., Teorías bayesian.}
}

@book{lunn_bugs_2012,
	address = {Boca Raton, FL},
	title = {The {BUGS} {Book}: {A} {Practical} {Introduction} to {Bayesian} {Analysis}},
	isbn = {978-1-58488-849-9},
	shorttitle = {The {BUGS} {Book}},
	abstract = {Bayesian statistical methods have become widely used for data analysis and modelling in recent years, and the BUGS software has become the most popular software for Bayesian analysis worldwide. Authored by the team that originally developed this software, The BUGS Book provides a practical introduction to this program and its use. The text presents complete coverage of all the functionalities of BUGS, including prediction, missing data, model criticism, and prior sensitivity. It also features a large number of worked examples and a wide range of applications from various disciplines.  The book introduces regression models, techniques for criticism and comparison, and a wide range of modelling issues before going into the vital area of hierarchical models, one of the most common applications of Bayesian methods. It deals with essentials of modelling without getting bogged down in complexity. The book emphasises model criticism, model comparison, sensitivity analysis to alternative priors, and thoughtful choice of prior distributions—all those aspects of the "art" of modelling that are easily overlooked in more theoretical expositions.   More pragmatic than ideological, the authors systematically work through the large range of "tricks" that reveal the real power of the BUGS software, for example, dealing with missing data, censoring, grouped data, prediction, ranking, parameter constraints, and so on. Many of the examples are biostatistical, but they do not require domain knowledge and are generalisable to a wide range of other application areas.   Full code and data for examples, exercises, and some solutions can be found on the book’s website.},
	language = {English},
	publisher = {Chapman and Hall/CRC},
	author = {Lunn, David and Jackson, Chris and Best, Nicky and Thomas, Andrew and Spiegelhalter, David},
	month = oct,
	year = {2012}
}

@book{gelman_data_2006,
	title = {Data {Analysis} {Using} {Regression} and {Multilevel}/{Hierarchical} {Models}},
	isbn = {978-1-139-46093-4},
	abstract = {Data Analysis Using Regression and Multilevel/Hierarchical Models, first published in 2007, is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout.},
	language = {en},
	publisher = {Cambridge University Press},
	author = {Gelman, Andrew and Hill, Jennifer},
	month = dec,
	year = {2006},
	keywords = {Mathematics / Probability \& Statistics / General, Political Science / General, Psychology / Assessment, Testing \& Measurement, Social Science / Research}
}

@book{gelman_bayesian_2013,
	title = {Bayesian {Data} {Analysis}, {Third} {Edition}},
	isbn = {978-1-4398-4095-5},
	abstract = {Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition   Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code   The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.},
	language = {en},
	publisher = {CRC Press},
	author = {Gelman, Andrew and Carlin, John B. and Stern, Hal S. and Dunson, David B. and Vehtari, Aki and Rubin, Donald B.},
	month = nov,
	year = {2013},
	keywords = {Mathematics / Probability \& Statistics / General, Computers / Mathematical \& Statistical Software, Psychology / Research \& Methodology}
}

@book{kruschke_doing_2010,
	title = {Doing {Bayesian} {Data} {Analysis}: {A} {Tutorial} {Introduction} with {R}},
	isbn = {978-0-12-381486-9},
	shorttitle = {Doing {Bayesian} {Data} {Analysis}},
	abstract = {There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis tractable and accessible to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS, is for first year graduate students or advanced undergraduates and provides an accessible approach, as all mathematics is explained intuitively and with concrete examples. It assumes only algebra and ‘rusty’ calculus. Unlike other textbooks, this book begins with the basics, including essential concepts of probability and random sampling. The book gradually climbs all the way to advanced hierarchical modeling methods for realistic data. The text provides complete examples with the R programming language and BUGS software (both freeware), and begins with basic programming examples, working up gradually to complete programs for complex analyses and presentation graphics. These templates can be easily adapted for a large variety of students and their own research needs.The textbook bridges the students from their undergraduate training into modern Bayesian methods.-Accessible, including the basics of essential concepts of probability and random sampling -Examples with R programming language and BUGS software -Comprehensive coverage of all scenarios addressed by non-bayesian textbooks- t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis). -Coverage of experiment planning -R and BUGS computer programming code on website -Exercises have explicit purposes and guidelines for accomplishment},
	language = {en},
	publisher = {Academic Press},
	author = {Kruschke, John},
	month = nov,
	year = {2010},
	keywords = {Mathematics / Applied, Mathematics / General}
}

@article{montesinos-lopez_bayesian_2017,
	title = {A {Bayesian} {Poisson}-lognormal {Model} for {Count} {Data} for {Multiple}-{Trait} {Multiple}-{Environment} {Genomic}-{Enabled} {Prediction}},
	volume = {7},
	issn = {2160-1836},
	url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5427491/},
	doi = {10.1534/g3.117.039974},
	abstract = {When a plant scientist wishes to make genomic-enabled predictions of multiple traits measured in multiple individuals in multiple environments, the most common strategy for performing the analysis is to use a single trait at a time taking into account genotype × environment interaction (G × E), because there is a lack of comprehensive models that simultaneously take into account the correlated counting traits and G × E. For this reason, in this study we propose a multiple-trait and multiple-environment model for count data. The proposed model was developed under the Bayesian paradigm for which we developed a Markov Chain Monte Carlo (MCMC) with noninformative priors. This allows obtaining all required full conditional distributions of the parameters leading to an exact Gibbs sampler for the posterior distribution. Our model was tested with simulated data and a real data set. Results show that the proposed multi-trait, multi-environment model is an attractive alternative for modeling multiple count traits measured in multiple environments.},
	number = {5},
	urldate = {2018-11-13},
	journal = {G3: Genes{\textbar}Genomes{\textbar}Genetics},
	author = {Montesinos-López, Osval A. and Montesinos-López, Abelardo and Crossa, José and Toledo, Fernando H. and Montesinos-López, José C. and Singh, Pawan and Juliana, Philomin and Salinas-Ruiz, Josafhat},
	month = mar,
	year = {2017},
	pmid = {28364037},
	pmcid = {PMC5427491},
	pages = {1595--1606},
	file = {PubMed Central Full Text PDF:/Users/micl/Zotero/storage/8B4HTE4Z/Montesinos-López et al. - 2017 - A Bayesian Poisson-lognormal Model for Count Data .pdf:application/pdf}
}

@article{vehtari_practical_2017,
	title = {Practical {Bayesian} model evaluation using leave-one-out cross-validation and {WAIC}},
	volume = {27},
	issn = {1573-1375},
	url = {https://doi.org/10.1007/s11222-016-9696-4},
	doi = {10.1007/s11222-016-9696-4},
	abstract = {Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the posterior simulations of the parameter values. LOO and WAIC have various advantages over simpler estimates of predictive error such as AIC and DIC but are less used in practice because they involve additional computational steps. Here we lay out fast and stable computations for LOO and WAIC that can be performed using existing simulation draws. We introduce an efficient computation of LOO using Pareto-smoothed importance sampling (PSIS), a new procedure for regularizing importance weights. Although WAIC is asymptotically equal to LOO, we demonstrate that PSIS-LOO is more robust in the finite case with weak priors or influential observations. As a byproduct of our calculations, we also obtain approximate standard errors for estimated predictive errors and for comparison of predictive errors between two models. We implement the computations in an R package called loo and demonstrate using models fit with the Bayesian inference package Stan.},
	language = {en},
	number = {5},
	urldate = {2018-11-13},
	journal = {Statistics and Computing},
	author = {Vehtari, Aki and Gelman, Andrew and Gabry, Jonah},
	month = sep,
	year = {2017},
	keywords = {Bayesian computation, K-fold cross-validation, Leave-one-out cross-validation (LOO), Pareto smoothed importance sampling (PSIS), Stan, Widely applicable information criterion (WAIC)},
	pages = {1413--1432},
	file = {Submitted Version:/Users/micl/Zotero/storage/9K6CVP7H/Vehtari et al. - 2017 - Practical Bayesian model evaluation using leave-on.pdf:application/pdf}
}

@article{vehtari_pareto_2017,
	title = {Pareto {Smoothed} {Importance} {Sampling}},
	url = {http://arxiv.org/abs/1507.02646},
	abstract = {Importance weighting is a convenient general way to adjust for draws from the wrong distribution, but the resulting ratio estimate can be noisy when the importance weights have a heavy right tail, as routinely occurs when there are aspects of the target distribution not well captured by the approximating distribution. More stable estimates can be obtained by truncating the importance ratios. Here we present a new method for stabilizing importance weights using a generalized Pareto distribution fit to the upper tail of the distribution of the simulated importance ratios. The method includes stabilized effective sample estimates, Monte Carlo error estimates and convergence diagnostics.},
	urldate = {2018-11-13},
	journal = {arXiv:1507.02646 [stat]},
	author = {Vehtari, Aki and Gelman, Andrew and Gabry, Jonah},
	month = jul,
	year = {2015},
	note = {arXiv: 1507.02646},
	keywords = {Statistics - Computation, Statistics - Methodology},
	file = {arXiv\:1507.02646 PDF:/Users/micl/Zotero/storage/VTRN43F7/Vehtari et al. - 2015 - Pareto Smoothed Importance Sampling.pdf:application/pdf;arXiv.org Snapshot:/Users/micl/Zotero/storage/Z34R4UUH/1507.html:text/html}
}

@article{yao_using_2018,
	title = {Using {Stacking} to {Average} {Bayesian} {Predictive} {Distributions} (with {Discussion})},
	volume = {13},
	issn = {1936-0975, 1931-6690},
	url = {https://projecteuclid.org/euclid.ba/1516093227},
	doi = {10.1214/17-BA1091},
	abstract = {Bayesian model averaging is flawed in the ℳM{\textless}math alttext="\${\textbackslash}mathcal\{M\}\$" overflow="scroll"{\textgreater}{\textless}mi mathvariant="script"{\textgreater}M{\textless}/mi{\textgreater}{\textless}/math{\textgreater}-open setting in which the true data-generating process is not one of the candidate models being fit. We take the idea of stacking from the point estimation literature and generalize to the combination of predictive distributions. We extend the utility function to any proper scoring rule and use Pareto smoothed importance sampling to efficiently compute the required leave-one-out posterior distributions. We compare stacking of predictive distributions to several alternatives: stacking of means, Bayesian model averaging (BMA), Pseudo-BMA, and a variant of Pseudo-BMA that is stabilized using the Bayesian bootstrap. Based on simulations and real-data applications, we recommend stacking of predictive distributions, with bootstrapped-Pseudo-BMA as an approximate alternative when computation cost is an issue.},
	language = {EN},
	number = {3},
	urldate = {2018-11-13},
	journal = {Bayesian Analysis},
	author = {Yao, Yuling and Vehtari, Aki and Simpson, Daniel and Gelman, Andrew},
	month = sep,
	year = {2018},
	keywords = {Bayesian model averaging, model combination, predictive distribution, proper scoring rule, stacking, Stan},
	pages = {917--1007},
	file = {Full Text PDF:/Users/micl/Zotero/storage/N874HK4T/Yao et al. - 2018 - Using Stacking to Average Bayesian Predictive Dist.pdf:application/pdf;Snapshot:/Users/micl/Zotero/storage/PIEGINY7/1516093227.html:text/html}
}

@book{mcelreath2016,
  title={Statistical Rethinking: A Bayesian Course with Examples in R and Stan},
  author={McElreath, Richard},
  volume={122},
  year={2016},
  publisher={CRC Press}
}


@book{kruschke2014doing,
  title={Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan},
  author={Kruschke, John},
  year={2015},
  edition={2nd},
  publisher={Academic Press}
}