citations.bib

@BOOK{bda3,
  title     = "Bayesian Data Analysis, Third Edition",
  author    = "Gelman, Andrew and Carlin, John B and Stern, Hal S and Dunson,
               David B and Vehtari, Aki and Rubin, Donald B",
  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.",
  publisher = "CRC Press",
  edition   =  3,
  month     =  nov,
  year      =  2013,
  language  = "en",
  isbn      = "9781439840955"
}

@ARTICLE{Gelman2004-kh,
  title    = "Bayesian analysis of serial dilution assays",
  author   = "Gelman, Andrew and Chew, Ginger L and Shnaidman, Michael",
  abstract = "In a serial dilution assay, the concentration of a compound is
              estimated by combining measurements of several different
              dilutions of an unknown sample. The relation between
              concentration and measurement is nonlinear and heteroscedastic,
              and so it is not appropriate to weight these measurements
              equally. In the standard existing approach for analysis of these
              data, a large proportion of the measurements are discarded as
              being above or below detection limits. We present a Bayesian
              method for jointly estimating the calibration curve and the
              unknown concentrations using all the data. Compared to the
              existing method, our estimates have much lower standard errors
              and give estimates even when all the measurements are outside the
              ``detection limits.'' We evaluate our method empirically using
              laboratory data on cockroach allergens measured in house dust
              samples. Our estimates are much more accurate than those obtained
              using the usual approach. In addition, we develop a method for
              determining the ``effective weight'' attached to each
              measurement, based on a local linearization of the estimated
              model. The effective weight can give insight into the information
              conveyed by each data point and suggests potential improvements
              in design of serial dilution experiments.",
  journal  = "Biometrics",
  volume   =  60,
  number   =  2,
  pages    = "407--417",
  month    =  jun,
  year     =  2004,
  language = "en",
  issn     = "0006-341X",
  pmid     = "15180666",
  doi      = "10.1111/j.0006-341X.2004.00185.x"
}

@ARTICLE{Hoffman2011-nx,
  title         = "The {no-U-Turn} Sampler: Adaptively setting path lengths in
                   Hamiltonian Monte Carlo",
  author        = "Hoffman, Matthew D and Gelman, Andrew",
  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
                   \{\textbackslashepsilon\} and a desired number of steps L.
                   In particular, if L is too small then the algorithm exhibits
                   undesirable random walk behavior, while if L 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 L. 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 perform 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 \{\textbackslashepsilon\} on the fly based on
                   primal-dual averaging. NUTS can thus be used with no
                   hand-tuning at all. NUTS is also suitable for applications
                   such as BUGS-style automatic inference engines that require
                   efficient ``turnkey'' sampling algorithms.",
  month         =  nov,
  year          =  2011,
  copyright     = "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  archivePrefix = "arXiv",
  eprint        = "1111.4246",
  primaryClass  = "stat.CO",
  arxivid       = "1111.4246"
}

@ARTICLE{Neal2012-mu,
  title         = "{MCMC} using Hamiltonian dynamics",
  author        = "Neal, Radford M",
  abstract      = "Hamiltonian dynamics can be used to produce distant
                   proposals for the Metropolis algorithm, thereby avoiding the
                   slow exploration of the state space that results from the
                   diffusive behaviour of simple random-walk proposals. Though
                   originating in physics, Hamiltonian dynamics can be applied
                   to most problems with continuous state spaces by simply
                   introducing fictitious ``momentum'' variables. A key to its
                   usefulness is that Hamiltonian dynamics preserves volume,
                   and its trajectories can thus be used to define complex
                   mappings without the need to account for a hard-to-compute
                   Jacobian factor - a property that can be exactly maintained
                   even when the dynamics is approximated by discretizing time.
                   In this review, I discuss theoretical and practical aspects
                   of Hamiltonian Monte Carlo, and present some of its
                   variations, including using windows of states for deciding
                   on acceptance or rejection, computing trajectories using
                   fast approximations, tempering during the course of a
                   trajectory to handle isolated modes, and short-cut methods
                   that prevent useless trajectories from taking much
                   computation time.",
  month         =  jun,
  year          =  2012,
  archivePrefix = "arXiv",
  eprint        = "1206.1901",
  primaryClass  = "stat.CO",
  arxivid       = "1206.1901"
}

@ARTICLE{Betancourt2017-bp,
  title         = "A Conceptual Introduction to Hamiltonian Monte Carlo",
  author        = "Betancourt, Michael",
  abstract      = "Hamiltonian Monte Carlo has proven a remarkable empirical
                   success, but only recently have we begun to develop a
                   rigorous understanding of why it performs so well on
                   difficult problems and how it is best applied in practice.
                   Unfortunately, that understanding is confined within the
                   mathematics of differential geometry which has limited its
                   dissemination, especially to the applied communities for
                   which it is particularly important. In this review I provide
                   a comprehensive conceptual account of these theoretical
                   foundations, focusing on developing a principled intuition
                   behind the method and its optimal implementations rather of
                   any exhaustive rigor. Whether a practitioner or a
                   statistician, the dedicated reader will acquire a solid
                   grasp of how Hamiltonian Monte Carlo works, when it
                   succeeds, and, perhaps most importantly, when it fails.",
  month         =  jan,
  year          =  2017,
  archivePrefix = "arXiv",
  eprint        = "1701.02434",
  primaryClass  = "stat.ME",
  arxivid       = "1701.02434"
}

@ARTICLE{Betancourt2016-je,
  title         = "Diagnosing Suboptimal Cotangent Disintegrations in
                   Hamiltonian Monte Carlo",
  author        = "Betancourt, Michael",
  abstract      = "When properly tuned, Hamiltonian Monte Carlo scales to some
                   of the most challenging high-dimensional problems at the
                   frontiers of applied statistics, but when that tuning is
                   suboptimal the performance leaves much to be desired. In
                   this paper I show how suboptimal choices of one critical
                   degree of freedom, the cotangent disintegration, manifest in
                   readily observed diagnostics that facilitate the robust
                   application of the algorithm.",
  month         =  apr,
  year          =  2016,
  archivePrefix = "arXiv",
  eprint        = "1604.00695",
  primaryClass  = "stat.ME",
  arxivid       = "1604.00695"
}

@ARTICLE{Vehtari2017-st,
  title     = "Practical Bayesian model evaluation using leave-one-out cross-validation and {WAIC}",
  author    = "Vehtari, Aki and Gelman, Andrew and Gabry, Jonah",
  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.",
  journal   = "Stat. Comput.",
  publisher = "Springer Science and Business Media LLC",
  volume    =  27,
  number    =  5,
  pages     = "1413--1432",
  month     =  sep,
  year      =  2017,
  language  = "en",
  issn      = "0960-3174, 1573-1375",
  doi       = "10.1007/s11222-016-9696-4"
}

@Manual{R-loo,
  title = {loo: Efficient Leave-One-Out Cross-Validation and WAIC for Bayesian Models},
  author = {Aki Vehtari and Jonah Gabry and Mans Magnusson and Yuling Yao and Paul-Christian Bürkner and Topi Paananen and Andrew Gelman},
  year = {2020},
  note = {R package version 2.4.1},
  url = {https://CRAN.R-project.org/package=loo},
}

@Article{loo2017a,
  title = {Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC},
  author = {Aki Vehtari and Andrew Gelman and Jonah Gabry},
  year = {2017},
  journal = {Statistics and Computing},
  volume = {27},
  issue = {5},
  pages = {1413--1432},
  doi = {10.1007/s11222-016-9696-4},
}

@Article{loo2017b,
  title = {Using stacking to average Bayesian predictive distributions},
  author = {Yuling Yao and Aki Vehtari and Daniel Simpson and Andrew Gelman},
  year = {2017},
  journal = {Bayesian Analysis},
  doi = {10.1214/17-BA1091},
}

@ARTICLE{Navarro2019-pi,
  title    = "Between the Devil and the Deep Blue Sea: Tensions Between
              Scientific Judgement and Statistical Model Selection",
  author   = "Navarro, Danielle J",
  abstract = "Discussions of model selection in the psychological literature
              typically frame the issues as a question of statistical
              inference, with the goal being to determine which model makes the
              best predictions about data. Within this setting, advocates of
              leave-one-out cross-validation and Bayes factors disagree on
              precisely which prediction problem model selection questions
              should aim to answer. In this comment, I discuss some of these
              issues from a scientific perspective. What goal does model
              selection serve when all models are known to be systematically
              wrong? How might ``toy problems'' tell a misleading story? How
              does the scientific goal of explanation align with (or differ
              from) traditional statistical concerns? I do not offer answers to
              these questions, but hope to highlight the reasons why
              psychological researchers cannot avoid asking them.",
  journal  = "Computational Brain \& Behavior",
  volume   =  2,
  number   =  1,
  pages    = "28--34",
  month    =  mar,
  year     =  2019,
  issn     = "2522-087X",
  doi      = "10.1007/s42113-018-0019-z"
}

@ARTICLE{Sivula2020-yw,
  title         = "Uncertainty in Bayesian {Leave-One-Out} {Cross-Validation}
                   Based Model Comparison",
  author        = "Sivula, Tuomas and Magnusson, M{\aa}ns and Vehtari, Aki",
  abstract      = "Leave-one-out cross-validation (LOO-CV) is a popular method
                   for comparing Bayesian models based on their estimated
                   predictive performance on new, unseen, data. Estimating the
                   uncertainty of the resulting LOO-CV estimate is a complex
                   task and it is known that the commonly used standard error
                   estimate is often too small. We analyse the frequency
                   properties of the LOO-CV estimator and study the uncertainty
                   related to it. We provide new results of the properties of
                   the uncertainty both theoretically and empirically and
                   discuss the challenges of estimating it. We show that
                   problematic cases include: comparing models with similar
                   predictions, misspecified models, and small data. In these
                   cases, there is a weak connection in the skewness of the
                   sampling distribution and the distribution of the error of
                   the LOO-CV estimator. We show that it is possible that the
                   problematic skewness of the error distribution, which occurs
                   when the models make similar predictions, does not fade away
                   when the data size grows to infinity in certain situations.",
  month         =  aug,
  year          =  2020,
  archivePrefix = "arXiv",
  eprint        = "2008.10296",
  primaryClass  = "stat.ME",
  arxivid       = "2008.10296"
}

@ARTICLE{Vehtari2012-wn,
  title     = "A survey of Bayesian predictive methods for model assessment,
               selection and comparison",
  author    = "Vehtari, Aki and Ojanen, Janne",
  abstract  = "To date, several methods exist in the statistical literature for
               model assessment, which purport themselves specifically as
               Bayesian predictive methods. The decision theoretic assumptions
               on which these methods are based are not always clearly stated
               in the original articles, however. The aim of this survey is to
               provide a unified review of Bayesian predictive model assessment
               and selection methods, and of methods closely related to them.
               We review the various assumptions that are made in this context
               and discuss the connections between different approaches, with
               an emphasis on how each method approximates the expected utility
               of using a Bayesian model for the purpose of predicting future
               data.",
  journal   = "ssu",
  publisher = "Amer. Statist. Assoc., the Bernoulli Soc., the Inst. Math.
               Statist., and the Statist. Soc. Canada",
  volume    =  6,
  number    = "none",
  pages     = "142--228",
  month     =  jan,
  year      =  2012,
  keywords  = "62-02; 62C10; Bayesian; cross-validation; decision theory;
               Expected utility; information criteria; model assessment; Model
               selection; predictive; ;",
  language  = "en",
  issn      = "1935-7516",
  doi       = "10.1214/12-SS102"
}

@ARTICLE{Piironen2017-sa,
  title    = "Comparison of Bayesian predictive methods for model selection",
  author   = "Piironen, Juho and Vehtari, Aki",
  abstract = "The goal of this paper is to compare several widely used Bayesian
              model selection methods in practical model selection problems,
              highlight their differences and give recommendations about the
              preferred approaches. We focus on the variable subset selection
              for regression and classification and perform several numerical
              experiments using both simulated and real world data. The results
              show that the optimization of a utility estimate such as the
              cross-validation (CV) score is liable to finding overfitted
              models due to relatively high variance in the utility estimates
              when the data is scarce. This can also lead to substantial
              selection induced bias and optimism in the performance evaluation
              for the selected model. From a predictive viewpoint, best results
              are obtained by accounting for model uncertainty by forming the
              full encompassing model, such as the Bayesian model averaging
              solution over the candidate models. If the encompassing model is
              too complex, it can be robustly simplified by the projection
              method, in which the information of the full model is projected
              onto the submodels. This approach is substantially less prone to
              overfitting than selection based on CV-score. Overall, the
              projection method appears to outperform also the maximum a
              posteriori model and the selection of the most probable
              variables. The study also demonstrates that the model selection
              can greatly benefit from using cross-validation outside the
              searching process both for guiding the model size selection and
              assessing the predictive performance of the finally selected
              model.",
  journal  = "Stat. Comput.",
  volume   =  27,
  number   =  3,
  pages    = "711--735",
  month    =  may,
  year     =  2017,
  issn     = "0960-3174",
  doi      = "10.1007/s11222-016-9649-y"
}