-
Notifications
You must be signed in to change notification settings - Fork 7
/
citations.bib
381 lines (368 loc) · 20.5 KB
/
citations.bib
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
@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"
}