Approximate Bayesian computation: Difference between revisions

Revision as of 05:57, 5 September 2023

Revision as of 00:47, 15 November 2023

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To assess how severely the dimensionality of a data set affects the analysis within the context of ABC, analytical formulas have been derived for the error of the ABC estimators as functions of the dimension of the summary statistics.<ref name="Blum10" /><ref name="Fearnhead12" /> In addition, Blum and François have investigated how the dimension of the summary statistics is related to the mean squared error for different correction adjustments to the error of ABC estimators. It was also argued that dimension reduction techniques are useful to avoid the curse-of-dimensionality, due to a potentially lower-dimensional underlying structure of summary statistics.<ref name="Blum10" /> Motivated by minimizing the quadratic loss of ABC estimators, Fearnhead and Prangle have proposed a scheme to project (possibly high-dimensional) data into estimates of the parameter posterior means; these means, now having the same dimension as the parameters, are then used as summary statistics for ABC.<ref name="Fearnhead12" />

ABC can be used to infer problems in high-dimensional parameter spaces, although one should account for the possibility of overfitting (e.g., see the model selection methods in <ref name="Ratmann" /> and <ref name="Francois" />). However, the probability of accepting the simulated values for the parameters under a given tolerance with the ABC rejection algorithm typically decreases exponentially with increasing dimensionality of the parameter space (due to the global acceptance criterion).<ref name="Csillery" /> Although no computational method (based on ABC or not) seems to be able to break the curse-of-dimensionality, methods have recently been developed to handle high-dimensional parameter spaces under certain assumptions (e.g., based on polynomial approximation on sparse grids,<ref name="Gerstner" /> which could potentially heavily reduce the simulation times for ABC). However, the applicability of such methods is problem dependent, and the difficulty of exploring parameter spaces should in general not be underestimated. For example, the introduction of deterministic global parameter estimation led to reports that the global optima obtained in several previous studies of low-dimensional problems were incorrect.<ref name="Singer" /> For certain problems, it might therefore be difficult to know whether the model is incorrect or, [[#Small number of models|as discussed above]], whether the explored region of the parameter space is inappropriate.<ref name="Templeton2009a" /> More pragmatic approaches are to cut the scope of the problem through model reduction,<ref name="Csillery" /> discretisation of variables and the use of canonical models such as noisy models. Noisy models exploit information on the conditional independence between variables.<ref>{{cite journal|last1= Cardenas |first1=IC|title= On the use of Bayesian networks as a meta-modeling approach to analyse uncertainties in slope stability analysis|journal =Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards|date=2019|volume=13|issue=1|pages=53–65|doi=10.1080/17499518.2018.1498524|bibcode=2019GAMRE..13...53C |s2cid=216590427}}</ref>

==Software==

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| [https://cran.r-project.org/web/packages/EasyABC/index.html EasyABC<br> R package]

| Several algorithms for performing efficient ABC sampling schemes, including 4 sequential sampling schemes and 3 MCMC schemes.

| <ref>{{cite journal |title=EasyABC: performing efficient approximate Bayesian computation sampling schemes using R. |last1=Jabot |first1=F |last2=Faure |first2=T |last3=Dumoulin |first3=N |doi=10.1111/2041-210X.12050 |volume=4 |issue = 7|journal=Methods in Ecology and Evolution |pages=684–687 |year=2013|bibcode=2013MEcEv...4..684J |doi-access=free }}</ref><ref>{{cite web |url=https://cran.r-project.org/web/packages/EasyABC/vignettes/EasyABC.pdf |title=EasyABC: a vignette |last1=Jabot |first1=F |last2=Faure |first2=T |last3=Dumoulin |first3=N |date=2013-06-03 |access-date=2016-07-19 |archive-date=2016-08-18 |archive-url=https://web.archive.org/web/20160818132912/https://cran.r-project.org/web/packages/EasyABC/vignettes/EasyABC.pdf |url-status=dead }}</ref>

|-

| [http://www.theosysbio.bio.ic.ac.uk/resources/abc-sysbio ABC-SysBio]

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<ref name="Beaumont2010">{{cite journal | last1 = Beaumont | first1 = MA | year = 2010 | title = Approximate Bayesian Computation in Evolution and Ecology | journal = Annual Review of Ecology, Evolution, and Systematics | volume = 41 | pages = 379–406 | doi=10.1146/annurev-ecolsys-102209-144621}}</ref>

<ref name="Bharti">{{cite journal | last1 = Bharti | first1 = A | last2 = Briol | first2 = F.-X. | last3 = Pedersen | first3 = T | year = 2021 | title = A General Method for Calibrating Stochastic Radio Channel Models with Kernels | journal = IEEE Transactions on Antennas and Propagation | volume = 70 | issue = 6 | pages = 3986–4001 | doi=10.1109/TAP.2021.3083761| arxiv = 2012.09612 | s2cid = 233880538 }}</ref>

<ref name="Bertorelle">{{cite journal | last1 = Bertorelle | first1 = G | last2 = Benazzo | first2 = A | last3 = Mona | first3 = S | year = 2010 | title = ABC as a flexible framework to estimate demography over space and time: some cons, many pros | journal = Molecular Ecology | volume = 19 | issue = 13| pages = 2609–2625 | doi=10.1111/j.1365-294x.2010.04690.x| pmid = 20561199 | bibcode = 2010MolEc..19.2609B | s2cid = 12129604 | doi-access = free }}</ref>

<ref name="Csillery">{{cite journal | last1 = Csilléry | first1 = K | last2 = Blum | first2 = MGB | last3 = Gaggiotti | first3 = OE | last4 = François | first4 = O | year = 2010 | title = Approximate Bayesian Computation (ABC) in practice | journal = Trends in Ecology & Evolution | volume = 25 | issue = 7| pages = 410–418 | doi=10.1016/j.tree.2010.04.001| pmid = 20488578 | s2cid = 13957079 }}</ref>

<ref name="Rubin">{{cite journal | last1 = Rubin | first1 = DB | year = 1984 | title = Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician | journal = The Annals of Statistics | volume = 12 | issue = 4| pages = 1151–1172 | doi=10.1214/aos/1176346785| doi-access = free }}</ref>

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<ref name="Sisson">{{cite journal | last1 = Sisson | first1 = SA | last2 = Fan | first2 = Y | last3 = Tanaka | first3 = MM | year = 2007 | title = Sequential Monte Carlo without likelihoods | journal = Proc Natl Acad Sci U S A | volume = 104 | issue = 6| pages = 1760–1765 | doi=10.1073/pnas.0607208104| pmid = 17264216 | pmc = 1794282 | bibcode = 2007PNAS..104.1760S | doi-access = free }}</ref>

<ref name="Wegmann">{{cite journal | last1 = Wegmann | first1 = D | last2 = Leuenberger | first2 = C | last3 = Excoffier | first3 = L | year = 2009 | title = Efficient approximate Bayesian computation coupled with Markov chain Monte Carlo without likelihood | journal = Genetics | volume = 182 | issue = 4| pages = 1207–1218 | doi=10.1534/genetics.109.102509| pmid = 19506307 | pmc = 2728860 }}</ref>

<ref name="Templeton2008">{{cite journal | last1 = Templeton | first1 = AR | year = 2008 | title = Nested clade analysis: an extensively validated method for strong phylogeographic inference | journal = Molecular Ecology | volume = 17 | issue = 8| pages = 1877–1880 | doi=10.1111/j.1365-294x.2008.03731.x| pmid = 18346121 | pmc = 2746708| bibcode = 2008MolEc..17.1877T }}</ref>

<ref name="Templeton2009a">{{cite journal | last1 = Templeton | first1 = AR | year = 2009 | title = Statistical hypothesis testing in intraspecific phylogeography: nested clade phylogeographical analysis vs. approximate Bayesian computation | journal = Molecular Ecology | volume = 18 | issue = 2| pages = 319–331 | doi=10.1111/j.1365-294x.2008.04026.x| pmid = 19192182 | pmc = 2696056| bibcode = 2009MolEc..18..319T }}</ref>

<ref name="Templeton2009b">{{cite journal | last1 = Templeton | first1 = AR | year = 2009 | title = Why does a method that fails continue to be used? The answer | journal = Evolution | volume = 63 | issue = 4| pages = 807–812 | doi=10.1111/j.1558-5646.2008.00600.x| pmid = 19335340 | pmc = 2693665 }}</ref>

<ref name="Berger">{{cite journal | last1 = Berger | first1 = JO | last2 = Fienberg | first2 = SE | last3 = Raftery | first3 = AE | last4 = Robert | first4 = CP | year = 2010 | title = Incoherent phylogeographic inference | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 107 | issue = 41| pages = E157 | doi=10.1073/pnas.1008762107| pmid = 20870964 | bibcode = 2010PNAS..107E.157B | pmc = 2955098 | doi-access = free }}</ref>

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<ref name="Blum2010">{{cite journal | last1 = Blum | first1 = M | last2 = Francois | first2 = O | year = 2010 | title = Non-linear regression models for approximate Bayesian computation | journal = Stat Comp | volume = 20 | pages = 63–73 | doi=10.1007/s11222-009-9116-0| arxiv = 0809.4178 | s2cid = 2403203 }}</ref>

<ref name="Leuenberger2009">{{cite journal | last1 = Leuenberger | first1 = C | last2 = Wegmann | first2 = D | year = 2009 | title = Bayesian Computation and Model Selection Without Likelihoods | journal = Genetics | volume = 184 | issue = 1| pages = 243–252 | doi=10.1534/genetics.109.109058| pmid = 19786619 | pmc = 2815920 }}</ref>

<ref name="Beaumont2010b">{{cite journal | last1 = Beaumont | first1 = MA | last2 = Nielsen | first2 = R | last3 = Robert | first3 = C | last4 = Hey | first4 = J | last5 = Gaggiotti | first5 = O |display-authors=et al | year = 2010 | title = In defence of model-based inference in phylogeography | journal = Molecular Ecology | volume = 19 | issue = 3| pages = 436–446 | doi=10.1111/j.1365-294x.2009.04515.x| pmid = 29284924 | pmc = 5743441 | bibcode = 2010MolEc..19..436B }}</ref>

<!-- <ref name="Csillery2010">{{cite journal | last1 = Csilléry | first1 = K | last2 = Blum | first2 = MGB | last3 = Gaggiotti | first3 = OE | last4 = Francois | first4 = O | year = 2010 | title = Invalid arguments against ABC: Reply to AR Templeton | journal = Trends in Ecology & Evolution | volume = 25 | pages = 490–491 | doi=10.1016/j.tree.2010.06.011}}</ref> -->

<ref name="Templeton2010">{{cite journal | last1 = Templeton | first1 = AR | year = 2010 | title = Coherent and incoherent inference in phylogeography and human evolution | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 107 | issue = 14| pages = 6376–6381 | doi=10.1073/pnas.0910647107| pmid = 20308555 | pmc = 2851988 | bibcode = 2010PNAS..107.6376T| doi-access = free }}</ref>

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<ref name="Bartlett63">{{cite journal | last1 = Bartlett | first1 = MS | year = 1963 | title = The spectral analysis of point processes | journal = Journal of the Royal Statistical Society, Series B | volume = 25 | pages = 264–296 }}</ref>

<ref name="Blum12">Blum MGB, Nunes MA, Prangle D, Sisson SA (2012) A comparative review of dimension reduction methods in approximate Bayesian computation. arxiv.org/abs/1202.3819</ref>

<ref name="Fearnhead12">{{cite journal | last1 = Fearnhead | first1 = P | last2 = Prangle | first2 = D | year = 2012 | title = Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation | journal = Journal of the Royal Statistical Society, Series B | volume = 74 | issue = 3| pages = 419–474 | doi=10.1111/j.1467-9868.2011.01010.x| citeseerx = 10.1.1.760.7753 | s2cid = 53861241 }}</ref>

<ref name="Blum10">Blum MGB (2010) Approximate Bayesian Computation: a nonparametric perspective, ''Journal of the American Statistical Association'' (105): 1178-1187</ref>

<!--<ref name="Marin11">Jean-Michel Marin, Pierre Pudlo, Christian P. Robert and Robin J. Ryder (2011) Approximate Bayesian computational methods, Statistics and Computing</ref>-->

<ref name="Cornuet08">{{cite journal | last1 = Cornuet | first1 = J-M | last2 = Santos | first2 = F | last3 = Beaumont | first3 = M |display-authors=et al | year = 2008 | title = Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation | journal = Bioinformatics | volume = 24 | issue = 23| pages = 2713–2719 | doi=10.1093/bioinformatics/btn514| pmid = 18842597 | pmc = 2639274 }}</ref>

<ref name="Csillery12">{{cite journal | last1 = Csilléry | first1 = K | last2 = François | first2 = O | last3 = Blum | first3 = MGB | year = 2012 | title = abc: an R package for approximate Bayesian computation (ABC) | journal = Methods in Ecology and Evolution | volume = 3 | issue = 3| pages = 475–479 | doi=10.1111/j.2041-210x.2011.00179.x| arxiv = 1106.2793 | bibcode = 2012MEcEv...3..475C | s2cid = 16679366 }}</ref>

<ref name="Liepe10">{{cite journal | last1 = Liepe | first1 = J | last2 = Barnes | first2 = C | last3 = Cule | first3 = E | last4 = Erguler | first4 = K | last5 = Kirk | first5 = P | last6 = Toni | first6 = T | last7 = Stumpf | first7 = MP | year = 2010 | title = ABC-SysBio—approximate Bayesian computation in Python with GPU support | journal = Bioinformatics | volume = 26 | issue = 14| pages = 1797–1799 | doi=10.1093/bioinformatics/btq278| pmid = 20591907 | pmc = 2894518 }}</ref>

<ref name="Hickerson07">{{cite journal | last1 = Hickerson | first1 = MJ | last2 = Stahl | first2 = E | last3 = Takebayashi | first3 = N | year = 2007 | title = msBayes: Pipeline for testing comparative phylogeographic histories using hierarchical approximate Bayesian computation | journal = BMC Bioinformatics | volume = 8 | issue = 268| pages = 1471–2105 | doi=10.1186/1471-2105-8-268| pmid = 17655753 | pmc = 1949838 | doi-access = free }}</ref>