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@article{Ku1966,
	Author = {H. H. Ku},
	Date-Added = {2016-02-22 19:09:32 +0000},
	Date-Modified = {2016-02-22 19:11:57 +0000},
	Journal = {J Res Nbs C Eng Inst},
	Number = {4},
	Pages = {263-273},
	Read = {1},
	Title = {Notes on the Use of Propagation of Error Formulas},
	Volume = {70},
	Year = {1966},
	Bdsk-File-1 = { }}

@article{bib:Gutenkunst2009,
	Author = {Ryan N Gutenkunst and Ryan D Hernandez and Scott H Williams and Carlos D Bustamante},
	Doi = {10.1371/journal.pgen.1000695},
	Journal = {PLoS Genet},
	Pages = {e1000695},
	Title = {Inferring the Joint Demographic History of Multiple Populations from Multidimensional {SNP} Frequency Data},
	Volume = {5},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1371/journal.pgen.1000695}}

@article{bib:Hernandez2007,
	Abstract = {Population genetic analyses often use polymorphism data from one species,
	and orthologous genomic sequences from closely related outgroup species.
	These outgroup sequences are frequently used to identify ancestral
	alleles at segregating sites and to compare the patterns of polymorphism
	and divergence. Inherent in such studies is the assumption of parsimony,
	which posits that the ancestral state of each single nucleotide polymorphism
	(SNP) is the allele that matches the orthologous site in the outgroup
	sequence, and that all nucleotide substitutions between species have
	been observed. This study tests the effect of violating the parsimony
	assumption when mutation rates vary across sites and over time. Using
	a context-dependent mutation model that accounts for elevated mutation
	rates at CpG dinucleotides, increased propensity for transitional
	versus transversional mutations, as well as other directional and
	contextual mutation biases estimated along the human lineage, we
	show (using both simulations and a theoretical model) that enough
	unobserved substitutions could have occurred since the divergence
	of human and chimpanzee to cause many statistical tests to spuriously
	reject neutrality. Moreover, using both the chimpanzee and rhesus
	macaque genomes to parsimoniously identify ancestral states causes
	a large fraction of the data to be removed while not completely alleviating
	problem. By constructing a novel model of the context-dependent mutation
	process, we can correct polymorphism data for the effect of ancestral
	misidentification using a single outgroup.},
	Author = {Ryan D Hernandez and Scott H Williamson and Carlos D Bustamante},
	Doi = {10.1093/molbev/msm108},
	Institution = {Biological Statistics and Computational Biology, Cornell University, NY, USA.},
	Journal = {Mol Biol Evol},
	Keywords = {Animals; Evolution, Molecular; Genetics, Population; Humans; Macaca mulatta; Mutation; Pan troglodytes; Polymorphism, Single Nucleotide; Selection (Genetics); Variation (Genetics)},
	Month = {Aug},
	Number = {8},
	Owner = {ryang},
	Pages = {1792--1800},
	Pii = {msm108},
	Pmid = {17545186},
	Timestamp = {2008.06.04},
	Title = {Context dependence, ancestral misidentification, and spurious signatures of natural selection.},
	Url = {http://dx.doi.org/10.1093/molbev/msm108},
	Volume = {24},
	Year = {2007},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/molbev/msm108}}

@article{bib:Hudson2002,
	Abstract = {A Monte Carlo computer program is available to generate samples drawn
	from a population evolving according to a Wright-Fisher neutral model.
	The program assumes an infinite-sites model of mutation, and allows
	recombination, gene conversion, symmetric migration among subpopulations,
	and a variety of demographic histories. The samples produced can
	be used to investigate the sampling properties of any sample statistic
	under these neutral models.},
	Author = {Richard R Hudson},
	Institution = {Department of Ecology and Evolution, University of Chicago, 1101 E. 57th Street, Chicago, IL 60637, USA. rr-hudson@uchicago.edu},
	Journal = {Bioinformatics},
	Keywords = {Computational Biology; Gene Conversion; Genetics, Population; Models, Genetic; Monte Carlo Method; Recombination, Genetic; Software; Variation (Genetics)},
	Month = {Feb},
	Number = {2},
	Owner = {ryang},
	Pages = {337--338},
	Pmid = {11847089},
	Timestamp = {2008.08.13},
	Title = {Generating samples under a {W}right-{F}isher neutral model of genetic variation.},
	Volume = {18},
	Year = {2002}}

@article{bib:Pierce1986,
	Author = {Pierce, Donald A. and Schafer, Daniel W.},
	Copyright = {Copyright {\copyright} 1986 American Statistical Association},
	Issn = {01621459},
	Journal = {J Am Stat Assoc},
	Jstor_Articletype = {primary_article},
	Jstor_Formatteddate = {Dec., 1986},
	Number = {396},
	Pages = {977--986},
	Publisher = {American Statistical Association},
	Title = {Residuals in Generalized Linear Models},
	Url = {http://www.jstor.org/stable/2289071},
	Volume = {81},
	Year = {1986},
	Bdsk-Url-1 = {http://www.jstor.org/stable/2289071}}

@article{bib:Weir1984,
	Author = {B S Weir and C Clark Cockerham},
	Journal = {Evolution},
	Number = {6},
	Owner = {ryang},
	Pages = {1358--1370},
	Timestamp = {2008.08.13},
	Title = {Estimating {F}-statistics for the analysis of population structure},
	Volume = {38},
	Year = {1984}}

@article{bib:Wiuf2006,
	Abstract = {Composite likelihood methods have become very popular for the analysis
	of large-scale genomic data sets because of the computational intractability
	of the basic coalescent process and its generalizations: It is virtually
	impossible to calculate the likelihood of an observed data set spanning
	a large chromosomal region without using approximate or heuristic
	methods. Composite likelihood methods are approximate methods and,
	in the present article, assume the likelihood is written as a product
	of likelihoods, one for each of a number of smaller regions that
	together make up the whole region from which data is collected. A
	very general framework for neutral coalescent models is presented
	and discussed. The framework comprises many of the most popular coalescent
	models that are currently used for analysis of genetic data. Assume
	data is collected from a series of consecutive regions of equal size.
	Then it is shown that the observed data forms a stationary, ergodic
	process. General conditions are given under which the maximum composite
	estimator of the parameters describing the model (e.g. mutation rates,
	demographic parameters and the recombination rate) is a consistent
	estimator as the number of regions tends to infinity.},
	Author = {Carsten Wiuf},
	Doi = {10.1007/s00285-006-0031-0},
	Institution = {Bioinformatics Research Center, University of Aarhus, H{\o}egh-Guldbergsgade 10, Building 1090, 8000 Aarhus C, Denmark. wiuf@birc.au.dk},
	Journal = {J Math Biol},
	Keywords = {Base Sequence; Data Interpretation, Statistical; Genome; Likelihood Functions; Models, Genetic},
	Month = {Nov},
	Number = {5},
	Owner = {ryang},
	Pages = {821--841},
	Pmid = {16960689},
	Timestamp = {2008.08.13},
	Title = {Consistency of estimators of population scaled parameters using composite likelihood.},
	Url = {http://dx.doi.org/10.1007/s00285-006-0031-0},
	Volume = {53},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00285-006-0031-0}}

@article{Self1987,
	Abstract = {Abstract Large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described. Specifically, the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived. These results generalize the work of Moran (1971), Chant (1974), and Chernoff (1954). Some of Chant's results are shown to be incorrect. The approach used in deriving these results follows from comments made by Moran and Chant. The problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate Gaussian distribution from a sample of size 1. In this representation the Gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator. Thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the Gaussian random variable onto the region of admissible values for the mean. A variety of examples is provided for which the limiting distributions of likelihood ratio statistics are mixtures of chi-squared distributions. One example is provided with a nuisance parameter on the boundary for which the asymptotic distribution is not a mixture of chi-squared distributions. Abstract Large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described. Specifically, the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived. These results generalize the work of Moran (1971), Chant (1974), and Chernoff (1954). Some of Chant's results are shown to be incorrect. The approach used in deriving these results follows from comments made by Moran and Chant. The problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate Gaussian distribution from a sample of size 1. In this representation the Gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator. Thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the Gaussian random variable onto the region of admissible values for the mean. A variety of examples is provided for which the limiting distributions of likelihood ratio statistics are mixtures of chi-squared distributions. One example is provided with a nuisance parameter on the boundary for which the asymptotic distribution is not a mixture of chi-squared distributions.},
	Author = {Self, Steven G. and Liang, Kung-yee},
	Issn = {0162-1459},
	Journal = {J. Am. Stat. Assoc.},
	Keywords = {Boundary},
	Number = {398},
	Pages = {605--610},
	Publisher = {Taylor \& Francis},
	Title = {{Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions}},
	Url = {http://www.tandfonline.com/doi/abs/10.1080/01621459.1987.10478472$\backslash$nhttp://www.jstor.org/stable/info/2289471},
	Volume = {82},
	Year = {1987},
	Bdsk-Url-1 = {http://www.tandfonline.com/doi/abs/10.1080/01621459.1987.10478472$%5Cbackslash$nhttp://www.jstor.org/stable/info/2289471}}

@article{Coffman2016,
	Author = {Coffman, Alec J and Hsieh, PingHsun and Gravel, Simon and Gutenkunst, Ryan N},
	Title = {{Computationally efficient composite likelihood statistics for demographic inference}},
	Year = {2016},
        journal = {Mol. Biol. Evol.},
        volume={33},
        pages={591--593}}
