Although genome-wide association studies have successfully identified thousands of risk loci for complex traits, only a handful of the biologically causal variants, responsible for association at these loci, have been successfully identified. Current statistical methods for identifying causal variants at risk loci either use the strength of the association signal in an iterative conditioning framework or estimate probabilities for variants to be causal. A main drawback of existing methods is that they rely on the simplifying assumption of a single causal variant at each risk locus, which is typically invalid at many risk loci. In this work, we propose a new statistical framework that allows for the possibility of an arbitrary number of causal variants when estimating the posterior probability of a variant being causal. A direct benefit of our approach is that we predict a set of variants for each locus that under reasonable assumptions will contain all of the true causal variants with a high confidence level (e.g., 95%) even when the locus contains multiple causal variants. We use simulations to show that our approach provides 20-50% improvement in our ability to identify the causal variants compared to the existing methods at loci harboring multiple causal variants. We validate our approach using empirical data from an expression QTL study of CHI3L2 to identify new causal variants that affect gene expression at this locus. CAVIAR is publicly available online at http://genetics.cs.ucla.edu/caviar/.A LTHOUGH genome-wide association studies (GWAS) reproducibly identified thousands of risk loci (Hakonarson et al. 2007;Sladek et al. 2007;Zeggini et al. 2007; Yang et al. 2011a,b;Kottgen et al. 2013;Lu et al. 2013;Ripke et al. 2013), only a handful of causal genetic variants (i.e., variants that biologically alter disease risk) have been found (Altshuler et al. 2008;Manolio et al. 2008;McCarthy et al. 2008), thus prohibiting the mechanistic understanding of the genetic basis of common diseases. The linkage disequilibrium (LD) (Pritchard and Przeworski 2001;Reich et al. 2001) structure of the human genome has greatly benefited GWAS in interrogating only a subset of all variants to assay common variation across the genome. Unfortunately, LD hinders the identification of causal variants at risk loci in fine-mapping studies as at each locus, there are often tens to hundreds of variants tightly linked to the reported associated single-nucleotide polymorphism (SNP) (Malo et al. 2008;Maller et al. 2012;Yang et al. 2012). In a continued effort to identify causal variants, many finemapping studies that assess genetic variation at known GWAS risk loci are currently underway (Bauer et al. 2013;Coram et al. 2013;Diogo et al. 2013;Gong et al. 2013;Marigorta and Navarro 2013;Peters et al. 2013;Wu et al. 2013).Fine-mapping studies typically follow a two-step procedure. First, a statistical analysis of the association signal is performed to identify a minimum set of SNPs that can explain the signal. Second, the SNPs that ar...