A new Bayesian approach for QTL mapping of family data.

In this paper, we propose a new Bayesian approach for QTL mapping of family data. The main purpose is to model a phenotype as a function of QTLs' effects. The model considers the detailed familiar dependence and it does not rely on random effects. It combines the probability for Mendelian inheritance of parents' genotype and the correlation between flanking markers and QTLs. This is an advance when compared with models which use only Mendelian segregation or only the correlation between markers and QTLs to estimate transmission probabilities. We use the Bayesian approach to estimate the number of QTLs, their location and the additive and dominance effects. We compare the performance of the proposed method with variance component and LASSO models using simulated and GAW17 data sets. Under tested conditions, the proposed method outperforms other methods in aspects such as estimating the number of QTLs, the accuracy of the QTLs' position and the estimate of their effects. The results of the application of the proposed method to data sets exceeded all of our expectations.

Clustering distributions with the marginalized nested Dirichlet process.

We introduce a marginal version of the nested Dirichlet process to cluster distributions or histograms. We apply the model to cluster genes by patterns of gene-gene interaction. The proposed approach is based on the nested partition that is implied in the original construction of the nested Dirichlet process. It allows simulation exact inference, as opposed to a truncated Dirichlet process approximation. More importantly, the construction highlights the nature of the nested Dirichlet process as a nested partition of experimental units. We apply the proposed model to inference on clustering genes related to DNA mismatch repair (DMR) by the distribution of gene-gene interactions with other genes. Gene-gene interactions are recorded as coefficients in an auto-logistic model for the co-expression of two genes, adjusting for copy number variation, methylation and protein activation. These coefficients are extracted from an online database, called Zodiac, computed based on The Cancer Genome Atlas (TCGA) data. We compare results with a variation of k-means clustering that is set up to cluster distributions, truncated NDP and a hierarchical clustering method. The proposed inference shows favorable performance, under simulated conditions and also in the real data sets.

A generalized mixture model applied to diabetes incidence data.

We present a generalization of the usual (independent) mixture model to accommodate a Markovian first-order mixing distribution. We propose the data-driven reversible jump, a Markov chain Monte Carlo (MCMC) procedure, for estimating the a posteriori probability for each model in a model selection procedure and estimating the corresponding parameters. Simulated datasets show excellent performance of the proposed method in the convergence, model selection, and precision of parameters estimates. Finally, we apply the proposed method to analyze USA diabetes incidence datasets.

Data-Driven Reversible Jump for QTL Mapping.

We propose a birth-death-merge data-driven reversible jump (DDRJ) for multiple-QTL mapping where the phenotypic trait is modeled as a linear function of the additive and dominance effects of the unknown QTL genotypes. We compare the performance of the proposed methodology, usual reversible jump (RJ) and multiple-interval mapping (MIM), using simulated and real data sets. Compared with RJ, DDRJ shows a better performance to estimate the number of QTLs and their locations on the genome mainly when the QTLs effect is moderate, basically as a result of better mixing for transdimensional moves. The inclusion of a merge step of consecutive QTLs in DDRJ is efficient, under tested conditions, to avoid the split of true QTL's effects between false QTLs and, consequently, selection of the wrong model. DDRJ is also more precise to estimate the QTLs location than MIM in which the number of QTLs need to be specified in advance. As DDRJ is more efficient to identify and characterize QTLs with smaller effect, this method also appears to be useful and brings contributions to identifying single-nucleotide polymorphisms (SNPs) that usually have a small effect on phenotype.