arXiv subjects

Yongtao Guan

Publications and source records attributed to Yongtao Guan.

24 records · Page 2Linked to original sources

arXiv2013

Estimating daily nitrogen dioxide level: Exploring traffic effects

Data used to assess acute health effects from air pollution typically have good temporal but poor spatial resolution or the opposite. A modified longitudinal model was developed that sought to improve resolution in both domains by bringing together data from three sources to estimate daily levels of nitrogen dioxide ($\mathrm {NO}_2$) at a geographic location. Monthly $\mathrm {NO}_2$ measurements at 316 sites were made available by the Study of Traffic, Air quality and Respiratory health (STAR). Four US Environmental Protection Agency monitoring stations have hourly measurements of $\mathrm {NO}_2$. Finally, the Connecticut Department of Transportation provides data on traffic density on major roadways, a primary contributor to $\mathrm {NO}_2$ pollution. Inclusion of a traffic variable improved performance of the model, and it provides a method for estimating exposure at points that do not have direct measurements of the outcome. This approach can be used to estimate daily variation in levels of $\mathrm {NO}_2$ over a region.

stat.AP↗

arXiv2013

Detecting the structure of haplotypes, local ancestry and excessive local European ancestry in Mexicans

We present a two-layer hidden Markov model to detect structure of haplotypes for unrelated individuals. This allows modeling two scales of linkage disequilibrium (one within a group of haplotypes and one between groups), thereby taking advantage of rich haplotype information to infer local ancestry for admixed individuals. Our method outperforms competing state-of-art methods, particularly for regions of small ancestral track lengths. Applying our method to Mexican samples in HapMap3, we found five coding regions, ranging from $0.3 -1.3$ megabase (Mb) in lengths, that exhibit excessive European ancestry (average dosage > 1.6). A particular interesting region of 1.1Mb (with average dosage 1.95) locates on Chromosome 2p23 that harbors two genes, PXDN and MYT1L, both of which are associated with autism and schizophrenia. In light of the low prevalence of autism in Hispanics, this region warrants special attention. We confirmed our findings using Mexican samples from the 1000 genomes project. A software package implementing methods described in the paper is freely available at \url{http://bcm.edu/cnrc/mcmcmc}

q-bio.QM↗

arXiv2013

Quasi-likelihood for Spatial Point Processes

Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates. When Cox or cluster process models are used to accommodate clustering not accounted for by the available covariates, likelihood based inference becomes computationally cumbersome due to the complicated nature of the likelihood function and the associated score function. It is therefore of interest to consider alternative more easily computable estimating functions. We derive the optimal estimating function in a class of first-order estimating functions. The optimal estimating function depends on the solution of a certain Fredholm integral equation which in practice is solved numerically. The approximate solution is equivalent to a quasi-likelihood for binary spatial data and we therefore use the term quasi-likelihood for our optimal estimating function approach. We demonstrate in a simulation study and a data example that our quasi-likelihood method for spatial point processes is both statistically and computationally efficient.

stat.ME↗

arXiv2012

Small World MCMC with Tempering: Ergodicity and Spectral Gap

When sampling a multi-modal distribution $π(x)$, $x\in \rr^d$, a Markov chain with local proposals is often slowly mixing; while a Small-World sampler \citep{guankrone} -- a Markov chain that uses a mixture of local and long-range proposals -- is fast mixing. However, a Small-World sampler suffers from the curse of dimensionality because its spectral gap depends on the volume of each mode. We present a new sampler that combines tempering, Small-World sampling, and producing long-range proposals from samples in companion chains (e.g. Equi-Energy sampler). In its simplest form the sampler employs two Small-World chains: an exploring chain and a sampling chain. The exploring chain samples $π_t(x) \propto π(x)^{1/t}$, $t\in [1,\infty)$, and builds up an empirical distribution. Using this empirical distribution as its long-range proposal, the sampling chain is designed to have a stationary distribution $π(x)$. We prove ergodicity of the algorithm and study its convergence rate. We show that the spectral gap of the exploring chain is enlarged by a factor of $t^{d}$ and that of the sampling chain is shrunk by a factor of $t^{-d}$. Importantly, the spectral gap of the exploring chain depends on the "size" of $π_t(x)$ while that of sampling chain does not. Overall, the sampler enlarges a severe bottleneck at the cost of shrinking a mild one, hence achieves faster mixing. The penalty on the spectral gap of the sampling chain can be significantly alleviated when extending the algorithm to multiple chains whose temperatures $\{t_k\}$ follow a geometric progression. If we allow $t_k \rightarrow 0$, the sampler becomes a global optimizer.

stat.ME↗

arXiv2011

Bayesian variable selection regression for genome-wide association studies and other large-scale problems

We consider applying Bayesian Variable Selection Regression, or BVSR, to genome-wide association studies and similar large-scale regression problems. Currently, typical genome-wide association studies measure hundreds of thousands, or millions, of genetic variants (SNPs), in thousands or tens of thousands of individuals, and attempt to identify regions harboring SNPs that affect some phenotype or outcome of interest. This goal can naturally be cast as a variable selection regression problem, with the SNPs as the covariates in the regression. Characteristic features of genome-wide association studies include the following: (i) a focus primarily on identifying relevant variables, rather than on prediction; and (ii) many relevant covariates may have tiny effects, making it effectively impossible to confidently identify the complete "correct" subset of variables. Taken together, these factors put a premium on having interpretable measures of confidence for individual covariates being included in the model, which we argue is a strength of BVSR compared with alternatives such as penalized regression methods. Here we focus primarily on analysis of quantitative phenotypes, and on appropriate prior specification for BVSR in this setting, emphasizing the idea of considering what the priors imply about the total proportion of variance in outcome explained by relevant covariates. We also emphasize the potential for BVSR to estimate this proportion of variance explained, and hence shed light on the issue of "missing heritability" in genome-wide association studies.

stat.AP↗

arXiv2007

Small-world MCMC and convergence to multi-modal distributions: From slow mixing to fast mixing

We compare convergence rates of Metropolis--Hastings chains to multi-modal target distributions when the proposal distributions can be of ``local'' and ``small world'' type. In particular, we show that by adding occasional long-range jumps to a given local proposal distribution, one can turn a chain that is ``slowly mixing'' (in the complexity of the problem) into a chain that is ``rapidly mixing.'' To do this, we obtain spectral gap estimates via a new state decomposition theorem and apply an isoperimetric inequality for log-concave probability measures. We discuss potential applicability of our result to Metropolis-coupled Markov chain Monte Carlo schemes.

math.PR↗