Spatial probit models for multivariate ordinal data: computational efficiency and parameter identifiability

2013 Summer.Includes bibliographical references.The Colorado Natural Heritage Program (CNHP) at Colorado State University evaluates Colorado's rare and at-risk species and habitats and promotes conservation of biological resources. One of the goals of the program is to determine the condition of wetlands across the state of Colorado. The data collected are measurements, or metrics, representing landscape condition, biotic condition, hydrologic condition, and physiochemical condition in river basins statewide. The metrics differ in variable type, including binary, ordinal, count, and continuous response data. It is common practice to uniformly discretize the metrics into ordinal values and combine them using a weighted-average to obtain a univariate measure of wetland condition. The weights assigned to each metric are based on best professional judgement. The motivation of this work was to improve on the user-defined weights by developing a statistical model to estimate the weights using observed data. The challenges of creating a model that fulfills this requirement are many. First, the observed data are multivariate and consist of different variable types which we wish to preserve. Second, the multivariate response data are not independent across river basin because wetlands at close proximity are correlated. Third, we want the model to provide a univariate measure of wetland condition that can be compared across the state. Lastly, it is of interest to the ecologists to predict the univariate measure of wetland condition at unobserved locations requiring covariate information to be incorporated into the model. We propose a multivariate multilevel latent variable model to address these challenges. Latent continuous response variables are used to model the different types of response variables. An additional latent variable, or common factor, is used as a univariate measure of wetland condition. The mean of the common factor contains observable covariate data in order to predict at unobserved locations. The variance of the common factor is defined by a spatial covariance function to account for the dependence between wetlands. The majority of the metrics reported by the CNHP are ordinal. Therefore, our primary focus is modeling multivariate ordinal response data where binary data is a special case. Probit linear models and probit linear mixed models are examples of models for ordinal response data. Probit models are attractive in that they can be defined in terms of latent variables. Computational efficiency is a major issue when fitting multivariate latent variable models in a Bayesian framework using Markov chain Monte Carlo (MCMC). There is also a high computation cost for running MCMC when fitting geostatistical spatial models. Data augmentation and parameter expansion are both modeling techniques that can lead to optimal iterative sampling algorithms for MCMC. Data augmentation allows for simpler and more feasible simulation from a posterior distribution. Parameter expansion is a method for accelerating convergence of iterative sample algorithms and can enhance data augmentation algorithms. We propose data augmentation and parameter-expanded data augmentation algorithms for fitting MCMC to spatial probit models for binary and ordinal response data. Parameter identifiability is another challenge when fitting multivariate latent variable models due to the multivariate response data, number of parameters, unobserved latent variables, and spatial random effects. We investigate parameter identifiability for the common factor model for multivariate ordinal response data. We extend the common factor model to include covariates and spatial correlation so we can predict wetland condition at unobserved locations. The partial sill and range parameter of a spatial covariance function are difficult to estimate because they are near-nonidentifiable. We propose a new parameterization for the covariance function of the spatial probit model that leads to better mixing and faster convergence of the MCMC. Whereas our spatial probit model for ordinal response data follows the common factor model approach, there are other forms of the spatial probit model. We give a comprehensive comparison of two types of spatial probit models, which we refer to as the first-stage and second-stage spatial probit model. We discuss the implications of fitting each model and compare them in terms of their impact on parameter estimation and prediction at unobserved locations. We propose a new approximation for predicting ordinal response data that is both accurate and efficient. We apply the multivariate multilevel latent variable model to data collected in the North Platte and Rio Grande River Basins to evaluate wetland condition. We obtain statistically derived weights for each of the response metrics with confidence limits. Lastly, we predict the univariate measure of wetland condition at unobserved locations

SLIQ: Simple Linear Inequalities for Efficient Contig Scaffolding

Scaffolding is an important subproblem in "de novo" genome assembly in which mate pair data are used to construct a linear sequence of contigs separated by gaps. Here we present SLIQ, a set of simple linear inequalities derived from the geometry of contigs on the line that can be used to predict the relative positions and orientations of contigs from individual mate pair reads and thus produce a contig digraph. The SLIQ inequalities can also filter out unreliable mate pairs and can be used as a preprocessing step for any scaffolding algorithm. We tested the SLIQ inequalities on five real data sets ranging in complexity from simple bacterial genomes to complex mammalian genomes and compared the results to the majority voting procedure used by many other scaffolding algorithms. SLIQ predicted the relative positions and orientations of the contigs with high accuracy in all cases and gave more accurate position predictions than majority voting for complex genomes, in particular the human genome. Finally, we present a simple scaffolding algorithm that produces linear scaffolds given a contig digraph. We show that our algorithm is very efficient compared to other scaffolding algorithms while maintaining high accuracy in predicting both contig positions and orientations for real data sets.Comment: 16 pages, 6 figures, 7 table

pGQL: A probabilistic graphical query language for gene expression time courses

<p>Abstract</p> <p>Background</p> <p>Timeboxes are graphical user interface widgets that were proposed to specify queries on time course data. As queries can be very easily defined, an exploratory analysis of time course data is greatly facilitated. While timeboxes are effective, they have no provisions for dealing with noisy data or data with fluctuations along the time axis, which is very common in many applications. In particular, this is true for the analysis of gene expression time courses, which are mostly derived from noisy microarray measurements at few unevenly sampled time points. From a data mining point of view the robust handling of data through a sound statistical model is of great importance.</p> <p>Results</p> <p>We propose probabilistic timeboxes, which correspond to a specific class of Hidden Markov Models, that constitutes an established method in data mining. Since HMMs are a particular class of probabilistic graphical models we call our method Probabilistic Graphical Query Language. Its implementation was realized in the free software package pGQL. We evaluate its effectiveness in exploratory analysis on a yeast sporulation data set.</p> <p>Conclusions</p> <p>We introduce a new approach to define dynamic, statistical queries on time course data. It supports an interactive exploration of reasonably large amounts of data and enables users without expert knowledge to specify fairly complex statistical models with ease. The expressivity of our approach is by its statistical nature greater and more robust with respect to amplitude and frequency fluctuation than the prior, deterministic timeboxes.</p

Impact of biopower generation on eastern US forests

Biopower, electricity generated from biomass, is a major source of renewable energy in the US. About ten percent of US non-hydro renewable electricity in 2020 was generated from biomass. Despite significant growth in woody biomass use for electricity in recent decades, a systematic assessment of associated impacts on forest resources is lacking. This study assessed associations between biopower generation, and selected timberland structure indicators and carbon stocks across 438 areas surrounding wood-using and coal-burning power plants in the Eastern US from 2005 to 2017. Timberland areas around plants generating biopower were associated with more live and standing-dead trees, and carbon in their respective stocks, than comparable areas of neighboring plants only burning coal. We also detected an inverse association between the number of biopower plants and number of live and dead trees, and respective carbon stocks. We discerned an upward temporal trajectory in carbon stocks within live trees with continued biopower generation. We found no significant differences related to the amount of MWh biopower generation within the analysis areas. Net impacts of biopower descriptors on timberland attributes point to a positive trend in selected ecological conditions and carbon balances. The upward temporal trend in carbon stocks with longer generation of wood-based biopower may point to a plausibly sustainable contribution to the decarbonization of the US electricity sector

Identifying and characterizing extrapolation in multivariate response data

Extrapolation is defined as making predictions beyond the range of the data used to estimate a statistical model. In ecological studies, it is not always obvious when and where extrapolation occurs because of the multivariate nature of the data. Previous work on identifying extrapolation has focused on univariate response data, but these methods are not directly applicable to multivariate response data, which are more and more common in ecological investigations. In this paper, we extend previous work that identified extrapolation by applying the predictive variance from the univariate setting to the multivariate case. We illustrate our approach through an analysis of jointly modeled lake nutrients and indicators of algal biomass and water clarity in over 7000 inland lakes from across the Northeast and Mid-west US. In addition, we illustrate novel exploratory approaches for identifying regions of covariate space where extrapolation is more likely to occur using classification and regression trees.Comment: 28 pages, 2 supplementary files, 6 main figures, 2 supplementary figures, 2 supplementary table

Evaluation of reference genes for RT-qPCR studies in the seagrass zostera muelleri exposed to light limitation

Seagrass meadows are threatened by coastal development and global change. In the face of these pressures, molecular techniques such as reverse transcription quantitative real-time PCR (RT-qPCR) have great potential to improve management of these ecosystems by allowing early detection of chronic stress. In RT-qPCR, the expression levels of target genes are estimated on the basis of reference genes, in order to control for RNA variations. Although determination of suitable reference genes is critical for RT-qPCR studies, reports on the evaluation of reference genes are still absent for the major Australian species Zostera muelleri subsp. capricorni (Z. muelleri). Here, we used three different software (geNorm, NormFinder and Bestkeeper) to evaluate ten widely used reference genes according to their expression stability in Z. muelleri exposed to light limitation. We then combined results from different software and used a consensus rank of four best reference genes to validate regulation in Photosystem I reaction center subunit IV B and Heat Stress Transcription factor A- gene expression in Z. muelleri under light limitation. This study provides the first comprehensive list of reference genes in Z. muelleri and demonstrates RT-qPCR as an effective tool to identify early responses to light limitation in seagrass

SeagrassDB: An open-source transcriptomics landscape for phylogenetically profiled seagrasses and aquatic plants

© 2018, The Author(s). Seagrasses and aquatic plants are important clades of higher plants, significant for carbon sequestration and marine ecological restoration. They are valuable in the sense that they allow us to understand how plants have developed traits to adapt to high salinity and photosynthetically challenged environments. Here, we present a large-scale phylogenetically profiled transcriptomics repository covering seagrasses and aquatic plants. SeagrassDB encompasses a total of 1,052,262 unigenes with a minimum and maximum contig length of 8,831 bp and 16,705 bp respectively. SeagrassDB provides access to 34,455 transcription factors, 470,568 PFAM domains, 382,528 prosite models and 482,121 InterPro domains across 9 species. SeagrassDB allows for the comparative gene mining using BLAST-based approaches and subsequent unigenes sequence retrieval with associated features such as expression (FPKM values), gene ontologies, functional assignments, family level classification, Interpro domains, KEGG orthology (KO), transcription factors and prosite information. SeagrassDB is available to the scientific community for exploring the functional genic landscape of seagrass and aquatic plants at: http://115.146.91.129/index.php