Ultra-Fast Approximate Inference Using Variational Functional Mixed Models.

While Bayesian functional mixed models have been shown effective to model functional data with various complex structures, their application to extremely high-dimensional data is limited due to computational challenges involved in posterior sampling. We introduce a new computational framework that enables ultra-fast approximate inference for high-dimensional data in functional form. This framework adopts parsimonious basis to represent functional observations, which facilitates efficient compression and parallel computing in basis space. Instead of performing expensive Markov chain Monte Carlo sampling, we approximate the posterior distribution using variational Bayes and adopt a fast iterative algorithm to estimate parameters of the approximate distribution. Our approach facilitates a fast multiple testing procedure in basis space, which can be used to identify significant local regions that reflect differences across groups of samples. We perform two simulation studies to assess the performance of approximate inference, and demonstrate applications of the proposed approach by using a proteomic mass spectrometry dataset and a brain imaging dataset. Supplementary materials are available online.

Estimating mutation rates in a Markov branching process using approximate Bayesian computation.

Estimating microbial mutation rates is an essential task in evolutionary biology, with wide range applications in related fields such as virology, epidemiology, clinic and public health, and antibiotic research. Significant progress has been made on this research since 1943 when Luria-Delbrück fluctuation analysis was first introduced. However, existing estimators of mutation rates are heavily reliant on model assumptions in fluctuation analysis, and become less applicable to real microbial experiments which deviate from the model assumptions. To overcome this difficulty, we propose to model fluctuation experimental data by a two-type Markov branching process (MBP) and use approximate Bayesian computation (ABC) to estimate the mutation probability parameters. Such an ABC-based mutation rate estimator is based on intensive simulations from the mutation process, thereby taking advantage of modern computing power. Most importantly, its likelihood-free feature allows more complex and realistic setups of the mutation process, especially when the distribution of the number of mutants cannot be easily derived. To further improve computation efficiency, we use a Gaussian process surrogate to substitute the simulator in the ABC algorithm, and call the resulting estimator GPS-ABC. Simulation studies show that, when used to estimate constant mutation rate in MBP, ABC-based estimators generally outperform traditional moment or likelihood-based estimators. When mutations occur in two stages, i.e., in MBP with a piece-wise constant mutation rate function, traditional mutation rate estimators become not applicable, yet GPS-ABC still achieves reasonable estimates. Finally, the proposed GPS-ABC estimator is used to analyze real fluctuation experimental datasets for studying drug resistance.

A validation study for a bat-inspired sonar sensing simulator.

Many species of bats rely on echoes to forage and navigate in densely vegetated environments. Foliage echoes in some cases can help bats gather information about the environment, whereas in others may generate clutter that can mask prey echoes during foraging. It is therefore important to study foliage echoes and their role in bat's sensory ecology. In our prior work, a foliage echo simulator has been developed; simulated echoes has been compared with field recordings using a biomimetic sonar head. In this work, we improve the existing simulator by allowing more flexible experimental setups and enabling a closer match with the experiments. Specifically, we add additional features into the simulator including separate directivity patterns for emitter and receiver, the ability to place emitter and receiver at distinct locations, and multiple options to orient the foliage to mimic natural conditions like strong wind. To study how accurately the simulator can replicate the real echo-generating process, we compare simulated echoes with experimental echoes measured by ensonifying a single leaf across four different species of trees. We further extend the prior work on estimating foliage parameters to estimating a map of the environment.

Association testing for binary trees-A Markov branching process approach.

We propose a new approach to test associations between binary trees and covariates. In this approach, binary-tree structured data are treated as sample paths of binary fission Markov branching processes (bMBP). We propose a generalized linear regression model and developed inference procedures for association testing, including variable selection and estimation of covariate effects. Simulation studies show that these procedures are able to accurately identify covariates that are associated with the binary tree structure by impacting the rate parameter of the bMBP. The problem of association testing on binary trees is motivated by modeling hierarchical clustering dendrograms of pixel intensities in biomedical images. By using semi-synthetic data generated from a real brain-tumor image, our simulation studies show that the bMBP model is able to capture the characteristics of dendrogram trees in brain-tumor images. Our final analysis of the glioblastoma multiforme brain-tumor data from The Cancer Imaging Archive identified multiple clinical and genetic variables that are potentially associated with brain-tumor heterogeneity.

Estimate the Unknown Environment with Biosonar Echoes-A Simulation Study.

Unmanned aerial vehicles (UAVs) have shown great potential in various applications such as surveillance, search and rescue. To perform safe and efficient navigation, it is vitally important for a UAV to evaluate the environment accurately and promptly. In this work, we present a simulation study for the estimation of foliage distribution as a UAV equipped with biosonar navigates through a forest. Based on a simulated forest environment, foliage echoes are generated by using a bat-inspired bisonar simulator. These biosonar echoes are then used to estimate the spatial distribution of both sparsely and densely distributed tree leaves. While a simple batch processing method is able to estimate sparsely distributed leaf locations well, a wavelet scattering technique coupled with a support vector machine (SVM) classifier is shown to be effective to estimate densely distributed leaves. Our approach is validated by using multiple setups of leaf distributions in the simulated forest environment. Ninety-seven percent accuracy is obtained while estimating thickly distributed foliage.

A simulation framework for bio-inspired sonar sensing with Unmanned Aerial Vehicles.

We introduce a unified simulation framework that generates natural sensing environments and produces biosonar echoes under various sensing scenarios. This framework produces rich sensory data with environmental information completely known, thus can be used for the training of robotic algorithms for biosonar-based Unmanned Aerial Vehicles. The simulated environment consists of random trees with full geometry of the tree foliage. To simulate a single tree, we adopt the Lindenmayer system to generate the initial branching pattern and integrate that with the available measurements of the 3D computer-aided design object files to create natural-looking branches, sub-branches, and leaves. A forest is formed by simulating trees at random locations generated by using an inhomogeneous Poisson process. While our simulated environments can be generally used for testing other sensors and training robotic algorithms, in this study we focus on testing bat-inspired Unmanned Aerial Vehicles that recreate bat's flying behavior through biosonar sensors. To this end, we also introduce an foliage echo simulator that produces biosonar echoes while mimicking bat's biosonar system. We demonstrate the application of the proposed simulation framework by generating real-world scenarios with multiple trees and computing the resulting impulse responses under static or dynamic motions of an Unmanned Aerial Vehicle.

[Characteristics and Sources Apportionment of Fine Particulate Matter in a Typical Coastal City During the Heating Period].

To clarify the pollution characteristics and sources of PM2.5 in Weihai during the heating period, PM2.5 samples from ambient air were collected at three routine air quality monitoring sites from January to March 2018. The OC, EC, water-soluble ions, and elements in PM2.5 were analyzed, and the sources of PM2.5 were identified using the PMF model. The results showed that the average daily mass concentration of PM2.5 was (33.80±22.45) µg·m-3, and the NO3-, NH4+, SO42-, OC, and EC were the main components of PM2.5. As a coastal city, the Cl- ratio was relatively high in PM2.5. Meanwhile, the compositions of PM2.5 were affected by the emission of pollutants with local industrial characteristics. Both NO3-/SO42- and OC/EC showed that mobile sources had a high contribution during the heating period. The acid-base ions in water-soluble ions showed that PM2.5 is weakly alkaline, and NH4+ is excessive. NH4+ mainly existed in the form of NH4NO3 and (NH4)2SO4. During the polluted period, the concentration of secondary pollutants significantly increased, and the mass concentrations of NH4+, NO3-, SO42-, OC, and EC were 4.21, 5.27, 3.23, 2.02, and 1.81 times that of the cleaning period, respectively. The PMF model showed that secondary aerosols were the major source of PM2.5, accounting for 32.4%-36.0% of PM2.5. The contributions of vehicle exhaust, coal combustion, biomass burning, and dust were 15.6%-18.9%, 12.1%-17.8%, 9.0%-10.4%, and 8.6%-11.3%, respectively, while the contributions of process emission (2.1%-8.3%), non-road mobile sources (2.4%-3.7%), and sea salt (3.5%-5.6%) were less.

Precision Implementation of Minimal Erythema Dose (MED) Testing to Assess Individual Variation in Human Inflammatory Response.

Minimal erythema dose (MED) testing is frequently used in clinical settings for determining the smallest amount of ultraviolet (UV) irradiation necessary to produce erythema (inflammatory reddening) on the surface of the skin. In this context, the MED is regarded as a key factor in determining starting doses for UV phototherapy for common skin conditions such as psoriasis and eczema. In research settings, MED testing also has potential to be a powerful tool for assessing within- and between-persons variation in inflammatory responses. However, MED testing has not been widely adopted for use in research settings, likely owing to a lack of published guidelines, which is a barrier to obtaining reproducible results from this assay. Also, protocols and equipment for establishing MED vary widely, making it difficult to compare results across laboratories. Here, we describe a precise and reproducible method to induce and measure superficial erythema using newly designed protocols and methods that can easily be adapted to other equipment and laboratory environments. The method described here includes detail on procedures that will allow extrapolation of a standardized dosage schedule to other equipment so that this protocol can be adapted to any UV radiation source.

vi-HMM: a novel HMM-based method for sequence variant identification in short-read data.

BACKGROUND: Accurate and reliable identification of sequence variants, including single nucleotide polymorphisms (SNPs) and insertion-deletion polymorphisms (INDELs), plays a fundamental role in next-generation sequencing (NGS) applications. Existing methods for calling these variants often make simplified assumptions of positional independence and fail to leverage the dependence between genotypes at nearby loci that is caused by linkage disequilibrium (LD). RESULTS AND CONCLUSION: We propose vi-HMM, a hidden Markov model (HMM)-based method for calling SNPs and INDELs in mapped short-read data. This method allows transitions between hidden states (defined as "SNP," "Ins," "Del," and "Match") of adjacent genomic bases and determines an optimal hidden state path by using the Viterbi algorithm. The inferred hidden state path provides a direct solution to the identification of SNPs and INDELs. Simulation studies show that, under various sequencing depths, vi-HMM outperforms commonly used variant calling methods in terms of sensitivity and F1 score. When applied to the real data, vi-HMM demonstrates higher accuracy in calling SNPs and INDELs.

Robust and Gaussian spatial functional regression models for analysis of event-related potentials.

Event-related potentials (ERPs) summarize electrophysiological brain response to specific stimuli. They can be considered as correlated functions of time with both spatial correlation across electrodes and nested correlations within subjects. Commonly used analytical methods for ERPs often focus on pre-determined extracted components and/or ignore the correlation among electrodes or subjects, which can miss important insights, and tend to be sensitive to outlying subjects, time points or electrodes. Motivated by ERP data in a smoking cessation study, we introduce a Bayesian spatial functional regression framework that models the entire ERPs as spatially correlated functional responses and the stimulus types as covariates. This novel framework relies on mixed models to characterize the effects of stimuli while simultaneously accounting for the multilevel correlation structure. The spatial correlation among the ERP profiles is captured through basis-space Matérn assumptions that allow either separable or nonseparable spatial correlations over time. We induce both adaptive regularization over time and spatial smoothness across electrodes via a correlated normal-exponential-gamma (CNEG) prior on the fixed effect coefficient functions. Our proposed framework includes both Gaussian models as well as robust models using heavier-tailed distributions to make the regression automatically robust to outliers. We introduce predictive methods to select among Gaussian vs. robust models and models with separable vs. non-separable spatiotemporal correlation structures. Our proposed analysis produces global tests for stimuli effects across entire time (or time-frequency) and electrode domains, plus multiplicity-adjusted pointwise inference based on experiment-wise error rate or false discovery rate to flag spatiotemporal (or spatio-temporal-frequency) regions that characterize stimuli differences, and can also produce inference for any prespecified waveform components. Our analysis of the smoking cessation ERP data set reveals numerous effects across different types of visual stimuli.

A Unified Analysis of Structured Sonar-terrain Data using Bayesian Functional Mixed Models.

Sonar emits pulses of sound and uses the reflected echoes to gain information about target objects. It offers a low cost, complementary sensing modality for small robotic platforms. While existing analytical approaches often assume independence across echoes, real sonar data can have more complicated structures due to device setup or experimental design. In this paper, we consider sonar echo data collected from multiple terrain substrates with a dual-channel sonar head. Our goals are to identify the differential sonar responses to terrains and study the effectiveness of this dual-channel design in discriminating targets. We describe a unified analytical framework that achieves these goals rigorously, simultaneously, and automatically. The analysis was done by treating the echo envelope signals as functional responses and the terrain/channel information as covariates in a functional regression setting. We adopt functional mixed models that facilitate the estimation of terrain and channel effects while capturing the complex hierarchical structure in data. This unified analytical framework incorporates both Gaussian models and robust models. We fit the models using a full Bayesian approach, which enables us to perform multiple inferential tasks under the same modeling framework, including selecting models, estimating the effects of interest, identifying significant local regions, discriminating terrain types, and describing the discriminatory power of local regions. Our analysis of the sonar-terrain data identifies time regions that reflect differential sonar responses to terrains. The discriminant analysis suggests that a multi- or dual-channel design achieves target identification performance comparable with or better than a single-channel design.

Identification of Differentially Methylated Sites with Weak Methylation Effects.

Deoxyribonucleic acid (DNA) methylation is an epigenetic alteration crucial for regulating stress responses. Identifying large-scale DNA methylation at single nucleotide resolution is made possible by whole genome bisulfite sequencing. An essential task following the generation of bisulfite sequencing data is to detect differentially methylated cytosines (DMCs) among treatments. Most statistical methods for DMC detection do not consider the dependency of methylation patterns across the genome, thus possibly inflating type I error. Furthermore, small sample sizes and weak methylation effects among different phenotype categories make it difficult for these statistical methods to accurately detect DMCs. To address these issues, the wavelet-based functional mixed model (WFMM) was introduced to detect DMCs. To further examine the performance of WFMM in detecting weak differential methylation events, we used both simulated and empirical data and compare WFMM performance to a popular DMC detection tool methylKit. Analyses of simulated data that replicated the effects of the herbicide glyphosate on DNA methylation in Arabidopsis thaliana show that WFMM results in higher sensitivity and specificity in detecting DMCs compared to methylKit, especially when the methylation differences among phenotype groups are small. Moreover, the performance of WFMM is robust with respect to small sample sizes, making it particularly attractive considering the current high costs of bisulfite sequencing. Analysis of empirical Arabidopsis thaliana data under varying glyphosate dosages, and the analysis of monozygotic (MZ) twins who have different pain sensitivities-both datasets have weak methylation effects of <1%-show that WFMM can identify more relevant DMCs related to the phenotype of interest than methylKit. Differentially methylated regions (DMRs) are genomic regions with different DNA methylation status across biological samples. DMRs and DMCs are essentially the same concepts, with the only difference being how methylation information across the genome is summarized. If methylation levels are determined by grouping neighboring cytosine sites, then they are DMRs; if methylation levels are calculated based on single cytosines, they are DMCs.

Identifying Transcriptional Regulatory Modules Among Different Chromatin States in Mouse Neural Stem Cells.

Gene expression regulation is a complex process involving the interplay between transcription factors and chromatin states. Significant progress has been made toward understanding the impact of chromatin states on gene expression. Nevertheless, the mechanism of transcription factors binding combinatorially in different chromatin states to enable selective regulation of gene expression remains an interesting research area. We introduce a nonparametric Bayesian clustering method for inhomogeneous Poisson processes to detect heterogeneous binding patterns of multiple proteins including transcription factors to form regulatory modules in different chromatin states. We applied this approach on ChIP-seq data for mouse neural stem cells containing 21 proteins and observed different groups or modules of proteins clustered within different chromatin states. These chromatin-state-specific regulatory modules were found to have significant influence on gene expression. We also observed different motif preferences for certain TFs between different chromatin states. Our results reveal a degree of interdependency between chromatin states and combinatorial binding of proteins in the complex transcriptional regulatory process. The software package is available on Github at - https://github.com/BSharmi/DPM-LGCP.

A simplified model of biosonar echoes from foliage and the properties of natural foliages.

Foliage echoes could play an important role in the sensory ecology of echolocating bats, but many aspects of their sensory information content remain to be explored. A realistic numerical model for these echoes could support the development of hypotheses for the relationship between foliage properties and echo parameters. In prior work by the authors, a simple foliage model based on circular disks distributed uniformly in space has been developed. In the current work, three key simplifications used in this model have been examined: (i) representing leaves as circular disks, (ii) neglecting shading effects between leaves, and (iii) the uniform spatial distribution of the leaves. The target strengths of individual leaves and shading between them have been examined in physical experiments, whereas the impact of the spatial leaf distribution has been studied by modifying the numerical model to include leaf distributions according to a biomimetic model for natural branching patterns (L-systems). Leaf samples from a single species (leatherleaf arrowwood) were found to match the relationship between size and target strength of the disk model fairly well, albeit with a large variability part of which could be due to unaccounted geometrical features of the leaves. Shading between leaf-sized disks did occur for distances below 50 cm and could hence impact the echoes. Echoes generated with L-system models in two distinct tree species (ginkgo and pine) showed consistently more temporal inhomogeneity in the envelope amplitudes than a reference with uniform distribution. However, these differences were small compared to effects found in response to changes in the relative orientation of simulated sonar beam and foliage. These findings support the utility of the uniform leaf distribution model and suggest that bats could use temporal inhomogeneities in the echoes to make inferences regarding the relative positioning of their sonar and a foliage.

Multivariate functional response regression, with application to fluorescence spectroscopy in a cervical pre-cancer study.

Many scientific studies measure different types of high-dimensional signals or images from the same subject, producing multivariate functional data. These functional measurements carry different types of information about the scientific process, and a joint analysis that integrates information across them may provide new insights into the underlying mechanism for the phenomenon under study. Motivated by fluorescence spectroscopy data in a cervical pre-cancer study, a multivariate functional response regression model is proposed, which treats multivariate functional observations as responses and a common set of covariates as predictors. This novel modeling framework simultaneously accounts for correlations between functional variables and potential multi-level structures in data that are induced by experimental design. The model is fitted by performing a two-stage linear transformation-a basis expansion to each functional variable followed by principal component analysis for the concatenated basis coefficients. This transformation effectively reduces the intra-and inter-function correlations and facilitates fast and convenient calculation. A fully Bayesian approach is adopted to sample the model parameters in the transformed space, and posterior inference is performed after inverse-transforming the regression coefficients back to the original data domain. The proposed approach produces functional tests that flag local regions on the functional effects, while controlling the overall experiment-wise error rate or false discovery rate. It also enables functional discriminant analysis through posterior predictive calculation. Analysis of the fluorescence spectroscopy data reveals local regions with differential expressions across the pre-cancer and normal samples. These regions may serve as biomarkers for prognosis and disease assessment.

A computational model for biosonar echoes from foliage.

Since many bat species thrive in densely vegetated habitats, echoes from foliage are likely to be of prime importance to the animals' sensory ecology, be it as clutter that masks prey echoes or as sources of information about the environment. To better understand the characteristics of foliage echoes, a new model for the process that generates these signals has been developed. This model takes leaf size and orientation into account by representing the leaves as circular disks of varying diameter. The two added leaf parameters are of potential importance to the sensory ecology of bats, e.g., with respect to landmark recognition and flight guidance along vegetation contours. The full model is specified by a total of three parameters: leaf density, average leaf size, and average leaf orientation. It assumes that all leaf parameters are independently and identically distributed. Leaf positions were drawn from a uniform probability density function, sizes and orientations each from a Gaussian probability function. The model was found to reproduce the first-order amplitude statistics of measured example echoes and showed time-variant echo properties that depended on foliage parameters. Parameter estimation experiments using lasso regression have demonstrated that a single foliage parameter can be estimated with high accuracy if the other two parameters are known a priori. If only one parameter is known a priori, the other two can still be estimated, but with a reduced accuracy. Lasso regression did not support simultaneous estimation of all three parameters. Nevertheless, these results demonstrate that foliage echoes contain accessible information on foliage type and orientation that could play a role in supporting sensory tasks such as landmark identification and contour following in echolocating bats.

Dynamic Substrate for the Physical Encoding of Sensory Information in Bat Biosonar.

Horseshoe bats have dynamic biosonar systems with interfaces for ultrasonic emission (reception) that change shape while diffracting the outgoing (incoming) sound waves. An information-theoretic analysis based on numerical and physical prototypes shows that these shape changes add sensory information (mutual information between distant shape conformations <20%), increase the number of resolvable directions of sound incidence, and improve the accuracy of direction finding. These results demonstrate that horseshoe bats have a highly effective substrate for dynamic encoding of sensory information.

A Bayesian analysis of quantal bioassay experiments incorporating historical controls via Bayes factors.

This paper addresses model-based Bayesian inference in the analysis of data arising from bioassay experiments. In such experiments, increasing doses of a chemical substance are given to treatment groups (usually rats or mice) for a fixed period of time (usually 2 years). The goal of such an experiment is to determine whether an increased dosage of the chemical is associated with increased probability of an adverse effect (usually presence of adenoma or carcinoma). The data consists of dosage, survival time, and the occurrence of the adverse event for each unit in the study. To determine whether such relationship exists, this paper proposes using Bayes factors to compare two probit models, the model that assumes increasing dose effects and the model that assumes no dose effect. These models account for the survival time of each unit through a Poly-k type correction. In order to increase statistical power, the proposed approach allows the incorporation of information from control groups from previous studies. The proposed method is able to handle data with very few occurrences of the adverse event. The proposed method is compared with a variation of the Peddada test via simulation and is shown to have higher power. We demonstrate the method by applying it to the two bioassay experiment datasets previously analyzed by other authors. Copyright © 2017 John Wiley & Sons, Ltd.

Functional CAR models for large spatially correlated functional datasets.

We develop a functional conditional autoregressive (CAR) model for spatially correlated data for which functions are collected on areal units of a lattice. Our model performs functional response regression while accounting for spatial correlations with potentially nonseparable and nonstationary covariance structure, in both the space and functional domains. We show theoretically that our construction leads to a CAR model at each functional location, with spatial covariance parameters varying and borrowing strength across the functional domain. Using basis transformation strategies, the nonseparable spatial-functional model is computationally scalable to enormous functional datasets, generalizable to different basis functions, and can be used on functions defined on higher dimensional domains such as images. Through simulation studies, we demonstrate that accounting for the spatial correlation in our modeling leads to improved functional regression performance. Applied to a high-throughput spatially correlated copy number dataset, the model identifies genetic markers not identified by comparable methods that ignore spatial correlations.

Mammalian Brain Development is Accompanied by a Dramatic Increase in Bipolar DNA Methylation.

DNA methylation is an epigenetic mechanism critical for tissue development and cell specification. Mammalian brains consist of many different types of cells with assumedly distinct DNA methylation profiles, and thus some genomic loci may demonstrate bipolar DNA methylation pattern, i.e. hypermethylated in one cell subset but hypomethylated in others. Currently, how extensive methylation patterns vary among brain cells is unknown and bipolar methylated genomic loci remain largely unexplored. In this study, we implemented a procedure to infer cell-subset specific methylated (CSM) loci from the methylomes of human and mouse frontal cortices at different developmental stages. With the genome-scale hairpin bisulfite sequencing approach, we demonstrated that the majority of CSM loci predicted likely resulted from the methylation differences among brain cells rather than from asymmetric DNA methylation between DNA double strands. Correlated with enhancer-associated histone modifications, putative CSM loci increased dramatically during early stages of brain development and were enriched for GWAS variants associated with neurological disorder-related diseases/traits. Altogether, this study provides a procedure to identify genomic regions showing methylation differences in a mixed cell population and our results suggest that a set of cis-regulatory elements are primed in early postnatal life whose functions may be compromised in human neurological disorders.