Bayesian Analysis Method Research Articles

Cryopreservation ofPrunus padusseeds: emphasising the significance of Bayesian methods for data analysis

Conservation of Prunus padus L., a tree of high ecological and pharmacological importance, has been evaluated by storing seeds at subzero (−20 °C and −80 °C) and cryogenic (−196 °C) temperatures for various durations. The effect of the seed’s water content (WC) ranging from 3.5% to 21.1%, fresh weight basis, and the effect of cooling and rewarming procedures on seed viability was investigated. Emergence of seedlings was observed for 40%–55% of the noncryopreserved seeds, with no significant effect of WC. The same seedling emergence was recorded for seeds cryopreserved by direct immersion in liquid nitrogen within the WC range of 3.5%–15.0%. Seeds rehydrated above 17% WC were unable to tolerate cryopreservation. Seedling emergence was not affected by cooling regime but decreased by 10% after stepwise rewarming compared with rapid rewarming in a water bath or on air. No reduction in seedling emergence was recorded after storage at −20 °C, −80 °C, and −196 °C for 1 h, 1 week, and 1 month. We recommend seed storage at subzero or cryogenic temperatures as an effective conservation option for P. padus and possibly other Prunus species. We also demonstrated high effectiveness and reliability of Bayesian statistical methods for analyzing binomial data such as the data obtained in seed conservation experiments.

Dynamic approach to linear statistical calibration with an application in microwave radiometry

ABSTRACTThe problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the ‘classical’ approach and the ‘inverse’ regression approach. Both of these models are static models and are used to estimate exact measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe it. The Bayesian time series analysis method of Dynamic Linear Models can be used to monitor the evolution of the measures, thus introducing a dynamic approach to statistical calibration. The research presented employs a new approach to performing statistical calibration. A simulation study in the context of microwave radiometry is conducted that compares the dynamic model to traditional static frequentist and Bayesian approaches. The focus of the study is to understand how well the dynamic statistical calibration method performs under various signal-to-noise ratios, r.

Bayesian methods for event analysis of intracellular currents

BackgroundInvestigation of neural circuit functioning often requires statistical interpretation of events in subthreshold electrophysiological recordings. This problem is non-trivial because recordings may have moderate levels of structured noise and events may have distinct kinetics. In addition, novel experimental designs that combine optical and electrophysiological methods will depend upon statistical tools that combine multimodal data. New methodWe present a Bayesian approach for inferring the timing, strength, and kinetics of post-synaptic currents (PSCs) from voltage-clamp electrophysiological recordings on a per event basis. The simple generative model for a single voltage-clamp recording flexibly extends to include additional structure to enable experiments designed to probe synaptic connectivity. ResultsWe validate the approach on simulated and real data. We also demonstrate that extensions of the basic PSC detection algorithm can handle recordings contaminated with optically evoked currents, and we simulate a scenario in which calcium imaging observations, available for a subset of neurons, can be fused with electrophysiological data to achieve higher temporal resolution. Comparison with existing methodsWe apply this approach to simulated and real ground truth data to demonstrate its higher sensitivity in detecting small signal-to-noise events and its increased robustness to noise compared to standard methods for detecting PSCs. ConclusionsThe new Bayesian event analysis approach for electrophysiological recordings should allow for better estimation of physiological parameters under more variable conditions and help support new experimental designs for circuit mapping.

Molecular Phylogeny of Cypridoid Freshwater Ostracods (Crustacea: Ostracoda), Inferred from 18S and 28S rDNA Sequences.

With the aim of exploring phylogenetic relationships within Cypridoidea, the most species-rich superfamily among the podocopidan ostracods, we sequenced nearly the entire 18S rRNA gene (18S) and part of the 28S rRNA gene (28S) for 22 species in the order Podocopida, with representatives from all the major cypridoid families. We conducted phylogenetic analyses using the methods of maximum likelihood, minimum evolution, and Bayesian analysis. Our analyses showed monophyly for Cyprididae, one of the four families currently recognized in Cypridoidea. Candonidae turned out to be paraphyletic, and included three clades corresponding to the subfamilies Candoninae, Paracypridinae, and Cyclocypridinae. We propose restricting the name Candonidae s. str. to comprise what is now Candoninae, and raising Paracypridinae and Cyclocyprininae to family rank within the superfamily Cypridoidea.

Indefinite integral automatic analysis mechanism research and development—Using integrals involving quadratic square roots as an example

Using the capabilities of the knowledge structure theory, the researcher prepared a model for the experts’ knowledge structure of the valid test items of the university Calculus topic “trigonometric substitution of indefinite integral about integrands involving quadratic square root”. After the Calculus course was taught and tested, this knowledge structure model was combined with Bayesian network analysis to find the best recognition rate of Bayesian network and to identify easily the error types that students might make in learning “trigonometric substitution” unit. Then, the statistical information was analyzed using the Bayesian probability analysis methods to establish the “trigonometric substitution” unit model as an example of a Bayesian network adaptive diagnostic test system, to determine four established Bayesian network models to compare their recognition rates, and to establish this structure could be used as the foundation for developing remedial teaching approaches.

Lithium and age of pre-main sequence stars: the case of Parenago 1802

With the aim to test the present capability of the stellar surface lithium abundance in providing an estimation for the age of PMS stars, we analyze the case of the detached, double-lined, eclipsing binary system PAR 1802. For this system, the lithium age has been compared with the theoretical one, as estimated by applying a Bayesian analysis method on a large grid of stellar evolutionary models. The models have been computed for several values of chemical composition and mixing length, by means of the code FRANEC updated with the Trojan Horse reaction rates involving lithium burning.

Weighing the fog of war: Illustrating the power of Bayesian methods for historical analysis through the Battle of the Dogger Bank

ABSTRACTThe application of scientific methods to historical situations is restricted by the existence of a single outcome with no possibility of repetition. However, new computational methods make quantitative historical analysis possible. The authors apply methods of approximate Bayesian computation to simulate a naval engagement of the First World War, the Battle of the Dogger Bank. They demonstrate that the battle's outcome was highly unlikely, with significant implications both for subsequent actions and for historical understanding. Dogger Bank exemplifies the view that Bayesian methods offer historians the tool they need to grapple with the evolving probabilities of historical events, giving a sound scientific basis for counterfactual history and opening up a wealth of possibilities for analysis.

No association between soil constituents and amyotrophic lateral sclerosis relative risk in Ireland

IntroductionWe have recently mapped ALS spatial risk in Ireland using Bayesian and cluster analysis methods at electoral division (ED) and small area (SA) levels. As a number of metal elements (both minerals and toxins) have been proposed as risk factors for ALS, here we extend this analysis to include soil constituents from the Irish National Soils Database as Bayesian conditional auto-regression covariates to determine associations with small area ALS risk. MethodsData on 45 different soil parameters were obtained under license from National Soils Database (via Irish EPA). We interpolated average values of each soil constituent for each small area using ordinary kriging. All cases of ALS in Ireland from January 1995 to December 2013 were identified from the Irish ALS register and observed and age and gender standardised expected cases were calculated for each SA. Besag-York-Mollié (BYM) models were then built including each parameter from the national soils database in turn as a Bayesian covariate in the BYM model. Models were compared using the deviance information criterion (DIC) and separate models were built for ALS subtypes. Results1701 ALS patients were included – 959 (56%) were male, 938 (55%) had limb onset ALS. 315 Bayesian models were built in total. Of the 315 models built, only one resulted in a coefficient that did not overlap zero. For limb onset cases, total magnesium had a mean coefficient of 0.319 (credible interval 0.033–0.607). DiscussionWe report the first spatial analysis of potential association between ALS and soil minerals using a population-based dataset collected over 18 years. Our sole non-zero finding is likely a random finding due to the high number of models built. We did not find any evidence to support soil mineral and toxin levels as risk factors for ALS. However as soil parameters are an ecological assessment of exposure in a given area, individual level measures of exposure are required.

Risk Assessment for Ecological Planning of Arid Inland River Basins Under Hydrological and Management Uncertainties

The Shiyanghe river basin, an arid inland basin of northwest China, is taken as an example to analyze the risk for achieving the ecological planning objective in arid inland river basins under uncertainty conditions. Hydrology and management uncertainties that affect the accomplishment of ecological planning objective are analyzed quantitatively with the methods of Bayesian theory based Probabilistic model, scenario analysis and interval analysis. Bayesian probabilistic analysis method was used to analyze the hydrological uncertainties in the form of probability and interval distributions in planning period, while the scenario analysis method and interval method were used to analyze the managing uncertainties in the form of interval numbers. Instead of the ecological risk analysis, which for arid inland river basin, of studying the impact of environmental and human factor on ecological system, water resources and environment, we focused on analysing the possible impact of hydrological and management uncertainty factor on the ecological planning, and forecasting the degree of the completion under the uncertainty. Our study provided the probabilities of achieving ecological planning objective and the possible deviation of different scenarios. The more local water resources and higher level of local water resource utilization and management appeared to lead higher probability to achieve the ecological objective. This study can help environment and water resource managers and planner to formulate a rational planning for arid inland river basins under hydrological and management uncertainty.

On analysis of longitudinal clinical trials with missing data using reference-based imputation

ABSTRACTReference-based imputation (RBI) methods have been proposed as sensitivity analyses for longitudinal clinical trials with missing data. The RBI methods multiply impute the missing data in treatment group based on an imputation model built using data from the reference (control) group. The RBI will yield a conservative treatment effect estimate as compared to the estimate obtained from multiple imputation (MI) under missing at random (MAR). However, the RBI analysis based on the regular MI approach can be overly conservative because it not only applies discount to treatment effect estimate but also posts penalty on the variance estimate. In this article, we investigate the statistical properties of RBI methods, and propose approaches to derive accurate variance estimates using both frequentist and Bayesian methods for the RBI analysis. Results from simulation studies and applications to longitudinal clinical trial datasets are presented.

An objective Bayesian analysis of the two-parameter half-logistic distribution based on progressively type-II censored samples

ABSTRACTThis paper develops an objective Bayesian analysis method for estimating unknown parameters of the half-logistic distribution when a sample is available from the progressively Type-II censoring scheme. Noninformative priors such as Jeffreys and reference priors are derived. In addition, derived priors are checked to determine whether they satisfy probability-matching criteria. The Metropolis–Hasting algorithm is applied to generate Markov chain Monte Carlo samples from these posterior density functions because marginal posterior density functions of each parameter cannot be expressed in an explicit form. Monte Carlo simulations are conducted to investigate frequentist properties of estimated models under noninformative priors. For illustration purposes, a real data set is presented, and the quality of models under noninformative priors is evaluated through posterior predictive checking.

Vehicle and pedestrian safety impacts of signal timing optimization in a dense urban street network

Intersection signal timing optimization is expected to affect both traffic mobility and safety. However, in safety impacts analysis, the existing studies mainly focus on estimating changes in vehicle crashes without addressing the influence of pedestrian related crashes. This study aims to simultaneously assess the overall impacts of vehicle and pedestrian crashes caused by signal timing optimization in dense urban street networks. An empirical Bayesian analysis method was introduced to estimate the safety impacts of intersection signal timing optimization in an urban street network in terms of vehicle-to-vehicle and vehicle-to-pedestrian crashes at intersections, as well as single and multiple vehicle crashes on street segments. A computational experiment was performed to apply the proposed method to the Chicago central business district that includes 875 signalized intersections and 2016 roadway segments. Results show that vehicle-to-vehicle and vehicle-to-pedestrian crashes at intersections are decreased in different crash severity levels and types, especially for angle and rear-end ones after signal timing optimization. Similar results are found for multi-vehicle rear-end crashes on street segments. These indicate that intersection signal timing optimization in dense urban street networks has a potential for improving traffic mobility, vehicle and pedestrian safety at intersections, and vehicle safety on street segments.

Probability of detection of minute defects by ultrasonic automated testing equipment in view of Bayesian inference

AbstractThe method of Bayesian analysis of confidence in the testing evidence collected during ultrasonic automated testing of high quality aluminum ingots for minute defects of sub-millimeter size is discussed. These test results are assessed in the view of true or false evidence. The analysis demonstrates the significant influence of false evidence on the confidence in the test outcome where the evidence is skewed in the direction of false positive. At the same time the influence of the false negative evidence is shown to be more muted. To minimize the risk of false rejection of ingots with “ghost” indications not representing the physical defects, the off-line ingot retesting by an A-scan with defect waveform verification is implemented. Retesting of fabricated blanks made of the ingots previously passed the ingot testing is used to minimize the risk of passing products with defects earlier undetected.

A Comparison of Frequentist and Bayesian Model Based Approaches for Missing Data Analysis: Case Study with a Schizophrenia Clinical Trial

Missing data are common in clinical trials and could lead to biased estimation of treatment effects. The National Research Council (NRC) report suggests that sensitivity analysis on missing data mechanism should be a mandatory component of the primary reporting of findings from clinical trials, and regulatory agencies are requesting more thorough sensitivity analyses from sponsors. However, recent literature research showed that missing data were almost always inadequately handled. This is partially due to the lack of standard software packages and straightforward implementation platform. With recent availability of flexible Bayesian software packages such as WinBUGS, SAS Proc MCMC, and Stan, it is relatively simple to develop Bayesian methods to address complex missing data problems while incorporating the uncertainty. In this article, we present a case study from the DIA Bayesian Scientific Working Group (BSWG) on Bayesian approaches for missing data analysis. We illustrate how to use Bayesian approaches to fit a few commonly used frequentist missing data models. The properties, advantage, and flexibility of the Bayesian analysis methods will be discussed using a case study based on a schizophrenia clinical trial. Supplementary materials for this article are available online.

The complete mitochondrial genome of Anthus hodgsoni (Passeriformes: Motacillidae)

Anthus hodgsoni is a species of small passerine bird in the family Motacillidae, which is widely distributed. In this study, we determined the complete mitochondrial genome of A. hodgsoni. The result showed that the total length of the mitochondrial genome was 16,886 bp and contained 2 ribosomal RNA genes, 22 transfer RNA genes, 13 protein-coding genes and 1 control region. The phylogenetic tree was reconstructed using the Bayesian analysis method and divided into four genera, Anthus, Dendronanthus, Motacilla and Tmetothylacus. The A. hodgsoni which we determined was clustered into genus Anthus and received strong support.

Applying Bayesian statistics to the study of psychological trauma: A suggestion for future research.

Several contemporary researchers have noted the virtues of Bayesian methods of data analysis. Although debates continue about whether conventional or Bayesian statistics is the "better" approach for researchers in general, there are reasons why Bayesian methods may be well suited to the study of psychological trauma in particular. This article describes how Bayesian statistics offers practical solutions to the problems of data non-normality, small sample size, and missing data common in research on psychological trauma. After a discussion of these problems and the effects they have on trauma research, this article explains the basic philosophical and statistical foundations of Bayesian statistics and how it provides solutions to these problems using an applied example. Results of the literature review and the accompanying example indicates the utility of Bayesian statistics in addressing problems common in trauma research. Bayesian statistics provides a set of methodological tools and a broader philosophical framework that is useful for trauma researchers. Methodological resources are also provided so that interested readers can learn more.

Mitochondrial genome of Pachytriton feii (Urodela: Salamandridae)

abstractIn this paper, the complete mitochondrial genome of Pachytriton feii is sequenced and reported for the first time. In our result, the complete mitochondrial genome of P. feii is 16 293 bp in length. Similar to the typical mtDNA of vertebrates, it contained 37 genes (13 protein-coding genes, 2 rRNA genes, and 22 tRNA genes) and 1 non-coding region (D-loop). All the genes in P. feii were distributed on the H-strand, except for the ND6 subunit gene and eight tRNA genes which were encoded on the L-strand. The phylogenetic tree was reconstructed using the Bayesian analysis method and contained two major clades. Among Pachytriton (P. feii, Pachytriton labiatus, and Pachytriton brevipes), Paramesotriton laoensis make up the first lineage.

STAR CLUSTER PROPERTIES IN TWO LEGUS GALAXIES COMPUTED WITH STOCHASTIC STELLAR POPULATION SYNTHESIS MODELS

We investigate a novel Bayesian analysis method, based on the Stochastically Lighting Up Galaxies (slug) code, to derive the masses, ages, and extinctions of star clusters from integrated light photometry. Unlike many analysis methods, slug correctly accounts for incomplete IMF sampling, and returns full posterior probability distributions rather than simply probability maxima. We apply our technique to 621 visually-confirmed clusters in two nearby galaxies, NGC 628 and NGC 7793, that are part of the Legacy Extragalactic UV Survey (LEGUS). LEGUS provides Hubble Space Telescope photometry in the NUV, U, B, V, and I bands. We analyze the sensitivity of the derived cluster properties to choices of prior probability distribution, evolutionary tracks, IMF, metallicity, treatment of nebular emission, and extinction curve. We find that slug's results for individual clusters are insensitive to most of these choices, but that the posterior probability distributions we derive are often quite broad, and sometimes multi-peaked and quite sensitive to the choice of priors. In contrast, the properties of the cluster population as a whole are relatively robust against all of these choices. We also compare our results from slug to those derived with a conventional non-stochastic fitting code, Yggdrasil. We show that slug's stochastic models are generally a better fit to the observations than the deterministic ones used by Yggdrasil. However, the overall properties of the cluster populations recovered by both codes are qualitatively similar.

ScreenBEAM: a novel meta-analysis algorithm for functional genomics screens via Bayesian hierarchical modeling.

Functional genomics (FG) screens, using RNAi or CRISPR technology, have become a standard tool for systematic, genome-wide loss-of-function studies for therapeutic target discovery. As in many large-scale assays, however, off-target effects, variable reagents' potency and experimental noise must be accounted for appropriately control for false positives. Indeed, rigorous statistical analysis of high-throughput FG screening data remains challenging, particularly when integrative analyses are used to combine multiple sh/sgRNAs targeting the same gene in the library. We use large RNAi and CRISPR repositories that are publicly available to evaluate a novel meta-analysis approach for FG screens via Bayesian hierarchical modeling, Screening Bayesian Evaluation and Analysis Method (ScreenBEAM). Results from our analysis show that the proposed strategy, which seamlessly combines all available data, robustly outperforms classical algorithms developed for microarray data sets as well as recent approaches designed for next generation sequencing technologies. Remarkably, the ScreenBEAM algorithm works well even when the quality of FG screens is relatively low, which accounts for about 80-95% of the public datasets. R package and source code are available at: https://github.com/jyyu/ScreenBEAM. ac2248@columbia.edu, jose.silva@mssm.edu, yujiyang@gmail.com Supplementary data are available at Bioinformatics online.

A fast and high performance multiple data integration algorithm for identifying human disease genes.

BackgroundIntegrating multiple data sources is indispensable in improving disease gene identification. It is not only due to the fact that disease genes associated with similar genetic diseases tend to lie close with each other in various biological networks, but also due to the fact that gene-disease associations are complex. Although various algorithms have been proposed to identify disease genes, their prediction performances and the computational time still should be further improved.ResultsIn this study, we propose a fast and high performance multiple data integration algorithm for identifying human disease genes. A posterior probability of each candidate gene associated with individual diseases is calculated by using a Bayesian analysis method and a binary logistic regression model. Two prior probability estimation strategies and two feature vector construction methods are developed to test the performance of the proposed algorithm.ConclusionsThe proposed algorithm is not only generated predictions with high AUC scores, but also runs very fast. When only a single PPI network is employed, the AUC score is 0.769 by using F2 as feature vectors. The average running time for each leave-one-out experiment is only around 1.5 seconds. When three biological networks are integrated, the AUC score using F3 as feature vectors increases to 0.830, and the average running time for each leave-one-out experiment takes only about 12.54 seconds. It is better than many existing algorithms.