Framework Of Statistical Model Research Articles

Statistical modeling of daily and subdaily stream temperatures: Application to the Methow River Basin, Washington

Management of water temperatures in the Columbia River Basin (Washington) is critical because water projects have substantially altered the habitat of Endangered Species Act listed species, such as salmon, throughout the basin. This is most important in tributaries to the Columbia, such as the Methow River, where the spawning and rearing life stages of these cold water fishes occurs. Climate change projections generally predict increasing air temperatures across the western United States, with less confidence regarding shifts in precipitation. As air temperatures rise, we anticipate a corresponding increase in water temperatures, which may alter the timing and availability of habitat for fish reproduction and growth. To assess the impact of future climate change in the Methow River, we couple historical climate and future climate projections with a statistical modeling framework to predict daily mean stream temperatures. A K‐nearest neighbor algorithm is also employed to: (i) adjust the climate projections for biases compared to the observed record and (ii) provide a reference for performing spatiotemporal disaggregation in future hydraulic modeling of stream habitat. The statistical models indicate the primary drivers of stream temperature are maximum and minimum air temperature and stream flow and show reasonable skill in predictability. When compared to the historical reference time period of 1916–2006, we conclude that increases in stream temperature are expected to occur at each subsequent time horizon representative of the year 2020, 2040, and 2080, with an increase of 0.8 ± 1.9°C by the year 2080.

Relevance-based language modelling for recommender systems

Relevance-Based Language Models, commonly known as Relevance Models, are successful approaches to explicitly introduce the concept of relevance in the statistical Language Modelling framework of Information Retrieval. These models achieve state-of-the-art retrieval performance in the pseudo relevance feedback task. On the other hand, the field of recommender systems is a fertile research area where users are provided with personalised recommendations in several applications. In this paper, we propose an adaptation of the Relevance Modelling framework to effectively suggest recommendations to a user. We also propose a probabilistic clustering technique to perform the neighbour selection process as a way to achieve a better approximation of the set of relevant items in the pseudo relevance feedback process. These techniques, although well known in the Information Retrieval field, have not been applied yet to recommender systems, and, as the empirical evaluation results show, both proposals outperform individually several baseline methods. Furthermore, by combining both approaches even larger effectiveness improvements are achieved.

Mixed Modeling of Meta-Analysis P-Values (MixMAP) Suggests Multiple Novel Gene Loci for Low Density Lipoprotein Cholesterol

Informing missing heritability for complex disease will likely require leveraging information across multiple SNPs within a gene region simultaneously to characterize gene and locus-level contributions to disease phenotypes. To this aim, we introduce a novel strategy, termed Mixed modeling of Meta-Analysis P-values (MixMAP), that draws on a principled statistical modeling framework and the vast array of summary data now available from genetic association studies, to test formally for locus level association. The primary inputs to this approach are: (a) single SNP level p-values for tests of association; and (b) the mapping of SNPs to genomic regions. The output of MixMAP is comprised of locus level estimates and tests of association. In application of MixMAP to summary data from the Global Lipids Gene Consortium, we suggest twelve new loci (PKN, FN1, UGT1A1, PPARG, DMDGH, PPARD, CDK6, VPS13B, GAD2, GAB2, APOH and NPC1) for low-density lipoprotein cholesterol (LDL-C), a causal risk factor for cardiovascular disease and we also demonstrate the potential utility of MixMAP in small data settings. Overall, MixMAP offers novel and complementary information as compared to SNP-based analysis approaches and is straightforward to implement with existing open-source statistical software tools.

Diagnostic tools for hierarchical linear models

AbstractHierarchical structures are omnipresent in today's society—this is reflected in the data that we collect on all aspects of this society. Hierarchical linear models allow a representation of structural levels in a statistical modeling framework. Diagnostic tools are used to assess the quality of model estimation and explore features of the data not well described by the model. Residual and influence diagnostics are familiar tools for the classical regression model with independent observations. For hierarchical linear models, these diagnostic tools must be adjusted to reflect the dependence introduced by the nested data structure. Residual analysis now includes the assessment of distributional assumptions at each level of the model. This requires the use of level‐dependent residual quantities. Similarly, the parameter estimates may be influenced at each level of the model, requiring influence diagnostics that can pinpoint specific levels of the model, as well as specific aspects of the model. We present an overview of the diagnostic tools available for hierarchical linear models that are familiar from linear models. Additionally, we discuss the utility of the lineup protocol for residual analysis with complex models.WIREs Comput Stat2013, 5:48–61. doi: 10.1002/wics.1238This article is categorized under:Statistical Models > Bayesian ModelsStatistical and Graphical Methods of Data Analysis > Bayesian Methods and TheoryStatistical and Graphical Methods of Data Analysis > Modeling Methods and AlgorithmsStatistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization

Stock synthesis: A biological and statistical framework for fish stock assessment and fishery management

Stock synthesis (SS) is a statistical age-structured population modeling framework that has been applied in a wide variety of fish assessments globally. The framework is highly scalable from data-weak situations where it operates as an age-structured production model, to complex situations where it can flexibly incorporate multiple data sources and account for biological and environmental processes. SS implements compensatory population dynamics through use of a function relating mean recruitment to spawner reproductive output. This function enhances the ability of SS to operate in data-weak situations and enables it to estimate fishery management quantities such as fishing rates that would provide for maximum sustainable yield and to employ these rates in forecasts of potential yield and future stock status. Complex model configurations such as multiple areas and multiple growth morphs are possible, tag-recapture data can be used to aid estimation of movement rates among areas, and most parameters can change over time in response to environmental and ecosystem factors. SS is coded using Auto-Differentiation Model Builder, so inherits its powerful capability to efficiently estimate hundreds of parameters using either maximum likelihood or Bayesian inference. Output processing, principally through a package developed in R, enables rapid model diagnosis. Details of the underlying population dynamics and the statistical framework used within SS are provided.

Incorporating ecological principles into statistical models for the prediction of species’ distribution and abundance

Understanding the determinants of species’ distributions and abundances is a central theme in ecology. The development of statistical models to achieve this has a long history and the notion that the model should closely reflect underlying scientific understanding has encouraged ecologists to adopt complex statistical methods as they arise. In this paper we describe a Bayesian hierarchical model that reflects a conceptual ecological model of multi‐scaled environmental determinants of riverine fish species’ distributions and abundances. We illustrate this with distribution and abundance data of a small‐bodied fish species, the Empire gudgeon Hypseleotris galii, in the Mary and Albert Rivers, Queensland, Australia. Specifically, the model sought to address; 1) the extent that landscape‐scale abiotic variables can explain the species’ distribution compared to local‐scale variables, 2) how local‐scale abiotic variables can explain species’ abundances, and 3) how are these local‐scale relationships mediated by landscape‐scale variables. Overall, the model accounted for around 60% of variation in the distribution and abundance of H. galii. The findings show that the landscape‐scale variables explain much of the distribution of the species; however, there was considerable improvement in estimating the species’ distribution with the addition of local‐scale variables. There were many strong relationships between abundance and local‐scale abiotic variables; however, several of these relationships were mediated by some of the landscape‐scale variables. The extent of spatial autocorrelation in the data was relatively low compared to the distances among sampling reaches. Our findings exemplify that Bayesian statistical modelling provides a robust framework for statistical modelling that reflects our ecological understanding. This allows ecologists to address a range of ecological questions with a single unified probability model rather than a series of disconnected analyses.

A new statistical modeling and optimization framework for establishing high-resolution PM10 emission inventory – I. Stepwise regression model development and application

A new stepwise regression method was proposed in this study to develop a high-resolution emission inventory. Utilizing PM10 emission inventory as an example, a group of regression models for various industrial and non-industrial sectors were developed based on an emission case study of Handan region in northern China. The main data requirements of the regression models for industrial sectors were coal consumption, electricity consumption, other solid fuel consumption, and annual operating cost of exhaust gas control devices. The data requirements for non-industrial sector emission estimations were the area of construction sites, the length of transportation routes, the vehicle population, and the cultivated land area. The models were then applied to Tangshan region in northern China, and the results revealed that the developed regression models had relatively satisfactory performance. Modeling error at the regional level and county level was 17.0% and 30.4%, respectively. The regression models were also applied to other regions in northern China. The results indicated that the new method could generate emission estimations with significantly lower error than found in previous emission inventory studies. The modeling uncertainty due to the allocation of modeling input parameter value, from regional level to county level, was also discussed in this study. It was concluded that the new statistical method presented is a promising technique for the development and updating of high-resolution emission inventories based on easily obtained statistical data. It can be performed with data available from the current statistical reporting system in China. It does not require a detailed data investigation and survey, as is necessary by conventional “bottom-up” emission inventory investigation approach.

A new statistical modeling and optimization framework for establishing high-resolution PM10 emission inventory – II. Integrated air quality simulation and optimization for performance improvement

An integrated air quality simulation and optimization approach was proposed to improve the accuracy of the high-resolution PM10 emission inventories developed through regression models. A case study of Tangshan region in northern China was presented as an example. A linear programming optimization model was developed to minimize the mean error between simulated and monitored PM10 concentrations in different counties. A transfer coefficient matrix was used to represent source–receptor relationships and was developed through running a MM5-CMAQ air quality model. The results revealed that the proposed simulation–optimization approach could decrease the error of the PM10 emission inventory from 17.0 to 7.9% at the regional level, and from 31.44 to 14.17% at the county level. Accuracy improvement ranged from 0.39 to 61.44% for the study counties in Tangshan. The correlation coefficient between the estimated PM10 emissions and the monitored PM10 concentration in various counties was also increased from 0.82 to 0.91. Together with the regression models, the simulation–optimization method provides a promising and effective framework for developing high-accuracy and high-resolution air pollutant emission inventories.

A statistical and computational theory for robust and sparse Kalman smoothing

Kalman smoothers reconstruct the state of a dynamical system starting from noisy output samples. While the classical estimator relies on quadratic penalization of process deviations and measurement errors, extensions that exploit Piecewise Linear Quadratic (PLQ) penalties have been recently proposed in the literature. These new formulations include smoothers robust with respect to outliers in the data, and smoothers that keep better track of fast system dynamics, e.g. jumps in the state values. In addition to L2, well known examples of PLQ penalties include the L1, Huber and Vapnik losses. In this paper, we use a dual representation for PLQ penalties to build a statistical modeling framework and a computational theory for Kalman smoothing.We develop a statistical framework by establishing conditions required to interpret PLQ penalties as negative logs of true probability densities. Then, we present a computational framework, based on interior-point methods, that solves the Kalman smoothing problem with PLQ penalties and maintains the linear complexity in the size of the time series, just as in the L2 case. The framework presented extends the computational efficiency of the Mayne-Fraser and Rauch-Tung-Striebel algorithms to a much broader non-smooth setting, and includes many known robust and sparse smoothers as special cases.

DEVELOPING RECOMMENDATIONS FOR UNDERTAKING CPUE STANDARDISATION USING OBSERVER PROGRAM DATA

Abundance indices based on nominal CPUE do not take into account confounding factors such as fishing strategy and environmental conditions, that can decouple any underlying abundance signal in the catch rate. As such, the assumption that CPUE is proportional to abundance is frequently violated. CPUE standardisation is one of the common analyses applied. The aims of this paper were to provide a statistical modelling framework for conducting CPUE standardisations using the Observer Program data for bigeye tuna, yellowfin tuna, albacore and southern bluefin tuna, and provide a comparison in the trends between the nominal CPUEs and their standardised indices obtained. The CPUE standardisations were conducted on the Observer Program collected between 2005 and 2007, by applying GLM analysis using the Tweedie distribution. The results suggested that year, area, HBF and bait factors significantly influenced the nominal CPUEs for the four tuna species of interest. Some extreme peaks and troughs in the nominal time series were smoothed in the standardised CPUE time<br />series. The high degree of temporal variability that is still shown in the standardised CPUE trends suggests that the data are too sparse to give any meaningful indication of proxy abundance. Nevertheless, this may also suggest that variables used in the GLMs do not sufficiently account for all<br />of the confounding factors, or abundance may indeed be truly variable.

Application of propensity scores and potential outcomes to estimate effectiveness of traffic safety countermeasures: Exploratory analysis using intersection lighting data

More than 5.5 million police-reported traffic crashes occurred in the United States in 2009, resulting in 33,808 fatalities and more than 2.2 million injuries. Significant funds are expended annually by federal, state, and local transportation agencies in an effort to reduce traffic crashes. Effective safety management involves selecting highway and street locations with potential for safety improvements; correctly diagnosing safety problems; identifying appropriate countermeasures; prioritizing countermeasure implementation at selected sites; and, evaluating the effectiveness of implemented countermeasures. Accurate estimation of countermeasure effectiveness is a critical component of the safety management process. In this study, a statistical modeling framework, based on propensity scores and potential outcomes, is described to estimate countermeasure effectiveness from non-randomized observational data. Average treatment effects are estimated using semi-parametric estimation methods. To demonstrate the framework, the average treatment effect of fixed roadway lighting at intersections in Minnesota is estimated. The results indicate that fixed roadway lighting reduces expected nighttime crashes by approximately 6%, which compares favorably to other, recent lighting-safety research findings.

An introduction to generalized linear models—third edition

- Introduces GLMs in a way that enables readers to understand the unifying structure that underpins them. - Discusses common concepts and principles of advanced GLMs, including nominal and ordinal regression, survival analysis, and longitudinal analysis. - Connects Bayesian analysis and MCMC methods to fit GLMs. - Contains numerous examples from business, medicine, engineering, and the social sciences. - Provides the example code for R, Stata, and WinBUGS to encourage implementation of the methods. - Offers the data sets and solutions to the exercises online. Continuing to emphasize numerical and graphical methods, An Introduction to Generalized Linear Models, Third Edition provides a cohesive framework for statistical modeling. This new edition of a bestseller has been updated with Stata, R, and WinBUGS code as well as three new chapters on Bayesian analysis. Like its predecessor, this edition presents the theoretical background of generalized linear models (GLMs) before focusing on methods for analyzing particular kinds of data. It covers normal, Poisson, and binomial distributions; linear regression models; classical estimation and model fitting methods; and frequentist methods of statistical inference. After forming this foundation, the authors explore multiple linear regression, analysis of variance (ANOVA), logistic regression, log-linear models, survival analysis, multilevel modeling, Bayesian models, and Markov chain Monte Carlo (MCMC) methods. Using popular statistical software programs, this concise and accessible text illustrates practical approaches to estimation, model fitting, and model comparisons. It includes examples and exercises with complete data sets for nearly all the models covered.

Statistical guidance for experimental design and data analysis of mutation detection in rare monogenic mendelian diseases by exome sequencing.

Recently, whole-genome sequencing, especially exome sequencing, has successfully led to the identification of causal mutations for rare monogenic Mendelian diseases. However, it is unclear whether this approach can be generalized and effectively applied to other Mendelian diseases with high locus heterogeneity. Moreover, the current exome sequencing approach has limitations such as false positive and false negative rates of mutation detection due to sequencing errors and other artifacts, but the impact of these limitations on experimental design has not been systematically analyzed. To address these questions, we present a statistical modeling framework to calculate the power, the probability of identifying truly disease-causing genes, under various inheritance models and experimental conditions, providing guidance for both proper experimental design and data analysis. Based on our model, we found that the exome sequencing approach is well-powered for mutation detection in recessive, but not dominant, Mendelian diseases with high locus heterogeneity. A disease gene responsible for as low as 5% of the disease population can be readily identified by sequencing just 200 unrelated patients. Based on these results, for identifying rare Mendelian disease genes, we propose that a viable approach is to combine, sequence, and analyze patients with the same disease together, leveraging the statistical framework presented in this work.

A Dynamic Bivariate Poisson Model for Analysing and Forecasting Match Results in the English Premier League

Attack and defense strengths of football teams vary over time due to changes in the teams of players or their managers. We develop a statistical model for the analysis and forecasting of football match results which are assumed to come from a bivariate Poisson distribution with intensity coefficients that change stochastically over time. This development presents a novelty in the statistical time series analysis of match results from football or other team sports. Our treatment is based on state space and importance sampling methods which are computationally efficient. The out-of-sample performance of our methodology is verified in a betting strategy that is applied to the match outcomes from the 2010/11 and 2011/12 seasons of the English Premier League. We show that our statistical modeling framework can produce a significant positive return over the bookmaker's odds.

Protein Significance Analysis in Selected Reaction Monitoring (SRM) Measurements

Selected reaction monitoring (SRM) is a targeted mass spectrometry technique that provides sensitive and accurate protein detection and quantification in complex biological mixtures. Statistical and computational tools are essential for the design and analysis of SRM experiments, particularly in studies with large sample throughput. Currently, most such tools focus on the selection of optimized transitions and on processing signals from SRM assays. Little attention is devoted to protein significance analysis, which combines the quantitative measurements for a protein across isotopic labels, peptides, charge states, transitions, samples, and conditions, and detects proteins that change in abundance between conditions while controlling the false discovery rate. We propose a statistical modeling framework for protein significance analysis. It is based on linear mixed-effects models and is applicable to most experimental designs for both isotope label-based and label-free SRM workflows. We illustrate the utility of the framework in two studies: one with a group comparison experimental design and the other with a time course experimental design. We further verify the accuracy of the framework in two controlled data sets, one from the NCI-CPTAC reproducibility investigation and the other from an in-house spike-in study. The proposed framework is sensitive and specific, produces accurate results in broad experimental circumstances, and helps to optimally design future SRM experiments. The statistical framework is implemented in an open-source R-based software package SRMstats, and can be used by researchers with a limited statistics background as a stand-alone tool or in integration with the existing computational pipelines.

Analysis of shape isomer yields of heavy elements in the framework of dynamical-statistical model

Experimental data on shape isomer yield for α + 239 Pu reaction at E α lab = 20 – 29 MeV are analyzed in the framework of the combined dynamical statistical model. The possibility of determining the double humped fission barrier parameters are discussed for some Cm isotopes and it is shown that the depth of the second potential well should be smaller than the results of statistical model calculations.

SPATIO-TEMPORAL MODELING OF AIR POLLUTION INCORPORATING TIME-VARYING METEOROLOGY

Background and Aims: In the Southern California Children’s Health Study (CHS), we have measured ozone and oxides of nitrogen in 942 locations in 12 communities in two seasons for two weeks each, and particulate elemental and organic carbon at 217 locations for two 4-week periods in 8 of these communities. These measurements have been used in combination with various traffic-related predictors to build spatial models for pollution concentrations for all CHS subjects. However, wind patterns and regional pollution levels vary considerably over time and should be taken into account when assigning annual-average exposure levels. Methods: A theoretical form of the covariance in exposures at different locations as a function of spatial separation and wind can be derived by partial differential equations. We developed a statistical spatio-temporal modeling framework that incorporates the distribution of wind speeds and directions over time and estimates the exposure at unmeasured locations over time, based on concurrent measurements at other locations, the central site measurements, and a line source dispersion model for traffic (CALINE). These estimates are then integrated over time to obtain annual average exposures. Results: A model that included traffic-related covariates achieved cross-validated R2s of 0.60-0.79 for nitrogen oxides, with the major contributor being CALINE; incorporation of residual spatial correlation structure significantly improved model fit. Predictions of particulate EC were much poorer, (R2 < 0.3), indicating that traffic predictors alone are not suitable for all pollutants. Associations with lung function were significantly stronger for spatially modeled NOx pollution (p <.005) than with CALINE predictions or other traffic variables. Conclusions: Meteorological information, particularly wind speed and direction, improve the predictions of air pollution exposures. Novel ways of incorporating the functional form of winds into the spatial covariance structure of our prediction model are presented.

Polarization dynamics and non-equilibrium switching processes in ferroelectrics

Time- and temperature-dependent effects are critical for the operation of non-volatile memories based on ferroelectrics. In this paper, we assume a domain nucleation process of the polarization reversal and we discuss the polarization dynamics in the framework of a non-equilibrium statistical model. This approach yields analytical expressions which can be used to explain a wide range of time- and temperature-dependent effects in ferroelectrics. Domain wall velocity derived in this work is consistent with a domain wall creep behavior in ferroelectrics. In the limiting case of para-electric equilibrium, the model yields the well-known Curie law. We also present experimental P-E loops data obtained for soft ferroelectrics at various temperatures. The experimental coercive fields at various temperatures are well predicted by the coercive field formula derived in our theory.

Theoretical study of evaporation cross sections in the synthesis of very neutron-deficient nuclei

The synthesis of rare-earth neutron-deficient nuclei with large Z/N ratio {approx_equal}0.88 is studied within the framework of the standard statistical model. The fusion cross sections are calculated on the basis of the nuclear reaction video model. The deexcitation process is calculated with the help of the statistical code alice. It is found that the excitation functions can be predicted using a few exited experimental data by carefully choosing the input parameters in the statistical model. The results obtained show that a satisfactory description of the experimental evaporation cross sections requires a great reduction in the theoretical fission barriers.

Statistical inference for stochastic simulation models - theory and application

Statistical models are the traditional choice to test scientific theories when observations, processes or boundary conditions are subject to stochasticity. Many important systems in ecology and biology, however, are difficult to capture with statistical models. Stochastic simulation models offer an alternative, but they were hitherto associated with a major disadvantage: their likelihood functions can usually not be calculated explicitly, and thus it is difficult to couple them to well-established statistical theory such as maximum likelihood and Bayesian statistics. A number of new methods, among them Approximate Bayesian Computing and Pattern-Oriented Modelling, bypass this limitation. These methods share three main principles: aggregation of simulated and observed data via summary statistics, likelihood approximation based on the summary statistics, and efficient sampling. We discuss principles as well as advantages and caveats of these methods, and demonstrate their potential for integrating stochastic simulation models into a unified framework for statistical modelling.