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USGS2022

A practical guide to understanding and validating complex models using data simulations

Biologists routinely fit novel and complex statistical models to push the limits of our understanding. Examples include, but are not limited to, flexible Bayesian approaches (e.g. BUGS, stan), frequentist and likelihood-based approaches (e.g. packages lme4 ) and machine learning methods. These software and programs afford the user greater control and flexibility in tailoring complex hierarchical models. However, this level of control and flexibility places a higher degree of responsibility on the user to evaluate the robustness of their statistical inference. To determine how often biologists are running model diagnostics on hierarchical models, we reviewed 50 recently published papers in 2021 in the journal Nature Ecology & Evolution , and we found that the majority of published papers did not report any validation of their hierarchical models, making it difficult for the reader to assess the robustness of their inference. This lack of reporting likely stems from a lack of standardized guidance for best practices and standard methods. Here, we provide a guide to understanding and validating complex models using data simulations. To determine how often biologists use data simulation techniques, we also reviewed 50 recently published papers in 2021 in the journal Methods Ecology & Evolution . We found that 78% of the papers that proposed a new estimation technique, package or model used simulations or generated data in some capacity (18 of 23 papers); but very few of those papers (5 of 23 papers) included either a demonstration that the code could recover realistic estimates for a dataset with known parameters or a demonstration of the statistical properties of the approach. To distil the variety of simulations techniques and their uses, we provide a taxonomy of simulation studies based on the intended inference. We also encourage authors to include a basic validation study whenever novel statistical models are used, which in general, is easy to implement. Simulating data helps a researcher gain a deeper understanding of the models and their assumptions and establish the reliability of their estimation approaches. Wider adoption of data simulations by biologists can improve statistical inference, reliability and open science practices.

Methods in Ecology and Evolution↗

USGS2016

Fire in the Earth System: Bridging data and modeling research

Significant changes in wildfire occurrence, extent, and severity in areas such as western North America and Indonesia in 2015 have made the issue of fire increasingly salient in both the public and scientific spheres. Biomass combustion rapidly transforms land cover, smoke pours into the atmosphere, radiative heat from fires initiates dramatic pyrocumulus clouds, and the repeated ecological and atmospheric effects of fire can even impact regional and global climate. Furthermore, fires have a significant impact on human health, livelihoods, and social and economic systems. Modeling and databased methods to understand fire have rapidly coevolved over the past decade. Satellite and ground-based data about present-day fire are widely available for applications in research and fire management. Fire modeling has developed in part because of the evolution in vegetation and Earth system modeling efforts, but parameterizations and validation are largely focused on the present day because of the availability of satellite data. Charcoal deposits in sediment cores have emerged as a powerful method to evaluate trends in biomass burning extending back to the Last Glacial Maximum and beyond, and these records provide a context for present-day fire. The Global Charcoal Database version 3 compiled about 700 charcoal records and more than 1,000 records are expected for the future version 4. Together, these advances offer a pathway to explore how the strengths of fire data and fire modeling could address the weaknesses in the overall understanding of human-climate–fire linkages. A community of researchers studying fire in the Earth system with individual expertise that included paleoecology, paleoclimatology, modern ecology, archaeology, climate, and Earth system modeling, statistics, geography, biogeochemistry, and atmospheric science met at an intensive workshop in Massachusetts to explore new research directions and initiate new collaborations. Research themes, which emerged from the workshop participants via preworkshop surveys, focused on addressing the following questions: What are the climatic, ecological, and human drivers of fire regimes, both past and future? What is the role of humans in shaping historical fire regimes? How does fire ecology affect land cover changes, biodiversity, carbon storage, and human land uses? What are the historical fire trends and their impacts across biomes? Are their impacts local and/or regional? Are the fire trends in the last two decades unprecedented from a historical perspective? The workshop 1 aimed to develop testable hypotheses about fire, climate, vegetation, and human interactions by leveraging the confluence of proxy, observational, and model data related to decadal- to millennial-scale fire activity on our planet. New research directions focused on broad interdisciplinary approaches to highlight how knowledge about past fire activity could provide a more complete understanding of the predictive capacity of fire models and inform fire policy in the face of our changing climate.

Bulletin of the American Meteorological Society↗

USGS2001

Resource materials for a GIS spatial analysis course

This report consists of materials prepared for a GIS spatial analysis course offered as part of the Geography curriculum at the University of Nevada, Reno and the University of California at Santa Barbara in the spring of 2000. The report is intended to share information with instructors preparing spatial-modeling training and scientists with advanced GIS expertise. The students taking this class had completed each universities GIS curriculum and had a foundation in statistics as part of a science major. This report is organized into chapters that contain the following: Slides used during lectures, Guidance on the use of Arcview, Introduction to filtering in Arcview, Conventional and spatial correlation in Arcview, Tools for fuzzification in Arcview, Data and instructions for creating using ArcSDM for simple weights-of-evidence, fuzzy logic, and neural network models for Carlin-type gold deposits in central Nevada, Reading list on spatial modeling, and Selected student spatial-modeling posters from the laboratory exercises.

Open-File Report↗

USGS1993

Concentrations of tritium and strontium-90 in water from selected wells at the Idaho National Engineering Laboratory after purging one, two, and three borehole volumes

Water from 11 wells completed in the Snake River Plain aquifer at the Idaho National Engineering Laboratory was sampled as part of the U.S. Geological Survey's quality assurance program to determine the effect of purging different borehole volumes on tritium and strontium-90 concentrations. Wells were selected for sampling on the basis of the length of time it took to purge a borehole volume of water. Samples were collected after purging one, two, and three borehole volumes. The U.S. Department of Energy's Radiological and Environmental Sciences Laboratory provided analytical services. Statistics were used to determine the reproducibility of analytical results. The comparison between tritium and strontium-90 concentrations after purging one and three borehole volumes and two and three borehole volumes showed that all but two sample pairs with defined numbers were in statistical agreement. Results indicate that concentrations of tritium and strontium-90 are not affected measurably by the number of borehole volumes purged.

Water-Resources Investigations Report↗

USGS2022

Estimated daily mean streamflow in Iowa using the Flow-Duration Curve Transfer Method StreamStats application

The U.S. Geological Survey (USGS) operates many streamgages throughout the country that provide historical and real-time daily streamflow information. Accurate estimates of daily streamflow and the percentage of time that a certain volume of streamflow occurs or is exceeded in a stream is crucial information for structure design and other activities conducted by federal, state, and local officials. However, many important locations are ungaged and therefore lack the in-depth data provided at streamgages. The USGS provides hydrologic information like streamflow statistics and drainage basin characteristics in the web-based tool StreamStats (https://streamstats.usgs.gov/ss/). A newly released StreamStats functionality developed by the StreamStats development team working closely with USGS scientists in the Central Midwest Water Science Center incorporates flow-duration statistics already available at USGS streamgages to calculate daily mean streamflow estimates for rural, ungaged locations in Iowa [1].

Iowa↗

USGS2016

Daniel Goodman’s empirical approach to Bayesian statistics

Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty about the state of knowledge. Bayesian statistics has often been associated with the idea that knowledge is subjective and that a probability distribution represents a personal degree of belief. Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He sought to ground his Bayesian approach in data, and advocated the construction of a prior as an empirical histogram of “similar” cases. In this way, the posterior distribution that results from a Bayesian analysis combined comparable previous data with case-specific current data, using Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it was difficult in practice. If based on a true representation of our knowledge and uncertainty, Goodman argued that risk assessment and decision-making could be an exact science, despite the uncertainties. In his view, Bayesian statistics is a critical component of this science because a Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained that the Bayesian machinery, following the rules of conditional probability, offered the best legitimate inference from available data. We give an example of an informative prior in a recent study of Steller sea lion spatial use patterns in Alaska.

PeerJ↗

USGS2023

Obtaining and applying public data for training students in technical statistical writing: Case studies with data from U.S. Geological Survey and general ecological literature

Effective undergraduate statistical education requires training using real-world data. Textbook datasets seldom match the complexities and messiness of real-world data and finding these datasets can be challenging for educators. Consulting and industrial datasets often have nondisclosure agreements. Academic datasets often require subject area expertise beyond those of a general education or lack connections to real-world applications. Many governments, including the United States, now require the release of data from projects they directly complete or fund though grants and contracts. We show how statistical educators may find datasets and incorporate them into courses. Specifically, we use two examples from the U.S. Geological Survey (USGS) and one example from the ecology literature. We demonstrate the use of these datasets in an upper-level analysis of variance (ANOVA) class. In addition to describing how we found the datasets, we describe how to include them into course work and the course’s student assessments. We have used these datasets over multiple semesters and included student feedback from these courses. Although our examples focus on an ANOVA class, the general methods for finding data shared here could be used for statistical classes ranging from high school to graduate education. Supplementary materials for this article are available online.

Journal of Statistics and Data Science Education↗

USGS2021

Citizen science data collection for integrated wildlife population analyses

Citizen science, or community science, has emerged as a cost-efficient method to collect data for wildlife monitoring. To inform research and conservation, citizen science sampling designs should collect data that match the robust statistical analyses needed to quantify species and population patterns. Further increasing the contributions of citizen science, integrating citizen science data with other datasets and datatypes can improve population estimates and expand the spatiotemporal extent of inference. We demonstrate these points with a citizen science program called iSeeMammals developed in New York state in 2017 to supplement costly systematic spatial capture-recapture sampling by collecting opportunistic data from one-off observations, hikes, and camera traps. iSeeMammals has initially focused on the growing population of American black bear ( Ursus americanus ), with integrated analysis of iSeeMammals camera trap data with systematic data for a region with a growing bear population. The triumvirate of increased spatial and temporal coverage by at least twofold compared to systematic sampling, an 83% reduction in annual sampling costs, and improved density estimates when integrated with systematic data highlight the benefits of collecting presence-absence data in citizen science programs for estimating population patterns. Additional opportunities will come from applying presence-only data, which are oftentimes more prevalent than presence-absence data, to integrated models. Patterns in data submission and filtering also emphasize the importance of iteratively evaluating patterns in engagement, usability, and accessibility, especially focusing on younger adult and teenage demographics, to improve data quality and quantity. We explore how the development and use of integrated models may be paired with citizen science project design in order to facilitate repeated use of datasets in standalone and integrated analyses for supporting wildlife monitoring and informing conservation.

Frontiers in Ecology and Evolution↗

USGS2010

A general science-based framework for dynamical spatio-temporal models

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially-explicit processes that evolve over time. Correspondingly, in recent years there has been a significant amount of research on new statistical methodology for such models. Although descriptive models that approach the problem from the second-order (covariance) perspective are important, and innovative work is being done in this regard, many real-world processes are dynamic, and it can be more efficient in some cases to characterize the associated spatio-temporal dependence by the use of dynamical models. The chief challenge with the specification of such dynamical models has been related to the curse of dimensionality. Even in fairly simple linear, first-order Markovian, Gaussian error settings, statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters. In addition, this framework has allowed for the specification of science based parameterizations (and associated prior distributions) in which classes of deterministic dynamical models (e. g., partial differential equations (PDEs), integro-difference equations (IDEs), matrix models, and agent-based models) are used to guide specific parameterizations. Most of the focus for the application of such models in statistics has been in the linear case. The problems mentioned above with linear dynamic models are compounded in the case of nonlinear models. In this sense, the need for coherent and sensible model parameterizations is not only helpful, it is essential. Here, we present an overview of a framework for incorporating scientific information to motivate dynamical spatio-temporal models. First, we illustrate the methodology with the linear case. We then develop a general nonlinear spatio-temporal framework that we call general quadratic nonlinearity and demonstrate that it accommodates many different classes of scientific-based parameterizations as special cases. The model is presented in a hierarchical Bayesian framework and is illustrated with examples from ecology and oceanography. ?? 2010 Sociedad de Estad??stica e Investigaci??n Operativa.

Test↗

USGS2018

The potential for citizen science to produce reliable and useful information in ecology

We examined features of citizen science that influence data quality, inferential power, and usefulness in ecology. As background context for our examination, we considered topics such as ecological sampling (probability based, purposive, opportunistic), linkage between sampling technique and statistical inference(designbased,modelbased),andscientificparadigms(confirmatory,exploratory).Wedistinguished several types of citizen science investigations, from intensive research with rigorous protocols targeting clearly articulated questions to mass-participation internet-based projects with opportunistic data collection lacking samplingdesign,andexaminedoverarchingobjectives,design,analysis,volunteertraining,andperformance. We identified key features that influence data quality: project objectives, design and analysis, and volunteer training and performance. Projects with good designs, trained volunteers, and professional oversight can meet statistical criteria to produce high-quality data with strong inferential power and therefore are well suited for ecological research objectives. Projects with opportunistic data collection, little or no sampling design, and minimal volunteer training are better suited for general objectives related to public education or data exploration because reliable statistical estimation can be difficult or impossible. In some cases, statistically robust analytical methods, external data, or both may increase the inferential power of certain opportunistically collected data. Ecological management, especially by government agencies, frequently requires data suitable for reliable inference. With standardized protocols, state-of-the-art analytical methods, and well-supervised programs, citizen science can make valuable contributions to conservation by increasing the scope of species monitoring efforts. Data quality can be improved by adhering to basic principles of data collection and analysis, designing studies to provide the data quality required, and including suitable statistical expertise, thereby strengthening the science aspect of citizen science and enhancing acceptance by the scientific community and decision makers.

Conservation Biology↗

USGS2025

Impact of a place-based role-playing exercise on student sense of classroom community and science identity in a hydrology class

Fostering a sense of classroom community in earth science classes supports students’ sense of belonging within the classroom and the broader scientific community, helping them build a sense of identity as a geoscientist. This study examines the effects of incorporating a 2-week, collaborative role-playing activity on sense of classroom community and science identity in an introductory hydrology class. Students assumed roles of residents, medical center representatives, government employees, and environmental activists to learn about flooding through a community-centered lens, focusing on a flood event in Harris County, Texas during Tropical Storm Allison. Pre-post-surveys were given immediately before and after the learning module to evaluate classroom community, science identity using Likert scales, and hydrologist identity using a pictorial scale. Qualitative analysis of a short-answer question in which students defined “hydrologist” provided context for quantitative identity data. Post-survey data on classroom community shows an increase in mean agreement as compared to the pre-survey. This increase was statistically significant for four classroom community statements. Paired science identity data show small effect size and no significant change, but pictorial identity as a hydrologist shows significant growth. Social aspects of the role-playing activity did not significantly alter student’s already high science identity but altered their conceptions of the social implications of hydrology and increased identity as hydrologists. The significant increase in classroom community has important implications for using role-playing as an active learning strategy to enhance student learning experience by creating a positive classroom climate and connecting hydrology concepts to community needs.

Journal of Geoscience Education↗

USGS2020

Methods to quality assure, plot, summarize, interpolate, and extend groundwater-level information—Examples for the Mississippi River Valley alluvial aquifer

Large-scale computational investigations of groundwater levels are proposed to accelerate science delivery through a workflow spanning database assembly, statistics, and information synthesis and packaging. A water-availability study of the Mississippi River alluvial plain, and particularly the Mississippi River Valley alluvial aquifer (MRVA), is ongoing. Software (visGWDBmrva) has been released as part of the study that demonstrates groundwater informatics for the aquifer. Considerable water-level data collected by multiple agencies over a seven-state area exist (18,903 wells; 287,272 measurements [April 22, 2019]). Data and metadata quality assurance methods, basic statistics, hydrograph visualization, outlier identification, hypothesis testing, and time-series modeling are described. Two approaches (generalized additive models [GAMs] and support vector machines [SVMs]) are used for data interpolation and extension to monthly water-level estimates. Numerical congruence between GAM and SVM estimates will be useful to limit inclusion of monthly estimates from subsequent science activities.

Mississippi River valley↗

USGS1989

Optimal-adaptive filters for modelling spectral shape, site amplification, and source scaling

Optimal filtering techniques have been used successfully in various areas in science and engineering. They are based on statistical properties of the signal and the noise, and stochastic approximation theory. In addition to filtering, optimal filters can also be used for smoothing, prediction, and system identification. This paper introduces some applications of optimal filtering techniques to earthquake engineering by using the so-called ARMAX models. Three applications are presented: (a) spectral modelling of ground accelerations, (b) site amplification (i.e., the relationship between two records obtained at different sites during an earthquake), and (c) source scaling (i.e., the relationship between two records obtained at a site during two different earthquakes). A numerical example for each application is presented by using recorded ground motions. The results show that the optimal filtering techniques provide elegant solutions to above problems, and can be a useful tool in earthquake engineering.

Soil Dynamics and Earthquake Engineering↗

USGS2022

Yuma Ridgway’s rail selenium exposure and occupancy within managed and unmanaged emergent marshes at the Salton Sea

Yuma Ridgway’s rail ( Rallus obsoletus yumanensis , hereafter, rail) is an endangered species for which patches of emergent marsh within the Salton Sea watershed comprise a substantial part of habitat for the species’ disjointed range in the southwestern United States. These areas of emergent marsh include (1) marshes managed by federal (particularly the U.S. Fish and Wildlife Service’s Sonny Bono Salton Sea National Wildlife Refuge), state (California Department of Fish and Wildlife), and local (Imperial Irrigation District) resource agencies that are sustained by direct deliveries of Colorado River water and (2) unmanaged marshes sustained by agricultural drainage water. Management of rail habitat in this arid environment is complicated by increasingly limited availability of unimpaired freshwater owing to water management decisions associated with the Quantification Settlement Agreement and risks posed by potentially harmful concentrations of selenium found in agricultural drainage water that can readily bioaccumulate in aquatic food webs. To provide timely science for managers, herein we report summary statistics for managed and unmanaged emergent marshes sampled at the Salton Sea during the rail breeding season of 2016 pertaining to (1) selenium concentrations in food webs representing dietary pathways of selenium exposure and (2) patterns of rail occupancy and inter-marsh movements, estimated abundance, and regional population size of rail. For selenium-specific objectives, we sampled unfiltered surface water, midge larvae (Chironomidae), water boatmen (Corixidae), mosquitofish ( Gambusia spp.), and crayfish (Astacidae). Selenium samples were collected from 15 fixed sampling points, each in managed and unmanaged marshes, during late February, April, and June 2016, which corresponded to rail pre-nesting, nesting, and fledgling reproductive life-stages, respectively. Two areas within the two treatment types (managed versus unmanaged marsh) were of particular interest to help assess risks associated with changing sea dynamics and different water-management strategies: (1) a large unmanaged marsh (Morton Bay) unintentionally created in approximately 2008 when it became separated from the Salton Sea as water inflows began to drop and a berm formed from accumulated sediment and (2) a restored marsh (HZ9A) managed by the Sonny Bono Salton Sea National Wildlife Refuge, which is currently supplied with Colorado River water but may be sustained in the future by a blend of clean (that is, low selenium) Colorado River and agricultural drainage water with higher selenium from the Alamo River. Hence, baseline data for these marshes are important for future management decisions. We also report selenium concentrations in rail blood, head feathers, and breast feathers from rails captured as part of the movement study. Results indicated relatively higher risks from dietary selenium exposure for rails occupying unmanaged marshes compared to managed marshes and similar risks among unmanaged marshes. However, risks also were potentially elevated for rails occupying some managed marshes (that is, the Hazard Marshes), where relatively high proportions of Chironomidae and mosquitofish exceeded dietary thresholds for selenium effects on avian reproduction. For rail-specific objectives, we quantified occupancy and spatial distribution using call count data analyzed with imperfect detection models. Imperfect detection models allowed us to jointly estimate detection probability and abundance of detected rails in association with habitats. We then used estimates of detection probability and abundance at the habitat level to extrapolate rail population abundance for the Salton Sea region. Inter- and intra-marsh movements were described from over 5,000 locations obtained from 15 radio-marked rails. Resultant space use patterns indicated that, in general, selenium risk to individuals is not equally shared because of high levels of territoriality and very limited movement throughout the landscape. Moreover, the largest contiguous blocks of habitat are associated with unmanaged marshlands located on the former southeastern shoreline and outside traditional management areas and authorities. Thus, a substantial proportion of the rail population that is using unmanaged marsh on the southeastern shoreline may have disproportionate risk of elevated selenium exposure, yet how that risk translates to population-level effects remains unknown.

California↗

USGS2004

Evaluation of Methods Used for Estimating Selected Streamflow Statistics, and Flood Frequency and Magnitude, for Small Basins in North Coastal California

Accurate streamflow statistics are essential to water resource agencies involved in both science and decision-making. When long-term streamflow data are lacking at a site, estimation techniques are often employed to generate streamflow statistics. However, procedures for accurately estimating streamflow statistics often are lacking. When estimation procedures are developed, they often are not evaluated properly before being applied. Use of unevaluated or underevaluated flow-statistic estimation techniques can result in improper water-resources decision-making. The California State Water Resources Control Board (SWRCB) uses two key techniques, a modified rational equation and drainage basin area-ratio transfer, to estimate streamflow statistics at ungaged locations. These techniques have been implemented to varying degrees, but have not been formally evaluated. For estimating peak flows at the 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals, the SWRCB uses the U.S. Geological Surveys (USGS) regional peak-flow equations. In this study, done cooperatively by the USGS and SWRCB, the SWRCB estimated several flow statistics at 40 USGS streamflow gaging stations in the north coast region of California. The SWRCB estimates were made without reference to USGS flow data. The USGS used the streamflow data provided by the 40 stations to generate flow statistics that could be compared with SWRCB estimates for accuracy. While some SWRCB estimates compared favorably with USGS statistics, results were subject to varying degrees of error over the region. Flow-based estimation techniques generally performed better than rain-based methods, especially for estimation of December 15 to March 31 mean daily flows. The USGS peak-flow equations also performed well, but tended to underestimate peak flows. The USGS equations performed within reported error bounds, but will require updating in the future as peak-flow data sets grow larger. Little correlation was discovered between estimation errors and geographic locations or various basin characteristics. However, for 25-percentile year mean-daily-flow estimates for December 15 to March 31, the greatest estimation errors were at east San Francisco Bay area stations with mean annual precipitation less than or equal to 30 inches, and estimated 2-year/24-hour rainfall intensity less than 3 inches.

Scientific Investigations Report↗

USGS2009

Northern Prairie Wildlife Research Center

The Northern Prairie Wildlife Research Center (NPWRC) conducts integrated research to fulfill the Department of the Interior's responsibilities to the Nation's natural resources. Located on 600 acres along the James River Valley near Jamestown, North Dakota, the NPWRC develops and disseminates scientific information needed to understand, conserve, and wisely manage the Nation's biological resources. Research emphasis is primarily on midcontinental plant and animal species and ecosystems of the United States. During the center's 40-year history, its scientists have earned an international reputation for leadership and expertise on the biology of waterfowl and grassland birds, wetland ecology and classification, mammalian behavior and ecology, grassland ecosystems, and application of statistics and geographic information systems. To address current science challenges, NPWRC scientists collaborate with researchers from other U.S. Geological Survey centers and disciplines (Biology, Geography, Geology, and Water) and with biologists and managers in the Department of the Interior (DOI), other Federal agencies, State agencies, universities, and nongovernmental organizations. Expanding upon its scientific expertise and leadership, the NPWRC is moving in new directions, including invasive plant species, restoration of native habitats, carbon sequestration and marketing, and ungulate management on DOI lands.

Fact Sheet↗

USGS2020

Statistical methods in water resources

This text began as a collection of class notes for a course on applied statistical methods for hydrologists taught at the U.S. Geological Survey (USGS) National Training Center. Course material was formalized and organized into a textbook, first published in 1992 by Elsevier as part of their Studies in Environmental Science series. In 2002, the work was made available online as a USGS report. The text has now been updated as a USGS Techniques and Methods Report. It is intended to be a text in applied statistics for hydrology, environmental science, environmental engineering, geology, or biology that addresses distinctive features of environmental data. For example, water resources data tend to have many variables with a lower bound of zero, tend to be more skewed than data from many other disciplines, commonly contain censored data (less than values), and assumptions that the data are normally distributed are not appropriate. Computer-intensive methods (bootstrapping and permutation tests) now improve upon and replace the dependence on t-intervals, t-tests, and analysis of variance. A new chapter on sampling design addresses questions such as “How many observations do I need?” The chapter also presents distribution-free methods to help plan sampling efforts. The trends chapter has been updated to include the WRTDS (Weighted Regressions on Time, Discharge, and Season) method for analysis of water-quality data. This new version contains updated graphics and updated guidance on the use of statistical techniques. The text utilizes R, a programming language and open-source software environment, for all exercises and most graphics, and the R code used to generate figures and examples is provided for download.

Techniques and Methods↗

USGS2019

Bringing Bayesian models to life

Bringing Bayesian Models to Life empowers the reader to extend, enhance, and implement statistical models for ecological and environmental data analysis. We open the black box and show the reader how to connect modern statistical models to computer algorithms. These algorithms allow the user to fit models that answer their scientific questions without needing to rely on automated Bayesian software. We show how to handcraft statistical models that are useful in ecological and environmental science including: linear and generalized linear models, spatial and time series models, occupancy and capture-recapture models, animal movement models, spatio-temporal models, and integrated population-models.

Book↗