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Results for “Bernoulli”

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14 recordsLinked to original sources
USGS2002

Seepage meters and Bernoulli's revenge

Evaluation of seepage data from a network of 50 permanently deployed submarine seepage meters, specially constructed from fiberglass, indicates that the devices artificially advect (Bernoulli effect) shallow ground water. Reverse flow into the rock was not observed even when adjacent piezometers installed 2-m to 20-m below the rock-water interface indicated negative groundwater heads. Quantitative testing of five different designs, including conventional end-of-oil-drum designs, indicates that meters presenting positive relief on the sea floor are subject to the Bernoulli effect when placed in areas where there are waves and/or currents. Advection does not appear to be caused by flexing of the collection bags.

Florida↗
USGS2008

A Bernoulli Formulation of the Land-Use Portfolio Model

Decision making for natural-hazards mitigation can be sketched as knowledge available in advance (a priori), knowledge available later (a posteriori), and how consequences of the mitigation decision might be viewed once future outcomes are known. Two outcomes - mitigating for a hazard event that will occur, and not mitigating for a hazard event that will not occur - can be considered narrowly correct. Two alternative outcomes - mitigating for a hazard event that will not occur, and not mitigating for a hazard event that will occur - can be considered narrowly incorrect. The dilemma facing the decision maker is that mitigation choices must be made before the event, and often must be made with imperfect statistical techniques and imperfect data.

Open-File Report↗
USGS2026

Bayesian hierarchical model of lake whitefish cohort strength from sparse trawl data

Recruitment indices for rare or intermittently recruiting fishes are needed to compare year classes and evaluate recruitment drivers, but sparse trawl data with many zero-catch observations complicate estimation. We used fall bottom trawl data from New York, Pennsylvania, and Ohio surveys in Lake Erie's central and eastern basins to estimate annual relative cohort strength of age-0 lake whitefish ( Coregonus clupeaformis ) from 1992 to 2021 and evaluate whether a Bernoulli-Bernoulli presence-absence model retained enough information for an annual relative cohort strength index compared with a Binomial-Poisson count model. We fixed detection probability at 0.31 in the primary analysis and refit both models using alternative fixed values in sensitivity analyses. Among 2879 tows, 173 were positive and 368 fish were collected, with positive catches ranging from 1 to 20 fish. Annual catch per unit area and both models recovered a similar recruitment pattern, with variable recruitment from 1992 to 2005, little to no recruitment from 2006 to 2014, and renewed recruitment in most years from 2015 to 2021. Cohort rank order was stable across fixed detection values (Spearman r s = 0.996 to 1.000), and annual median estimates maintained high agreement with the primary analysis (Pearson r = 0.966 to 1.000). However, Bernoulli-Bernoulli estimates were not one-to-one with Binomial-Poisson estimates, and relative magnitude depended on assumed detection probability. These results indicate that the Bernoulli-Bernoulli simplification is adequate for recovering cohort strength patterns, but the Binomial-Poisson model is more appropriate for distinguishing relative cohort strength among years.

New York, Ohio, Pennsylvania↗
USGS2018

Using partial aggregation in spatial capture recapture

Spatial capture–recapture (SCR) models are commonly used for analysing data collected using noninvasive genetic sampling (NGS). Opportunistic NGS often leads to detections that do not occur at discrete detector locations. Therefore, spatial aggregation of individual detections into fixed detectors (e.g., centre of grid cells) is an option to increase computing speed of SCR analyses. However, it may reduce precision and accuracy of parameter estimations. Using simulations, we explored the impact that spatial aggregation of detections has on a trade‐off between computing time and parameter precision and bias, under a range of biological conditions. We used three different observation models: the commonly used Poisson and Bernoulli models, as well as a novel way to partially aggregate detections (Partially Aggregated Binary model [PAB]) to reduce the loss of information after aggregating binary detections. The PAB model divides detectors into K subdetectors and models the frequency of subdetectors with more than one detection as a binomial response with a sample size of K. Finally, we demonstrate the consequences of aggregation and the use of the PAB model using NGS data from the monitoring of wolverine ( Gulo gulo ) in Norway. Spatial aggregation of detections, while reducing computation time, does indeed incur costs in terms of reduced precision and accuracy, especially for the parameters of the detection function. SCR models estimated abundance with a low bias (<10%) even at high degree of aggregation, but only for the Poisson and PAB models. Overall, the cost of aggregation is mitigated when using the Poisson and PAB models. At the same level of aggregation, the PAB observation model out‐performs the Bernoulli model in terms of accuracy of estimates, while offering the benefits of a binary observation model (less assumptions about the underlying ecological process) over the count‐based model. We recommend that detector spacing after aggregation does not exceed 1.5 times the scale‐parameter of the detection function in order to limit bias. We recommend the use of the PAB observation model when performing spatial aggregation of binary data as it can mitigate the cost of aggregation, compared to the Bernoulli model.

Methods in Ecology and Evolution↗
USGS2019

Alongshore momentum balance over shoreface-connected ridges, Fire Island, NY

Hydrodynamic and hydrographic data collected on the inner shelf of Fire Island, NY, over a region of shoreface-connected ridges (SFCRs) are used to describe wind-driven circulation over uneven topographies along relatively straight coastlines. The data revealed a predominantly alongshore flow, under westward wind forcing, with localized offshore current veering over the SFCR crests associated with an onshore veering over the adjacent troughs. Momentum balance analysis of the observations revealed that local acceleration, advective acceleration, and bottom stress are balanced by wind stress and regional (>100 km) pressure gradient force. Numerical model results based on simulations of an idealized SFCR bathymetry, as in Warner et al. (2014) but forced with the observed winds, are used to verify the experimentally derived results and constraint inaccuracies in the momentum balance term relationships revealed using the field data. As with previous SFCR studies, our experimental results indicate a current veering over ridge crests. Veering is driven primarily by two processes: cross-shore variation of alongshore advective acceleration which creates cross-shore pressure gradient and drives flow (described as a Bernoulli-like process), and, bottom frictional-torque. A synthesis of the numerical and experimental data revealed that the total pressure gradient force can be considered as the sum of a local and a regional pressure gradient force. The former is correlated with the alongshore advective acceleration that develops over the crest of the ridges resembling a Bernoulli-like pressure-flow relationship. The regional pressure gradient force is related to wind stress with which maintains a strong, negative relationship. The realistic driving force analysis revealed the different contributions of the local and regional scale pressure gradients. Under realistic and variable wind conditions the regional pressure gradients are more important and the influence of the local scale pressure gradient increases as the flow reaches quasi steady-state conditions. A time scale of 6 hours was defined as the temporal scale required for the local pressure gradients to have an effect

New York↗
USGS2016

A goodness-of-fit test for occupancy models with correlated within-season revisits

Occupancy modeling is important for exploring species distribution patterns and for conservation monitoring. Within this framework, explicit attention is given to species detection probabilities estimated from replicate surveys to sample units. A central assumption is that replicate surveys are independent Bernoulli trials, but this assumption becomes untenable when ecologists serially deploy remote cameras and acoustic recording devices over days and weeks to survey rare and elusive animals. Proposed solutions involve modifying the detection-level component of the model (e.g., first-order Markov covariate). Evaluating whether a model sufficiently accounts for correlation is imperative, but clear guidance for practitioners is lacking. Currently, an omnibus goodnessof- fit test using a chi-square discrepancy measure on unique detection histories is available for occupancy models (MacKenzie and Bailey, Journal of Agricultural, Biological, and Environmental Statistics, 9, 2004, 300; hereafter, MacKenzie&ndash; Bailey test). We propose a join count summary measure adapted from spatial statistics to directly assess correlation after fitting a model. We motivate our work with a dataset of multinight bat call recordings from a pilot study for the North American Bat Monitoring Program. We found in simulations that our join count test was more reliable than the MacKenzie&ndash;Bailey test for detecting inadequacy of a model that assumed independence, particularly when serial correlation was low to moderate. A model that included a Markov-structured detection-level covariate produced unbiased occupancy estimates except in the presence of strong serial correlation and a revisit design consisting only of temporal replicates. When applied to two common bat species, our approach illustrates that sophisticated models do not guarantee adequate fit to real data, underscoring the importance of model assessment. Our join count test provides a widely applicable goodness-of-fit test and specifically evaluates occupancy model lack of fit related to correlation among detections within a sample unit. Our diagnostic tool is available for practitioners that serially deploy survey equipment as a way to achieve cost savings.

Ecology and Evolution↗
USGS2007

A simple model for calculating tsunami flow speed from tsunami deposits

This paper presents a simple model for tsunami sedimentation that can be applied to calculate tsunami flow speed from the thickness and grain size of a tsunami deposit (the inverse problem). For sandy tsunami deposits where grain size and thickness vary gradually in the direction of transport, tsunami sediment transport is modeled as a steady, spatially uniform process. The amount of sediment in suspension is assumed to be in equilibrium with the steady portion of the long period, slowing varying uprush portion of the tsunami. Spatial flow deceleration is assumed to be small and not to contribute significantly to the tsunami deposit. Tsunami deposits are formed from sediment settling from the water column when flow speeds on land go to zero everywhere at the time of maximum tsunami inundation. There is little erosion of the deposit by return flow because it is a slow flow and is concentrated in topographic lows. Variations in grain size of the deposit are found to have more effect on calculated tsunami flow speed than deposit thickness. The model is tested using field data collected at Arop, Papua New Guinea soon after the 1998 tsunami. Speed estimates of 14 m/s at 200 m inland from the shoreline compare favorably with those from a 1-D inundation model and from application of Bernoulli's principle to water levels on buildings left standing after the tsunami. As evidence that the model is applicable to some sandy tsunami deposits, the model reproduces the observed normal grading and vertical variation in sorting and skewness of a deposit formed by the 1998 tsunami.

Sedimentary Geology↗
USGS2010

Asymptotic distribution of the maximum deficit with correlated, partially regulated outflows

The asymptotic distribution of the maximum accumulated deficit with partially regulated, Markov-dependent net outflows having a Bernoulli distribution is derived, and the distribution for independent, continuous outflows is presented. It is demonstrated that under partial regulation the maximum deficit behaves as log n , where n is the length of the series; this is to be contrasted with the n ½ behavior exhibited by fully regulated outflows. Also, as would be expected, the presence of correlation tends to increase the magnitude and variability of the maximum deficit.

Water Resources Research↗
USGS2022

Predicted uranium and radon concentrations in New Hampshire (USA) groundwater—Using Multi Order Hydrologic Position as predictors

Two radioactive elements, uranium (U) and radon (Rn), which are of potential concern in New Hampshire (NH) groundwater, are investigated. Exceedance probability maps are tools to highlight locations where the concentrations of undesirable substances in the groundwater may be elevated. Two forms of statistical analysis are used to create exceedance probability maps for U and Rn in NH groundwater. The first, Boosted Regression Tree (BRT), was selected for estimating U exceedance values. It computes exceedance values directly using the Bernoulli distribution function. The second method of statistical analysis used for Rn to determine exceedance probabilities is ordinary least squares (OLS) regression. In the process of determining exceedance probabilities for U and Rn, the utility of a new dataset is investigated. That new predictor dataset is the Multi-Order Hydrologic Position (MOHP) dataset. MOHP raster datasets have been produced nationally for the conterminous United States at a 30-m resolution. The concept behind MOHP is that, for any given point on the earth's surface, there is the potential for a longer groundwater flow path as one goes deeper beneath the land surface. MOHP predictors were tested in both models. Three MOHP predictors were found useful in the BRT model and two in the OLS model. MOHP data were found useful as predictors along with other site characteristics in predicting U and Rn exceedance probabilities in New Hampshire groundwater.

New Hampshire↗
USGS2013

Mark-resight abundance estimation under incomplete identification of marked individuals

Often less expensive and less invasive than conventional mark–recapture, so-called 'mark-resight' methods are popular in the estimation of population abundance. These methods are most often applied when a subset of the population of interest is marked (naturally or artificially), and non-invasive sighting data can be simultaneously collected for both marked and unmarked individuals. However, it can often be difficult to identify marked individuals with certainty during resighting surveys, and incomplete identification of marked individuals is potentially a major source of bias in mark-resight abundance estimators. Previously proposed solutions are ad hoc and will tend to underperform unless marked individual identification rates are relatively high (>90%) or individual sighting heterogeneity is negligible. Based on a complete data likelihood, we present an approach that properly accounts for uncertainty in marked individual detection histories when incomplete identifications occur. The models allow for individual heterogeneity in detection, sampling with (e.g. Poisson) or without (e.g. Bernoulli) replacement, and an unknown number of marked individuals. Using a custom Markov chain Monte Carlo algorithm to facilitate Bayesian inference, we demonstrate these models using two example data sets and investigate their properties via simulation experiments. We estimate abundance for grassland sparrow populations in Pennsylvania, USA when sampling was conducted with replacement and the number of marked individuals was either known or unknown. To increase marked individual identification probabilities, extensive territory mapping was used to assign incomplete identifications to individuals based on location. Despite marked individual identification probabilities as low as 67% in the absence of this territorial mapping procedure, we generally found little return (or need) for this time-consuming investment when using our proposed approach. We also estimate rookery abundance from Alaskan Steller sea lion counts when sampling was conducted without replacement, the number of marked individuals was unknown, and individual heterogeneity was suspected as non-negligible. In terms of estimator performance, our simulation experiments and examples demonstrated advantages of our proposed approach over previous methods, particularly when marked individual identification probabilities are low and individual heterogeneity levels are high. Our methodology can also reduce field effort requirements for marked individual identification, thus, allowing potential investment into additional marking events or resighting surveys.

Methods in Ecology and Evolution↗
USGS2021

Effects of climate and land-use change on thermal springs recharge—A system-based coupled surface-water and groundwater-flow model for Hot Springs National Park, Arkansas

A three-dimensional hydrogeologic framework of the Hot Springs anticlinorium beneath Hot Springs National Park, Arkansas, was constructed to represent the complex hydrogeology of the park and surrounding areas to depths exceeding 9,000 feet below ground surface. The framework, composed of 6 rock formations and 1 vertical fault emplaced beneath the thermal springs, was discretized into 19 layers, 429 rows, and 576 columns and incorporated into a 3-dimensional steady-state groundwater-flow model constructed in MODFLOW-2005. Historical daily mean thermal spring flows were simulated for one stress period of approximately 34 years (1980–2014), chosen to represent the period of record for historical climate data used in the quantification of the boundary conditions. The groundwater-flow model was manually calibrated to historical daily mean thermal spring flows of 88,000 cubic feet per day observed over a 12-year period of record (1990–1995 and 1998–2005) at the thermal springs collection system. Calibration was achieved by calculating starting heads and general head boundary conditions from the Bernoulli equation and then adjusting the horizontal and vertical hydraulic conductivities of the rock formations and vertical fault and the hydraulic conductance of head-dependent flux boundaries. The groundwater-flow model was coupled to a surface-water model developed in the Precipitation-Runoff Modeling System (PRMS) by using PRMS-simulated gravity drainage as a specified flux recharge boundary condition in the groundwater-flow model. Together, the coupled models were used to (1) locate the areas of groundwater recharge to the thermal springs in the discretized hydrogeologic framework by using forward and reverse particle-tracking capabilities of MODPATH, (2) simulate the effects of variable recharge rates on the spring flows at the thermal springs, and (3) assess possible effects of climate and land-use change on the long-term variability of spring flows at the thermal springs. Forward and backward particle-tracking maps indicated that the most prevalent areas of recharge in the discretized hydrogeologic framework used in this study were within about 0.6–0.9 mile of the thermal springs. Forward particle tracking indicated a recharge area southwest of the thermal springs that corresponded to a location where the predominant lithologies are the Arkansas Novaculite, Hot Springs Sandstone, and Bigfork Chert. Backward particle tracking indicated a second localized area of recharge to the northeast of the thermal springs that corresponded to a location where the dominant lithology is the Bigfork Chert. The groundwater-flow model indicated that the most probable recharge formations are the Arkansas Novaculite, Bigfork Chert, and Hot Springs Sandstone. The simulated effects of climate and land-use changes on the variability of the spring-flow rates at the thermal springs generally resulted in reductions of thermal spring flow attributed to urban development and more extreme climates characterized by elevated mean surface air temperatures. The groundwater-flow model predicted a linear relation between the thermal spring discharge and the cumulative recharge volume applied to the hydrogeologic framework, and the positive slope of the predicted relation between recharge and simulated thermal spring flow indicates that more extreme precipitation events that supply more recharge may in fact increase the thermal spring-flow rates.

Arkansas↗
USGS2024

Detection probability and bias in machine-learning-based unoccupied aerial system non-breeding waterfowl surveys

Unoccupied aerial systems (UASs) may provide cheaper, safer, and more accurate and precise alternatives to traditional waterfowl survey techniques while also reducing disturbance to waterfowl. We evaluated availability and perception bias based on machine-learning-based non-breeding waterfowl count estimates derived from aerial imagery collected using a DJI Mavic Pro 2 on Missouri Department of Conservation intensively managed wetland Conservation Areas. UASs imagery was collected using a proprietary software for automated flight path planning in a back-and-forth transect flight pattern at ground sampling distances (GSDs) of 0.38–2.29 cm/pixel (15–90 m in altitude). The waterfowl in the images were labeled by trained labelers and simultaneously analyzed using a modified YOLONAS image object detection algorithm developed to detect waterfowl in aerial images. We used three generalized linear mixed models with Bernoulli distributions to model availability and perception (correct detection and false-positive) detection probabilities. The variation in waterfowl availability was best explained by the interaction of vegetation cover type, sky condition, and GSD, with more complex and taller vegetation cover types reducing availability at lower GSDs. The probability of the algorithm correctly detecting available birds showed no pattern in terms of vegetation cover type, GSD, or sky condition; however, the probability of the algorithm generating incorrect false-positive detections was best explained by vegetation cover types with features similar in size and shape to the birds. We used a modified Horvitz–Thompson estimator to account for availability and perception biases (including false positives), resulting in a corrected count error of 5.59 percent. Our results indicate that vegetation cover type, sky condition, and GSD influence the availability and detection of waterfowl in UAS surveys; however, using well-trained algorithms may produce accurate counts per image under a variety of conditions.

Missouri↗
USGS1999

Estimation of Renyi exponents in random cascades

We consider statistical estimation of the Re??nyi exponent ??(h), which characterizes the scaling behaviour of a singular measure ?? defined on a subset of Rd. The Re??nyi exponent is defined to be lim?????0 [{log M??(h)}/(-log ??)], assuming that this limit exists, where M??(h) = ??i??h(??i) and, for ??>0, {??i} are the cubes of a ??-coordinate mesh that intersect the support of ??. In particular, we demonstrate asymptotic normality of the least-squares estimator of ??(h) when the measure ?? is generated by a particular class of multiplicative random cascades, a result which allows construction of interval estimates and application of hypothesis tests for this scaling exponent. Simulation results illustrating this asymptotic normality are presented. ?? 1999 ISI/BS.

Bernoulli↗