Mathematical Statistics with Applications.

Loukas, S.; Mendenhall, William M.; Wackerly, Dennis D.; Scheaffer, Richard L.

doi:10.2307/2532372

Cited by 53 publications

(78 citation statements)

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“…Equations ( 2), ( 3), ( 4) are hypergeometric probabilities (see [4], for example) corresponding to the number of candies of each type in a random sample without replacement of size two from a container containing a type A and b type B candies. Starting from (a, b) candies on Day 0, and using conditional probabilities (2), (3), (4) of drawing two candies on each day, the resulting probability distribution of the number of days until the container becomes empty is shown in Table 3.…”

Section: From Manual Calculations To Computational Algorithmsmentioning

confidence: 99%

“…On paper, we economize writing down the probability vector by eliminating the leading (b − 1) zeros. Instead, we write, for example, "p2,4 = ( [4]…”

Section: From Manual Calculations To Computational Algorithmsmentioning

confidence: 99%

“…Note that the first day Johnny would eat two candies of opposite types is a geometric(ra,b) random variable (see [4]), where ra,b is the probability of drawing a mixed type of candies AB; that is,…”

Section: Johnny Learns To Optimizementioning

confidence: 99%

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Candy Lover Learns to Optimize

Anh

Rashid

Sarkar

2023

JPSS

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A container has two types of candies: Type A and Type B. Concerned about her child's well-being, a wise mom pronounces, “Each day, you can choose two candies from the container random. If they are of different types, you can eat them both. If they are of the same type, eat only one and return the other to the container.” We analyze the expected number of days needed to eat all candies in the container and the proportion of days the child eats two candies. Several other variations are either worked out or left for readers to solve.

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Section: From Manual Calculations To Computational Algorithmsmentioning

confidence: 99%

“…On paper, we economize writing down the probability vector by eliminating the leading (b − 1) zeros. Instead, we write, for example, "p2,4 = ( [4]…”

Section: From Manual Calculations To Computational Algorithmsmentioning

confidence: 99%

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Candy Lover Learns to Optimize

Anh

Rashid

Sarkar

2023

JPSS

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“…where ǫ ∼ N (0, σ 2 ) and ǫ is independent across different observations. A Bayesian estimation approach will be used and hence Bayes Theorem [21] is essential to obtain the posterior probability distribution for the parameters θ given the observed data Ũ (x, t), namely p(θ| Ũ (x, t)) is given by [20,17,19]:…”

Section: Prior Distributions Likelihood and Computationmentioning

confidence: 99%

“…For more on using the Bayesian framework for statistical inferences, see [17], [18]. Other techniques such as Method of Moments [19] or Maximum Likelihood [20] are not considered here and the authors have not found any literature where they are applied to FPDEs as likelihood is not differentiable with respect to α.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference on Fractional Advection-Diffusion Transport Systems

Boone¹,

Ghanam²

2023

Int. J. of Appl. Math.

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The field fractional partial differential equations has been greatly expanding with in the last 20 years as evidenced by the growing body of literature. The work has primarily been theoretical in nature as there has been limited availability of experimental data. This work demonstrates using simulated data, how one can utilize these models and apply them to real world data to make inferences about the parameter values, predictions at future values and even what forcing mechanism was used to generate the data. This is done using a Bayesian approach that employs Markov chain Monte Carlo techniques. The proposed approach is evaluated using simulation studies concerning credible interval coverage probabilities and highest posterior model probabilities. The simulation study shows that the proposed method is effective for many parameters and that more work is needed to better estimate some physical coefficients.

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Shoreline slope influences movements of larval lampreys over dewatered substrate

Liedtke,

Harris,

Gray

2024

Aquaculture Fish & Fisheries

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Larval lampreys are filter feeders that live for several years burrowed in fine sediments in freshwater streams. Stream side channels and edges, where larval lampreys gather, are vulnerable to natural and human‐caused dewatering. Water level reductions can strand and kill thousands of larval lampreys, in part because many remain burrowed until their habitats are exposed, at which point larvae must emerge and attempt to move over dewatered substrate to locate wetted habitat. Dewatering for restoration efforts or seasonal closures of irrigation canals can be done slowly to reduce lamprey strandings, but in some settings, mechanisms are lacking to control the dewatering rate. Phased dewatering, where water level is reduced in stages separated by periods of static water level, could provide options when dewatering rate cannot be tightly controlled. To guide this phased approach, information is needed on the movement capability of larval lampreys. We examined larval lamprey (Entosphenus tridentatus and Lampetra spp.) movement distance and rate over dewatered substrate at shoreline slopes of 1%, 5%, 10% and 20% in a laboratory setting and modelled results using gamma regression models. Model results suggest both movement distance and movement rate increased with increasing slope and increasing larval length. We used the models to predict minimum distances and rates that 90%, 75% and 50% of medium‐sized (75 mm) lampreys would move over dewatered substrates on slopes of 1%–20%. The models predicted that 50% of larvae could move distances of ≥31 cm at rates of ≥0.7 mm/s on a 1% slope and distances of ≥502 cm at rates of ≥8.6 mm/s on a 20% slope. We present an example scenario of how information on larval movement capabilities and shoreline slope could guide phased dewatering events to limit impacts to lampreys.

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Mathematical Statistics with Applications.

Cited by 53 publications

References 0 publications

Candy Lover Learns to Optimize

Candy Lover Learns to Optimize

Statistical Inference on Fractional Advection-Diffusion Transport Systems

Shoreline slope influences movements of larval lampreys over dewatered substrate

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