Mathematics and Statisticshttp://hdl.handle.net/11122/9742021-04-21T20:16:03Z2021-04-21T20:16:03ZA Bayesian mixed multistate open-robust design mark-recapture model to estimate heterogeneity in transition rates in an imperfectly detected systemBadger, Janelle J.http://hdl.handle.net/11122/118962021-03-05T01:01:47Z2020-12-01T00:00:00ZA Bayesian mixed multistate open-robust design mark-recapture model to estimate heterogeneity in transition rates in an imperfectly detected system
Badger, Janelle J.
Multistate mark-recapture models have long been used to assess ecological and demographic parameters such as survival, phenology, and breeding rates by estimating transition rates among a series of latent or observable states. Here, we introduce a Bayesian mixed multistate open robust design mark recapture model (MSORD), with random intercepts and slopes to explore individual heterogeneity in transition rates and individual responses to covariates. We fit this model to simulated data sets to test whether the model could accurately and precisely estimate five parameters, set to known values a priori, under varying sampling schemes. To assess the behavior of the model integrated across replicate fits, we employed a two-stage hierarchical model fitting algorithm for each of the simulations. The majority of model fits showed no sign of inadequate convergence according to our metrics, with 81.25% of replicate posteriors for parameters of interest having general agreement among chains (r < 1.1). Estimates of posterior distributions for mean transition rates and standard deviation in random intercepts were generally well-defined. However, we found that models estimated the standard deviation in random slopes and the correlation among random effects relatively poorly, especially in simulations with low power to detect individuals (e.g. low detection rates, study duration, or secondary samples). We also apply this model to a dataset of 200 female grey seals breeding on Sable Island from 1985-2018 to estimate individual heterogeneity in reproductive rate and response to near-exponential population growth. The Bayesian MSORD estimated substantial variation among individuals in both mean transition rates and responses to population size. The correlation among effects trended positively, indicating that females with high reproductive performance (more positive intercept) were also more likely to respond better to population growth (more positive slope) and vice versa. Though our simulation results lend confidence to analyses using this method on well developed datasets on highly observable systems, we caution the use of this framework in sparse data situations.
Master's Project (M.S.) University of Alaska Fairbanks, 2020
2020-12-01T00:00:00ZAnalysis of GNAC Volleyball using the Bradley-Terry ModelKarwoski, Danielhttp://hdl.handle.net/11122/118702021-02-27T01:02:10Z2020-05-01T00:00:00ZAnalysis of GNAC Volleyball using the Bradley-Terry Model
Karwoski, Daniel
Ranking is the process by which a set of objects is assigned a linear ordering based on some property that they possess. Not surprisingly, there are many different methods of ranking used in a wide array of diverse applications; ranking plays a vital role in sports analysis, preference testing, search engine optimization, psychological research, and many other areas. One of the more popular ranking models is Bradley-Terry, which is a type of aggregation ranking that has been used mostly within the realm of sports. Bradley-Terry uses the outcome of individual matchups (paired-comparisons) to create rankings using maximum-likelihood estimation.
This project aims to briefly examine the motivation for modeling sporting events, review the history of ranking and aggregation-ranking, communicate the mathematical theory behind the Bradley-Terry model, and apply the model to a novel volleyball dataset.
Master's Project (M.S.) University of Alaska Fairbanks, 2020
2020-05-01T00:00:00ZSimulating distance sampling to estimate nest abundance on the Yukon-Kuskokwim Delta, AlaskaGallenberg, Elainehttp://hdl.handle.net/11122/118672021-02-27T01:01:50Z2020-05-01T00:00:00ZSimulating distance sampling to estimate nest abundance on the Yukon-Kuskokwim Delta, Alaska
Gallenberg, Elaine
The U.S. Fish and Wildlife Service currently conducts annual surveys to estimate bird nest abundance on the Yukon-Kuskokwim Delta, Alaska. The current method involves intensive searching on large plots with the goal of finding every nest on the plot. Distance sampling is a well-established transect-based method to estimate density or abundance that accounts for imperfect detection of objects. It relies on estimating the probability of detecting an object given its distance from the transect line, or the detection function. Simulations were done using R to explore whether distance sampling methods on the Yukon-Kuskokwim Delta could produce reliable estimates of nest abundance. Simulations were executed both with geographic strata based on estimated Spectacled Eider (Somateria fischeri) nest densities and without stratification. Simulations with stratification where more effort was allotted to high density areas tended to be more precise, but lacked the property of pooling robustness and assumed stratum boundaries would not change over time. Simulations without stratification yielded estimates with relatively low bias and variances comparable to current estimation methods. Distance sampling appears to be a viable option for estimating the abundance of nests on the Yukon-Kuskokwim Delta.
Master's Project (M.S.) University of Alaska Fairbanks, 2020
2020-05-01T00:00:00ZMultiple imputation of missing multivariate atmospheric chemistry time series data from Denali National ParkCharoonsophonsak, Chanachaihttp://hdl.handle.net/11122/118592021-02-26T01:01:48Z2020-05-01T00:00:00ZMultiple imputation of missing multivariate atmospheric chemistry time series data from Denali National Park
Charoonsophonsak, Chanachai
This paper explores a technique where we impute missing values for an incomplete dataset
via multiple imputation. Incomplete data is one of the most common issues in data analysis
and often occurs when measuring chemical and environmental data. The dataset that we
used in the model consists of 26 atmospheric particulates or elements that were measured
semiweekly in Denali National Park from 1988 to 2015. The collection days were alternating
between three and four days apart from 3/2/88 - 9/30/00 and being consistently collected
every three days apart from 10/3/00 - 12/29/15. For this reason, the data were initially
partitioned into two in case the separation between collection days would have an impact.
With further analysis, we concluded that the misalignments between the two datasets had
very little or no impact on our analysis and therefore combined the two. After running five
Markov chains of 1000 iterations we concluded that the model stayed consistent between
the five chains. We found out that in order to get a better understanding of how well the
imputed values did, more exploratory analysis on the imputed datasets would be required.
Master's Project (M.S.) University of Alaska Fairbanks, 2020
2020-05-01T00:00:00Z