Dissertations / Theses on the topic 'Population statistics'

We present a non-Gaussian and non-linear state-space model for the population dynamics of cod along the Norwegian Skagerak coast, embedded in the framework of a Bayesian hierarchical model. The model takes into account both process error, representing natural variability in the dynamics of a population, and observational error, reflecting the sampling process relating the observed data to true abundances. The data set on which our study is based, consists of samples of two juvenile age-groups of cod taken by beach seine hauls at a set of sample stations within several fjords along the coast. The age-structure population dynamics model, constituting the prior of the Bayesian model, is specified in terms of the recruitment process and the processes of survival for these two juvenile age-groups and the mature population, for which we have no data. The population dynamics is specified on abundances at the fjord level, and an explicit down-scaling from the fjord level to the level of the monitored stations is included in the likelihood, modelling the sampling process relating the observed counts to the underlying fjord abundances.

We take a sampling based approach to parameter estimation using Markov chain Monte Carlo methods. The properties of the model in terms of mixing and convergence of the MCMC algorithm and explored empirically on the basis of a simulated data set, and we show how the mixing properties can be improved by re-parameterisation. Estimation of the model parameters, and not the abundances, is the primary aim of the study, and we also propose an alternative approach to the estimation of the model parameters based on the marginal posterior distribution integrating over the abundances.

Based on the estimated model we illustrate how we can simulate the release of juvenile cod, imitating an experiment conducted in the early 20th century to resolve a controversy between a fisherman and a scientist who could not agree on the effect of releasing cod larvae on the mature abundance of cod. This controversy initiated the monitoring programme generating the data used in our study.

The Current Population Survey (CPS) is a multistage probability sample survey conducted by the U.S. Census Bureau and the Bureau of Labor Statistics (BLS). The 4-8-4 rotation design is applied to produce overlap in the sample across months. Several weighting steps are used to adjust the ultimate sample in each month to be representative of the population. In order to produce efficient estimates of labor force levels and month-to-month change, the so-called AK composite estimator combines current estimates from eight rotation panels and the previous month’s estimates to estimate current values. Values of coefficients A and K are chosen every decade or so for the nation. The Successive Difference Replicate (SDR) method and Balanced Repeated Replication (BRR) method are currently used by the CPS for estimating the variance of the AK Composite Estimates.

Instead of using constant CPS (A, K) values for AK Composite Estimator over time, one could find the monthly optimal coefficients ( A, K) that minimize the variance for measuring the monthly level of unemployment in the target population. The CPS (A, K) values are stable over time but can produce larger variance in some months, while the monthly optimal (A, K) values have lower variance within a month but high variability across months.

In order to make a compromise between the CPS (A, K) values and monthly optimal (A, K), a Hierarchical Bayesian method is proposed through modeling the obtained monthly optimal ( A, K)’s using a bivariate normal distribution. The parameters, including the mean vector and the variance-covariance matrix, are unknown in this distribution. In such case, a first step towards a more general model is to assume a conjugate prior distribution for the bivariate normal model. Computing the conditional posterior distribution can be approximated through simulation. In particular, it can be achieved by the Gibbs sampling algorithm with its sequential sampling. As the key to the success of this Hierarchical Bayesian method is that approximated distributions are improved as iteration goes on in the simulation, one needs to check the convergence of the simulated sequences. Then, the sample mean after a number of iterations in the simulation will serve as the Hierarchical Bayesian (HB) (A, K). The HB (A, K) estimates in effect produce a shrinkage between the CPS (A, K) values and the monthly optimal (A, K) values. The shrinkage of the estimates of the coefficients ( A, K) occurs by manipulating the certain hyperparameter in the model.

In this dissertation, detailed comparisons are made among the three estimators. The AK Estimator using the CPS (A, K) values, using the monthly optimal (A, K) values, and using the Hierarchical Bayesian (A,K) values are compared in terms of estimates produced, estimated variance, and estimated coefficients of variation. In each month of the data set, separate estimates using the three methods are produced.

In order to assess the performance of the proposed methods, a simulation study is implemented and summarized. In the CPS, eight rotating survey panels contribute to the overall estimate in each month. Each panel is measured in a month at one of its month-in- sample. The month-in- sample range from one to eight. In the simulation, month-in- sample values are generated as if replicate panels were available for estimation. These month-in-sample values are used as the original monthly panel estimates of unemployment to produce CPS-style (A, K) estimates, AK-estimates using monthly optimal ( A, K) values, and AK-estimates using Hierarchical Bayesian ( A, K) values. Performance of each method is evaluated on the simulated data by examining several criteria including bias, variance, and mean squared error.

The focus of this work is on faults, and the main issue is statistical analysis and stochastic modeling of faults and fault patterns in petroleum reservoirs. The thesis consists of Part I-V and Appendix A-C. The units can be read independently. Part III is written for a geophysical audience, and the topic of this part is fault and fracture size-frequency distributions. The remaining parts are written for a statistical audience, but can also be read by people with an interest in quantitative geology. The topic of Part I and II is statistical model choice for fault size distributions, with a samling algorithm for estimating Bayes factor. Part IV describes work on spatial modeling of fault geometry, and Part V is a short note on line partitioning. Part I, II and III constitute the main part of the thesis. The appendices are conference abstracts and papers based on Part I and IV.

This dissertation is dedicated to an exploration of "Wood's Method" -- a novel approach to fitting demographic transition matrices to age and sex population count data. Demographic transition matrices, otherwise known as "Leslie matrices," are extensively used to forecast population by age, sex, and other characteristics. Our implementation of Wood's Method simplifies the creation of age and sex population forecasts greatly by reducing the amount of data necessary to create a demographic transition matrix. Furthermore, the method can be used to infer a demographic component of change (one of migration, fertility, or mortality) if the other two components are specified.

In Chapter One, we introduce Wood's Method, as well as showing some illustrative examples. In Chapter Two, we evaluate the accuracy of Wood's Method by crossvalidating age and sex specific forecasts for 3,120 US counties. In Chapter Three, we present a simpler, alternative derivation of Wood's Method with an extensive example and show some extensions to the method made possible by this new formulation. In Chapter Four, we use the method to examine migration rates at the US County level and show important results regarding clustering of migration. Each chapters is independent of the others, but should be read in order.

To our knowledge, this is the first time Wood's Method has been used for forecasting human populations. We hope to show its viability as a forecasting and analysis method and sketch directions for further research.

In this work, I answer timely questions regarding tree growth, tree survival, and community change in California tree species, using a variety of sophisticated statistical and remote sensing tools. In Chapter 1, I address tree growth for a single tree species with a thorough explanation of hierarchical state-space models for forest inventory data. Understanding tree growth as a function of tree size is important for a multitude of ecological and management applications. Determining what limits growth is of central interest, and forest inventory permanent plots are an abundant source of long-term information but are highly complex. Observation error and multiple sources of shared variation make these data challenging to use for growth estimation. I account for these complexities and incorporate potential limiting factors into a hierarchical state-space model. I estimate the diameter growth of white fir in the Sierra Nevada of California from forest inventory data, showing that estimating such a model is feasible in a Bayesian framework using readily available modeling tools. In this forest, white fir growth depends strongly on tree size, total plot basal area, and unexplained variation between individual trees. Plot-level resource supply variables do not have a strong impact on inventory-size trees. This approach can be applied to other networks of permanent forest plots, leading to greater ecological insights on tree growth.

In Chapter 2, I expand my state-space modeling to examine survival in seven tree species, as well as investigating the results of modeling them in aggregate and comparing with the individual species models. Declining tree survival is a complex, well-recognized problem, but studies have been largely limited to relatively rare old-growth forests or low-diversity systems, and to models which are species-aggregated or cannot easily accommodate yearly climate variables. I estimate survival models for a relatively diverse second-growth forest in the Sierra Nevada of California using a hierarchical state-space framework. I account for a mosaic of measurement intervals and random plot variation, and I directly include yearly stand development variables alongside climate variables and topographic proxies for nutrient limitation. My model captures the expected dependence of survival on tree size. At the community level, stand development variables account for decreasing survival trends, but species-specific models reveal a diversity of factors influencing survival. Species time trends in survival do not always conform to existing theories of Sierran forest dynamics, and size relationships with survival differ for each species. Within species, low survival is concentrated in susceptible subsets of the population and single estimates of annual survival rates do not reflect this heterogeneity in survival. Ultimately only full population dynamics integrating these results with models of recruitment can address the potential for community shifts over time.

In Chapter 3, I combine statistical modeling with remote sensing techniques to investigate whether topographic variables influence changes in woody cover. In the North Coast of California, changes in fire management have resulted in conversion of oak woodland into coniferous forest, but the controls on this slow transition are unknown. Historical aerial imagery, in combination with Object-Based Image Analysis (OBIA), allows us to classify land cover types from the 1940s and compare these maps with recent cover. Few studies have used these maps to model drivers of cover change, partly due to two statistical challenges: 1) appropriately accounting for spatial autocorrelation and 2) appropriately modeling percent cover which is bounded between 0 and 100 and not normally distributed. I study the change in woody cover in California's North Coast using historical and recent high-spatial-resolution imagery. I classify the imagery using eCognition Developer and aggregate the resulting maps to the scale of a Digital Elevation Model (DEM) in order to understand topographic drivers of woody cover change. I use Generalized Additive Models (GAMs) with a quasi-binomial probability distribution to account for spatial autocorrelation and the boundedness of the percent woody cover variable. I find that historical woody cover has a consistent positive effect on current woody cover, and that the spatial term in the model is significant even after controlling for historical cover. Specific topographic variables emerge as important for different sites at different scales, but no overall pattern emerges across sites or scales for any of the topographic variables I tested. This GAM framework for modeling historical data is flexible and could be used with more variables, more flexible relationships with predictor variables, and larger scales. Modeling drivers of woody cover change from historical ecology data sources can be a valuable way to plan restoration and enhance ecological insight into landscape change.

I conclude that these techniques are promising but a framework is needed for sensitivity analysis, as modeling results can depend strongly on variable selection and model structure. (Abstract shortened by UMI.)

The purpose of this research was to investigate and elucidate the relationship between medication adherence and optimism-pessimism in a population of people living with HIV/AIDS. The first aim was to assess the association between optimism-pessimism and two different measures of medication adherence via two different multivariable models. The first measure of adherence was a self-report measure of the frequency with which a person missed their medications for various reasons where a higher score denoted less adherence to their current medication regimen. A robust Poisson regression model was used as the primary mechanism to analyze this measure of adherence. The second measure of adherence was an ordinal-scaled question that inquired about level of confidence to take medication as prescribed by a health care provider. An ordered logit regression (proportional odds regression) was used to analyze this measure of adherence. In both analyses, the quantification of optimism-pessimism on medication adherence began with unadjusted univariate models then progressed to fully-adjusted multivariable models. The second aim was to determine whether the hypothesized association between optimism-pessimism and medication adherence followed from the expression of optimism-pessimism as a single, bipolar metric or as two distinct, unipolar metrics. Both expressions of optimism-pessimism—the single continuum measure and the disaggregated unidimensional measures, respectively—were included in the multivariable models proposed in the first aim. The data used in this project came from a randomized controlled trial conducted between December 2005 and January 2007 by the International Nursing Network for HIV/AIDS Research. The findings from this research indicated that optimism (both dispositional and disaggregated) was positively associated with medication adherence in unadjusted and partially adjusted models but not when depression, quality of life, and self-efficacy were adjusted for. An exploratory analysis that led to the stratification of the sample by the median age, 44, returned a positive association between optimism and medication adherence across all models among subjects <44 years of age. A similar pattern was observed for the association between optimism and confidence to take medications as directed. The analysis of optimism-pessimism as a single continuum or as two independent constructs suggested that optimism and pessimism are not opposite ends of the same continuum but represent two unipolar dimensions. Medication adherence is central to benefits realized at both the individual- and population-levels and these findings help to elucidate the relationship between adequate adherence and a not-yet-fully-understood psychological factor, optimism-pessimism.