Line transect abundance estimation with uncertain detection on the trackline

Bibliography: leaves 225-233.After critically reviewing developments in line transect estimation theory to date, general likelihood functions are derived for the case in which detection probabilities are modelled as functions of any number of explanatory variables and detection of animals on the trackline (i.e. directly in the observer's path) is not certain. Existing models are shown to correspond to special cases of the general models. Maximum likelihood estimators are derived for some special cases of the general model and some existing line transect estimators are shown to correspond to maximum likelihood estimators for other special cases. The likelihoods are shown to be extensions of existing mark-recapture likelihoods as well as being generalizations of existing line transect likelihoods. Two new abundance estimators are developed. The first is a Horvitz-Thompson-like estimator which utilizes the fact that for point estimation of abundance the density of perpendicular distances in the population can be treated as known in appropriately designed line transect surveys. The second is based on modelling the probability density function of detection probabilities in the population. Existing line transect estimators are shown to correspond to special cases of the new Horvitz-Thompson-like estimator, so that this estimator, together with the general likelihoods, provides a unifying framework for estimating abundance from line transect surveys

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio

Robust and Efficient Statistical Inference for Clustered Observational Data in Comparative Effectiveness Research

Treatment allocations in observational studies are nonrandom and result in the confounding problem and potentially biase treatment effect estimates. Propensity score (PS) methods are commonly used in practice to address the confounding problem. Among different PS methods, PS regression is frequently used in clinical research. Even though the treatment effect estimate from the PS regression model is unbiased under the strongly ignorable treatment assignment assumption, the default variance estimate is biased. In the first topic of this dissertation, an improved variance estimator for the treatment effect estimate is proposed. Many observational data are clustered, for example, by physicians, and are therefore, not independent. A few PS methods consider correlated or clustered samples using mixed effects models with a strong normality assumption on the cluster effects. In the second part of this dissertation, a robust semi-nonparametric propensity score (SNP-PS) regression model is proposed. We relax the normality assumption and model the complex heterogeneity structure in treatment allocation process nonparametrically. The proposed SNP-PS model is robust and provides unbiased treatment effect estimates while parametric mixed effects PS models fail to do so when the cluster effects are non-normally distributed. We establish the asymptotic result for the treatment effect estimate and propose an unbiased variance estimator for it. Computationally, we propose an adaptive quadrature integration EM (expectation-maximization) algorithm to avoid potential large Monte Carlo errors of existing Monte Carlo EM algorithms. Many real world medical record data are not only clustered but also multilevel clustered with millions of samples and hundreds of thousands of clusters. The SNP-PS framework is in theory applicable to these large datasets. However, in practice, it is computationally prohibited. In the third topic of this dissertation, we propose a flexible mixed effects PS model (FM-PS) that is computationally efficient for large multilevel clustered data. The FM-PS model relaxes a critical independence assumption that the random effects are independent of the fixed effect covariates made in the standard mixed effects PS (SM-PS) models. The FM-PS model provides an unbiased treatment effect estimate regardless whether the independence assumption holds or not. Though the treatment effect estimate from the SM-PS model is biased when the independence assumption does not hold, it is unbiased and more efficient than the estimate from the FM-PS model when the independence assumption holds. We propose a likelihood ratio statistics for testing the independence assumption which allows us to choose between the FM-PS and SM-PS models. A cluster bootstrapping procedure to estimate the variance of treatment effect estimate is proposed. The FM-PS model is robust to various model misspecifications as demonstrated by our extensive simulations.Doctor of Philosoph

Statistical theory and methodology for remote sensing data analysis

A model is developed for the evaluation of acreages (proportions) of different crop-types over a geographical area using a classification approach and methods for estimating the crop acreages are given. In estimating the acreages of a specific croptype such as wheat, it is suggested to treat the problem as a two-crop problem: wheat vs. nonwheat, since this simplifies the estimation problem considerably. The error analysis and the sample size problem is investigated for the two-crop approach. Certain numerical results for sample sizes are given for a JSC-ERTS-1 data example on wheat identification performance in Hill County, Montana and Burke County, North Dakota. Lastly, for a large area crop acreages inventory a sampling scheme is suggested for acquiring sample data and the problem of crop acreage estimation and the error analysis is discussed

Efficient model fitting approaches for estimating abundance and demographic rates for marked and unmarked populations

Capture-recapture studies and the use of motion-sensor camera traps are common and becoming increasing popular for collecting data on wildlife populations. In this thesis, we focus on data collected from capture-recapture and camera trapping studies, and develop model fitting algorithms that are efficient for estimating the animal abundance for each study. In our first work, we restrict our study relating to individual heterogeneity in capture-recapture studies. We consider (i) continuous time-varying individual covariates and (ii) individual random effects. In general, the associated likelihood is not available in closed form but only expressible as an analytically intractable integral. The integration is specified over (i) the unknown individual covariate values (if an individual is not observed, its associated covariate value is also unknown) and (ii) the unobserved random effect terms. Previous approaches to dealing with these issues include numerical integration and Bayesian data augmentation techniques. However, as the number of individuals observed and/or capture occasions increases, these methods can become computationally expensive. Thus, we propose a new and efficient approach that approximates the analytically intractable integral in the likelihood via a Laplace approximation. We find that for the situations considered, the Laplace approximation performs as well as, or better, than alternative approaches, yet is substantially more efficient. In the second work, we focus on spatially-related individual heterogeneity in camera trapping studies. However, animal identification is not always feasible in practice due to poor quality images and/or individuals not having uniquely identifiable physical characteristics. Spatially explicit models for unmarked individuals permit the estimation of animal density when individuals cannot be uniquely identified. Due to the structure of these models, a Bayesian super-population (data augmentation) approach (SPA) is often used to fit the models to data, which involves specifying some reasonably "large" upper limit for the population. However, this approach presents computational challenges, particularly when dealing with larger populations, as demonstrated by the motivating dataset relating to barking deer (Muntiacus muntjak) collected in Ujung Kulon National Park (UKNP), Indonesia. In this second work, we develop new efficient algorithms in the Bayesian framework that do not require a priori specifying the upper population limit. We compare the performance of the different approaches using small datasets: relating to northern Parula and simulated data, and demonstrate that even with a relatively small dataset the new algorithms are consistently more efficient than the previous super-population approach. Finally, we apply the new algorithm to the large barking deer dataset, where the standard super-population approach is computationally very expensive. Our finding shows that the spatial density estimates of barking deer in the study area are between 12 and 13 animals per km$$^2$$ with 95% of credible interval ranging from 6 to 20 animals per km$$^2$$; the difference in the computational aspect between the two algorithms is particularly marked for the deer case study with the SPA algorithm taking substantially longer to implement compared to the new algorithm (by a factor of 4)

ESSAYS ON ESTIMATION OF NON-LINEAR STATE-SPACE MODELS

The first chapter of my thesis (co-authored with David N. DeJong, Jean-Francois Richard and Roman Liesenfeld) develops a numerical procedure that facilitates efficient likelihood evaluation and filtering in applications involving non-linear and non-Gaussian state-space models. These tasks require the calculation of integrals over unobservable state variables. We introduce an efficient procedure for calculating such integrals: the EIS-Filter. The procedure approximates necessary integrals using continuous approximations of target densities. Construction is achieved via efficient importance sampling, and approximating densities are adapted to fully incorporate current information. Extensive comparisons to the standard particle filter are presented using four diverse examples.The second chapter illustrates the use of copulas to create low-dimensional multivariate importance sampling densities. Copulas enable the problem of multivariate density approximation to be split into a sequence of simpler univariate density approximation problems for the marginals, with the dependence accounted by the copula parameter(s). This separation of the marginals from their dependence allows maximum flexibility in the selection of marginal densities. Combined with the EIS method for refining importance sampling densities, copula densities offer substantial flexibility in creating multivariate importance samplers. In a simulation exercise, we compare the accuracy of the copula-based EIS-Filter to the particle filter in evaluating the likelihood function and in obtaining filtered estimates of the latent variables.Reliability of growth forecasts critically depend on being able to anticipate/recognize shifts of the economy from recessions to expansions or vice versa. It is widely accepted that the processes that govern these shifts could be highly non-linear. In the third chapter (co-authored with David N. DeJong, Jean-Francois Richard and Roman Liesenfeld), we study regime shifts using a non-linear model of GDP growth. The model characterizes growth as following non-linear trajectories that fluctuate stochastically between alternative periods of general acceleration and deceleration. Also, we introduce a non-stochastic rule-based recession-dating method to forecast likely dates for the start of a recession and it length. Results indicate that the model is capable of exhibiting substantially non-linear behavior in its regime-specific latent process and hence is able to anticipate and detect regime-shifts accurately, improving the quality of growth forecasts obtained from it

Non-linear autoregressive processes

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