Bayesian Inference in Exponential and Pareto populations in the presence of Outliers

This thesis Entitled Bayesian inference in Exponential and pareto populations in the presence of outliers. The main theme of the present thesis is focussed on various estimation problems using the Bayesian appraoch, falling under the general category of accommodation procedures for analysing Pareto data containing outlier. In Chapter II. the problem of estimation of parameters in the classical Pareto distribution specified by the density function. In Chapter IV. we discuss the estimation of (1.19) when the sample contain a known number of outliers under three different data generating mechanisms, viz. the exchangeable model. Chapter V the prediction of a future observation based on a random sample that contains one contaminant. Chapter VI is devoted to the study of estimation problems concerning the exponential parameters under a k-outlier model.

A Bivariate Pareto Distribution with Freund’s Dependence Structure

Department of Statistics, Cochin University of Science and Technology

Calibrating the Gaussian multi-target tracking model

We present novel batch and online (sequential) versions of the expectation-maximisation (EM) algorithm for inferring the static parameters of a multiple target tracking (MTT) model. Online EM is of particular interest as it is a more practical method for long data sets since in batch EM, or a full Bayesian approach, a complete browse of the data is required between successive parameter updates. Online EM is also suited to MTT applications that demand real-time processing of the data. Performance is assessed in numerical examples using simulated data for various scenarios. For batch estimation our method significantly outperforms an existing gradient based maximum likelihood technique, which we show to be significantly biased. © 2014 Springer Science+Business Media New York.

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved

Meta-analysis of prevalence

Meta-analysis is a method to obtain a weighted average of results from various studies. In addition to pooling effect sizes, meta-analysis can also be used to estimate disease frequencies, such as incidence and prevalence. In this article we present methods for the meta-analysis of prevalence. We discuss the logit and double arcsine transformations to stabilise the variance. We note the special situation of multiple category prevalence, and propose solutions to the problems that arise. We describe the implementation of these methods in the MetaXL software, and present a simulation study and the example of multiple sclerosis from the Global Burden of Disease 2010 project. We conclude that the double arcsine transformation is preferred over the logit, and that the MetaXL implementation of multiple category prevalence is an improvement in the methodology of the meta-analysis of prevalence.

Global variation in the prevalence and incidence of major depressive disorder : a systematic review of the epidemiological literature

Background Summarizing the epidemiology of major depressive disorder (MDD) at a global level is complicated by significant heterogeneity in the data. The aim of this study is to present a global summary of the prevalence and incidence of MDD, accounting for sources of bias, and dealing with heterogeneity. Findings are informing MDD burden quantification in the Global Burden of Disease (GBD) 2010 Study. Method A systematic review of prevalence and incidence of MDD was undertaken. Electronic databases Medline, PsycINFO and EMBASE were searched. Community-representative studies adhering to suitable diagnostic nomenclature were included. A meta-regression was conducted to explore sources of heterogeneity in prevalence and guide the stratification of data in a meta-analysis. Results The literature search identified 116 prevalence and four incidence studies. Prevalence period, sex, year of study, depression subtype, survey instrument, age and region were significant determinants of prevalence, explaining 57.7% of the variability between studies. The global point prevalence of MDD, adjusting for methodological differences, was 4.7% (4.4–5.0%). The pooled annual incidence was 3.0% (2.4–3.8%), clearly at odds with the pooled prevalence estimates and the previously reported average duration of 30 weeks for an episode of MDD. Conclusions Our findings provide a comprehensive and up-to-date profile of the prevalence of MDD globally. Region and study methodology influenced the prevalence of MDD. This needs to be considered in the GBD 2010 study and in investigations into the ecological determinants of MDD. Good-quality estimates from low-/middle-income countries were sparse. More accurate data on incidence are also required.

Subpopulation triage: How to allocate conservation effort among populations

Threatened species often exist in a small number of isolated subpopulations. Given limitations on conservation spending, managers must choose from strategies that range from managing just one subpopulation and risking all other subpopulations to managing all subpopulations equally and poorly, thereby risking the loss of all subpopulations. We took an economic approach to this problem in an effort to discover a simple rule of thumb for optimally allocating conservation effort among subpopulations. This rule was derived by maximizing the expected number of extant subpopulations remaining given n subpopulations are actually managed. We also derived a spatiotemporally optimized strategy through stochastic dynamic programming. The rule of thumb suggested that more subpopulations should be managed if the budget increases or if the cost of reducing local extinction probabilities decreases. The rule performed well against the exact optimal strategy that was the result of the stochastic dynamic program and much better than other simple strategies (e.g., always manage one extant subpopulation or half of the remaining subpopulation). We applied our approach to the allocation of funds in 2 contrasting case studies: reduction of poaching of Sumatran tigers (Panthera tigris sumatrae) and habitat acquisition for San Joaquin kit foxes (Vulpes macrotis mutica). For our estimated annual budget for Sumatran tiger management, the mean time to extinction was about 32 years. For our estimated annual management budget for kit foxes in the San Joaquin Valley, the mean time to extinction was approximately 24 years. Our framework allows managers to deal with the important question of how to allocate scarce conservation resources among subpopulations of any threatened species. © 2008 Society for Conservation Biology.

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Near infrared reflectance spectroscopy (NIRS) to predict biological parameters of maize silage: effects of particle comminution, oven drying temperature and the presence of residual moisture

Maize silage nutritive quality is routinely determined by near infrared reflectance spectroscopy (NIRS). However, little is known about the impact of sample preparation on the accuracy of the calibration to predict biological traits. A sample population of 48 maize silages representing a wide range of physiological maturities was used in a study to determine the impact of different sample preparation procedures (i.e., drying regimes; the presence or absence of residual moisture; the degree of particle comminution) on resultant NIR prediction statistics. All silages were scanned using a total of 12 combinations of sample pre-treatments. Each sample preparation combination was subjected to three multivariate regression techniques to give a total of 36 predictions per biological trait. Increased sample preparations procedure, relative to scanning the unprocessed whole plant (WP) material, always resulted in a numerical minimisation of model statistics. However, the ability of each of the treatments to significantly minimise the model statistics differed. Particle comminution was the most important factor, oven-drying regime was intermediate, and residual moisture presence was the least important. Models to predict various biological parameters of maize silage will be improved if material is subjected to a high degree of particle comminution (i.e., having been passed through a 1 mm screen) and developed on plant material previously dried at 60 degrees C. The extra effort in terms of time and cost required to remove sample residual moisture cannot be justified. (c) 2005 Elsevier B.V. All rights reserved.

High resolution Northern Hemisphere wintertime mid-latitude dynamics during the Last Glacial Maximum

Hourly winter weather of the Last Glacial Maximum (LGM) is simulated using the Community Climate Model version 3 (CCM3) on a globally resolved T170 (75 km) grid. Results are compared to a longer LGM climatological run with the same boundary conditions and monthly saves. Hourly-scale animations are used to enhance interpretations. The purpose of the study is to explore whether additional insights into ice age conditions can be gleaned by going beyond the standard employment of monthly average model statistics to infer ice age weather and climate. Results for both LGM runs indicate a decrease in North Atlantic and increase in North Pacific cyclogenesis. Storm trajectories react to the mechanical forcing of the Laurentide Ice Sheet, with Pacific storms tracking over middle Alaska and northern Canada, terminating in the Labrador Sea. This result is coincident with other model results in also showing a significant reduction in Greenland wintertime precipitation – a response supported by ice core evidence. Higher-temporal resolution puts in sharper focus the close tracking of Pacific storms along the west coast of North America. This response is consistent with increased poleward heat transport in the LGM climatological run and could help explain “early” glacial warming inferred in this region from proxy climate records. Additional analyses shows a large increase in central Asian surface gustiness that support observational inferences that upper-level winds associated with Asian- Pacific storms transported Asian dust to Greenland during the LGM.

RUMOR PROCESSES ON N

We study four discrete-time stochastic systems on N, modeling processes of rumor spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumor. The appetite for spreading or hearing the rumor is represented by a set of random variables whose distributions may depend on the individuals. Our goal is to understand-based on the distribution of the random variables-whether the probability of having an infinite set of individuals knowing the rumor is positive or not.

NONHOMOGENEOUS RANDOM WALKS SYSTEMS ON Z

We consider a random walks system on Z in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove that if the process relies on efficient particles (i.e. those particles with a small probability of jumping to the left) being placed strategically on Z, then it might survive, having active particles at any time with positive probability. On the other hand, we may construct a process that dies out eventually almost surely, even if it relies on efficient particles. That is, we discuss what happens if particles are initially placed very far away from each other or if their probability of jumping to the right tends to I but not fast enough.

The influence of non-climate predictors at local and landscape resolutions depends on the autecology of the species

Species distribution models have come under criticism for being too simplistic for making robust future forecasts, partly because they assume that climate is the main determinant of geographical range at large spatial extents and coarse resolutions, with non-climate predictors being important only at finer scales. We suggest that this paradigm might be obscured by species movement patterns. To explore this we used contrasting kangaroo (family Macropodidae) case studies: two species with relatively small, stable home ranges (Macropus giganteus and M.robustus) and three species with more extensive, adaptive ranging behaviour (M.antilopinus, M.fuliginosus and M.rufus). We predicted that non-climate predictors will be most influential to model fit and predictive performance at local spatial resolution for the former species and at landscape resolution for the latter species. We compared residuals autocovariate - boosted regression tree (RAC-BRT) model statistics with and without species-specific non-climate predictors (habitat, soil, fire, water and topography), at local- and landscape-level spatial resolutions (5 and 50km). As predicted, the influence of non-climate predictors on model fit and predictive performance (compared with climate-only models) was greater at 50 compared with 5km resolution for M.rufus and M.fuliginosus and the opposite trend was observed for M.giganteus. The results for M.robustus and M.antilopinus were inconclusive. Also notable was the difference in inter-scale importance of climate predictors in the presence of non-climate predictors. In conclusion, differences in autecology, particularly relating to space use, may contribute to the importance of non-climate predictors at a given scale, not model scale per se. Further exploration of this concept across a range of species is encouraged and findings may contribute to more effective conservation and management of species at ecologically meaningful scales. © 2014 Ecological Society of Australia.

The exponential COM-Poisson distribution

The Conway-Maxwell Poisson (COMP) distribution as an extension of the Poisson distribution is a popular model for analyzing counting data. For the first time, we introduce a new three parameter distribution, so-called the exponential-Conway-Maxwell Poisson (ECOMP) distribution, that contains as sub-models the exponential-geometric and exponential-Poisson distributions proposed by Adamidis and Loukas (Stat Probab Lett 39:35-42, 1998) and KuAY (Comput Stat Data Anal 51:4497-4509, 2007), respectively. The new density function can be expressed as a mixture of exponential density functions. Expansions for moments, moment generating function and some statistical measures are provided. The density function of the order statistics can also be expressed as a mixture of exponential densities. We derive two formulae for the moments of order statistics. The elements of the observed information matrix are provided. Two applications illustrate the usefulness of the new distribution to analyze positive data.