1,628 research outputs found
UMSL Bulletin 2023-2024
The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp
Necessity of Rational Asset Price Bubbles in Two-Sector Growth Economies
We present plausible economic models in which an equilibrium with rational
asset price bubbles exists but equilibria with asset prices equal to
fundamental values do not. These economies feature multiple sectors with faster
economic growth than dividend growth. In our two-sector endogenous growth
model, entrepreneurs have access to a production technology subject to
idiosyncratic investment risk (tech sector) and trade a dividend-paying asset
(land). When leverage is relaxed beyond a critical value, the unique trend
stationary equilibrium exhibits a phase transition from the fundamental regime
to the bubbly regime with growth, implying the inevitability of bubbles with
loose financial conditions
UMSL Bulletin 2022-2023
The 2022-2023 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1087/thumbnail.jp
Pairwise versus mutual independence: visualisation, actuarial applications and central limit theorems
Accurately capturing the dependence between risks, if it exists, is an increasingly relevant topic of actuarial research. In recent years, several authors have started to relax the traditional 'independence assumption', in a variety of actuarial settings. While it is known that 'mutual independence' between random variables is not equivalent to their 'pairwise independence', this thesis aims to provide a better understanding of the materiality of this difference. The distinction between mutual and pairwise independence matters because, in practice, dependence is often assessed via pairs only, e.g., through correlation matrices, rank-based measures of association, scatterplot matrices, heat-maps, etc. Using such pairwise methods, it is possible to miss some forms of dependence. In this thesis, we explore how material the difference between pairwise and mutual independence is, and from several angles.
We provide relevant background and motivation for this thesis in Chapter 1, then conduct a literature review in Chapter 2.
In Chapter 3, we focus on visualising the difference between pairwise and mutual independence. To do so, we propose a series of theoretical examples (some of them new) where random variables are pairwise independent but (mutually) dependent, in short, PIBD. We then develop new visualisation tools and use them to illustrate what PIBD variables can look like. We showcase that the dependence involved is possibly very strong. We also use our visualisation tools to identify subtle forms of dependence, which would otherwise be hard to detect.
In Chapter 4, we review common dependence models (such has elliptical distributions and Archimedean copulas) used in actuarial science and show that they do not allow for the possibility of PIBD data. We also investigate concrete consequences of the 'nonequivalence' between pairwise and mutual independence. We establish that many results which hold for mutually independent variables do not hold under sole pairwise independent. Those include results about finite sums of random variables, extreme value theory and bootstrap methods. This part thus illustrates what can potentially 'go wrong' if one assumes mutual independence where only pairwise independence holds.
Lastly, in Chapters 5 and 6, we investigate the question of what happens for PIBD variables 'in the limit', i.e., when the sample size goes to infi nity. We want to see if the 'problems' caused by dependence vanish for sufficiently large samples. This is a broad question, and we concentrate on the important classical Central Limit Theorem (CLT), for which we fi nd that the answer is largely negative. In particular, we construct new sequences of PIBD variables (with arbitrary margins) for which a CLT does not hold. We derive explicitly the asymptotic distribution of the standardised mean of our sequences, which allows us to illustrate the extent of the 'failure' of a CLT for PIBD variables. We also propose a general methodology to construct dependent K-tuplewise independent (K an arbitrary integer) sequences of random variables with arbitrary margins. In the case K = 3, we use this methodology to derive explicit examples of triplewise independent sequences for which no CLT hold. Those results illustrate that mutual independence is a crucial assumption within CLTs, and that having larger samples is not always a viable solution to the problem of non-independent data
Beam scanning by liquid-crystal biasing in a modified SIW structure
A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
Taylor University Catalog 2023-2024
The 2023-2024 academic catalog of Taylor University in Upland, Indiana.https://pillars.taylor.edu/catalogs/1128/thumbnail.jp
Generalised latent variable models for location, scale, and shape parameters
Latent Variable Models (LVM) are widely used in social, behavioural, and educational sciences to uncover underlying associations in multivariate data using a smaller number of latent variables. However, the classical LVM framework has certain assumptions that can be restrictive in empirical applications. In particular, the distribution of the observed variables being from the exponential family and the latent variables influencing only the conditional mean of the observed variables. This thesis addresses these limitations and contributes to the current literature in two ways. First, we propose a novel class of models called Generalised Latent Variable Models for Location, Scale, and Shape parameters (GLVM-LSS). These models use linear functions of latent factors to model location, scale, and shape parameters of the items’ conditional distributions. By doing so, we model higher order moments such as variance, skewness, and kurtosis in terms of the latent variables, providing a more flexible framework compared to classical factor models. The model parameters are estimated using maximum likelihood estimation. Second, we address the challenge of interpreting the GLVM-LSS, which can be complex due to its increased number of parameters. We propose a penalised maximum likelihood estimation approach with automatic selection of tuning parameters. This extends previous work on penalised estimation in the LVM literature to cases without closed-form solutions. Our findings suggest that modelling the entire distribution of items, not just the conditional mean, leads to improved model fit and deeper insights into how the items reflect the latent constructs they are intended to measure. To assess the performance of the proposed methods, we conduct extensive simulation studies and apply it to real-world data from educational testing and public opinion research. The results highlight the efficacy of the GLVM-LSS framework in capturing complex relationships between observed variables and latent factors, providing valuable insights for researchers in various fields
Spatially dense stochastic epidemic models with infection-age dependent infectivity
We study an individual-based stochastic spatial epidemic model where the
number of locations and the number of individuals at each location both grow to
infinity. Each individual is associated with a random infectivity function,
which depends on the age of infection. Individuals are infected through
interactions across the locations with heterogeneous effects. The epidemic
dynamics in each location is described by the total force of infection, the
number of susceptible individuals, the number of infected individuals that are
infected at each time and have been infected for a certain amount of time, as
well as the number of recovered individuals. The processes can be described
using a time-space representation. We prove a functional law of large numbers
for these time-space processes, and in the limit, we obtain a set of time-space
integral equations. We then derive the PDE models from the limiting time-space
integral equations, in particular, the density (with respect to the infection
age) of the time-age-space integral equation for the number of infected
individuals tracking the age of infection satisfies a linear PDE in time and
age with an integral boundary condition. These integral equation and PDE limits
can be regarded as dynamics on graphons under certain conditions
University of Windsor Graduate Calendar 2023 Spring
https://scholar.uwindsor.ca/universitywindsorgraduatecalendars/1027/thumbnail.jp
Forested Watersheds and Water Supply: Exploring Effects of Wildfires, Silviculture, and Climate Change on Downstream Waters
Drinking water supplies for much of society originate in forests. To preserve the capability of these forests to produce clean and easily treatable water, source water supply and protection strategies focus in particular on potential disturbances to the landscape, which include prescribed forest harvesting and wildfires of varying intensity. While decades of work have revealed relationships between forest harvesting and stream flow response, there is a considerable lack of synthesis disentangling the interactions of climate, wildfires, stream flow, and water quality. Revealing the mechanisms for impacts on downstream waters after disturbances of harvesting and wildfire will greatly improve land and water management. In this dissertation, I combined synthesis of previously published or available data, novel mathematical analyses, and deterministic modeling to disentangle various disturbance effects and further our understanding of processes in forested watersheds. I broadly sought to explore how streamflow and water quality change after forest disturbances, and how new methods and analyses can provide insight into the biogeochemical and ecohydrologic processes changing during disturbances.
First, I examined the effect of wildfire on hydrology, and developed a novel Budyko decomposition method to separate climatic and disturbance effects on streamflow. Using a set of 17 watersheds in southern California, I showed that while traditional metrics like changes in flow or runoff ratio might not detect a disturbance effect from wildfire due to confounding climate signals, the Budyko framework can be used successfully for statistical change detection. The method was used to estimate hydrologic recovery timescales that varied between 5 and 45 years, with an increase of about 4 years of recovery time per 10% of the watershed burned.
Next, in Chapter 3 I used a meta-analysis approach to examine the effect of wildfire on water quality, using data from 121 catchments around the world. Analyzing the changes in concentrations of stream water nutrients, including carbon, nitrogen, and phosphorus, I showed that concentrations generally increased after fire. While a large amount of variability existed in the data, we found concurrent increases in the constituents after fire highlighting tight coupling of the biogeochemical cycles. Most interestingly, we found fire to increase the concentrations of biologically active nutrients like nitrate and phosphate at a greater rate than total nitrogen and phosphorus, with median increases of 40-60% in the nitrate to TN, and SRP to TP ratios.
Next, I conducted an analysis of both water quality and hydrology together after fire in Chapter 4, using a set of 29 wildfire-impacted watersheds in the United States. Concentration-discharge relationships can be used to reveal pathways and sources of elements exported from watersheds, and my overall hypothesis was that these relationships change in post-fire landscapes. I developed a new methodology, using k-means clustering, to classify watersheds as chemostatic, dilution, mobilization and chemodynamic, and explored how their position within the cluster changed in post-fire landscapes. I found that the behavior of nitrate and ammonium was increasingly chemostatic after fire, while behavior of total nitrogen, phosphorus, and organic phosphorus was increasingly mobilizing after fire.
Finally, I developed a coupled hydrology-vegetation-biogeochemistry model to simulate and elucidate processes controlling the impact of harvesting on downstream waters. I focused on the Turkey Lakes watershed where a significant amount of data has been collected on vegetation and soil nutrient dynamics, in addition to traditional streamflow and water quality metrics, and developed a novel multi-part calibration process that used measured data on stream, forest, and soil characteristics and dynamics. Future work would involve using the model to explore the data driven relationships that have been developed in the earlier chapters of the paper.
The work presented in this dissertation highlights new small and large-scale relationships between disturbances in forested watersheds and effects on downstream waters. With more threats predicted to escalate and overlap in the coming years, the novel results and methodologies that I have presented here should contribute to improving land and water management
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