Mathematical models are commonly used in science and industry to simulate complex physical processes. These models are implemented by computer codes which are often complex. For this reason, the codes are also expensive in terms of computation time, and this limits the number of simulations in an experiment. The codes are also deterministic, which means that output from a code has no measurement error. <br /><br /> One modelling approach in dealing with deterministic output from computer experiments is to assume that the output is composed of a drift component and systematic errors, which are stationary Gaussian stochastic processes. A Bayesian approach is desirable as it takes into account all sources of model uncertainty. Apart from prior specification, one of the main challenges in a complete Bayesian model is integration. We take a Bayesian approach with a Jeffreys prior on the model parameters. To integrate over the posterior, we use two approximation techniques on the log scaled posterior of the correlation parameters. First we approximate the Jeffreys on the untransformed parameters, this enables us to specify a uniform prior on the transformed parameters. This makes Markov Chain Monte Carlo (MCMC) simulations run faster. For the second approach, we approximate the posterior with a Normal density. <br /><br /> A large part of the thesis is focused on the problem of integration. Integration is often a goal in computer experiments and as previously mentioned, necessary for inference in Bayesian analysis. Sampling strategies are more challenging in computer experiments particularly when dealing with computationally expensive functions. We focus on the problem of integration by using a sampling approach which we refer to as "GaSP integration". This approach assumes that the integrand over some domain is a Gaussian random variable. It follows that the integral itself is a Gaussian random variable and the Best Linear Unbiased Predictor (BLUP) can be used as an estimator of the integral. We show that the integration estimates from GaSP integration have lower absolute errors. We also develop the Adaptive Sub-region Sampling Integration Algorithm (ASSIA) to improve GaSP integration estimates. The algorithm recursively partitions the integration domain into sub-regions in which GaSP integration can be applied more effectively. As a result of the adaptive partitioning of the integration domain, the adaptive algorithm varies sampling to suit the variation of the integrand. This "strategic sampling" can be used to explore the structure of functions in computer experiments.

Determining which genes are essential for growth of a bacterial organism is an important question to answer as it is useful for the discovery of drugs that inhibit critical biological functions of a pathogen. To evaluate essentiality, biologists often use transposon mutagenesis to disrupt genomic regions within an organism, revealing which genes are able to withstand disruption and are therefore not required for growth. The development of next-generation sequencing technology augments transposon mutagenesis by providing high-resolution sequence data that identifies the exact location of transposon insertions in the genome. Although this high-resolution information has already been used to assess essentiality at a genome-wide scale, no formal statistical model has been developed capable of quantifying significance. This thesis presents a formal Bayesian framework for analyzing sequence information obtained from transposon mutagenesis experiments. Our method assesses the statistical significance of gaps in transposon coverage that are indicative of essential regions through a Gumbel distribution, and utilizes a Metropolis-Hastings sampling procedure to obtain posterior estimates of the probability of essentiality for each gene. We apply our method to libraries of M. tuberculosis transposon mutants, to identify genes essential for growth in vitro, and show concordance with previous essentiality results based on hybridization. Furthermore, we show how our method is capable of identifying essential domains within genes, by detecting significant sub-regions of open-reading frames unable to withstand disruption. We show that several genes involved in PG biosynthesis have essential domains.

Software project management is one of the most critical activities in modern software development projects. Without realistic and objective management, the software development process cannot be managed in an effective way. There are three general problems in project management: effort estimation is not accurate, actual status is difficult to understand, and projects are often geographically dispersed. Estimating software development effort is one of the most challenging problems in project management. Various attempts have been made to solve the problem; so far, however, it remains a complex problem. The error rate of a renowned effort estimation model can be higher than 30% of the actual productivity. Therefore, inaccurate estimation results in poor planning and defies effective control of time and budgets in project management. In this research, we have built a productivity prediction model which uses productivity data from an ongoing project to reevaluate the initial productivity estimate and provides managers a better productivity estimate for project management. The actual status of the software project is not easy to understand due to problems inherent in software project attributes. The project attributes are dispersed across the various CASE (Computer-Aided Software Engineering) tools and are difficult to measure because they are not hard material like building blocks. In this research, we have created a productivity console which incorporates an expert system to measure project attributes objectively and provides graphical charts to visualize project status. The productivity console uses project attributes gathered in KB (Knowledge Base) of PAMPA II (Project Attributes Monitoring and Prediction Associate) that works with CASE tools and collects project attributes from the databases of the tools. The productivity console and PAMPA II work on a network, so geographically dispersed projects can be managed via the Internet without difficulty.

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Bayesian approaches are increasingly being used to embed mechanistic process models used into statistical state space frameworks for environmental prediction and forecasting applications. In this study, I focus on Bayesian State Space Models (SSMs) for modeling the temporal dynamics of carbon in terrestrial ecosystems. In Chapter 1, I provide an introduction to Ecological Forecasting, State Space Models, and the challenges of using State Space Models for Ecosystems. In Chapter 2, we provide a brief background on State Space Models and common methods of parameter estimation. In Chapter 3, we simulate data from an example model (DALECev) using driver data from the Talladega National Ecosystem Observatory Network (NEON) site and perform a simulation study to investigate its performance under varying frequencies of observation data. We show that as observation frequency decreases, the effective sample size of our precision estimates becomes too small to reliably make inference. We introduce a method of tuning the time resolution of the latent process, so that we can still use high-frequency flux data, and show that this helps to increase sampling efficiency of the precision parameters. Finally, we show that data cloning is a suitable method for assessing the identifiability of parameters in ecosystem models. In Chapter 4, we introduce a method for embedding positive process models into lognormal SSMs. Our approach, based off of moment matching, allows practitioners to embed process models with arbitrary variance structures into lognormally distributed stochastic process and observation components of a state space model. We compare and contrast the interpretations of our lognormal models to two existing approaches, the Gompertz and Moran-Ricker SSMs. We use our method to create four state space models based off the Gompertz and Moran-Ricker process models, two with a density dependent variance structure for the process and observations and two with a constant variance structure for the process and observations. We design and conduct a simulation study to compare the forecast performance of our four models to their counterparts under model mis-specification. We find that when the observation precision is estimated, the Gompertz model and its density dependent moment matching counterpart have the best forecasting performance under model mis-specification when measured by the average Ignorance score (IGN) and Continuous Ranked Probability Score (CRPS), even performing better than the true generating model across thirty different synthetic datasets. When observation precisions were fixed, all models except for the Gompertz displayed a significant improvement in forecasting performance for IGN, CRPS, or both. Our method was then tested on data from the NOAA Dengue Forecasting Challenge, where we found that our novel constant variance lognormal models had the best performance measured by CRPS, and also had the best performance for both CRPS and IGN for one and two week forecast horizons. This shows the importance of having a flexible method to embed sensible dynamics, as constant variance lognormal SSMs are not frequently used but perform better than the density dependent models here. In Chapter 5, we apply our lognormal moment matching method to embed the DALEC2 ecosystem model into the process component of a state space model using NEON data from University of Notre Dame Environmental Research Center (UNDE). Two different fitting methods are considered for our difficult problem: the updated Iterated Filtering algorithm (IF2) and the Particle Marginal Metropolis Hastings (PMMH) algorithm. We find that the IF2 algorithm is a more efficient algorithm than PMMH for our problem. Our IF2 global search finds candidate parameter values in thirty hours, while PMMH takes 82 hours and accepts only .12% of proposed samples. The parameter values obtained from our IF2 global search show good potential for out of sample prediction for Leaf Area Index and Net Ecosystem Exchange, although both have room for improvement in future work. Overall, the work done here helps to inform the application of state space models to ecological forecasting applications where data are not available for all stocks and transfers at the operational timestep for the ecosystem model, where large numbers of process parameters and long time series provide computational challenges, and where process uncertainty estimation is desired. / Doctor of Philosophy / With ecosystem carbon uptake expected to play a large role in climate change projections, it is important that we make our forecasts as informed as possible and account for as many sources of variation as we can. In this dissertation, we examine a statistical modeling framework called the State Space Model (SSM), and apply it to models of terrestrial ecosystem carbon. The SSM helps to capture numerous sources of variability that can contribute to the overall predictability of a physical process. We discuss challenges of using this framework for ecosystem models, and provide solutions to a number of problems that may arise when using SSMs. We develop methodology for ensuring that these models mimic the well defined upper and lower bounds of the physical processes that we are interested in. We use both real and synthetic data to test that our methods perform as desired, and provide key insights about their performance.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: We investigate the procedure of assigning probabilities to logical statements. The simplest case is that of equilibrium statistical mechanics and its fundamental assumption of equally likely states. Rederiving the formulation led us to question the assumption of logical independence inherent to the construction and speci cally its inability to update probability when data becomes available. Consequently we replace the assumption of logical independence with De Finetti's concept of exchangeability. To use the corresponding representation theorems of De Finetti requires us to assign prior distributions for some general parameter spaces. We propose the use of stability properties to identify suitable prior distributions. The combination of exchangeable likelihoods and corresponding prior distributions results in more general evidence distribution assignments. These new evidence assignments generalise the Shannon entropy to other entropy measures. The goal of these entropy formulations is to provide a general framework for constructing models. / AFRIKAANSE OPSOMMING: Ons ondersoek the prosedure om waarskynlikhede aan logiese stellings toe te ken. Die eenvoudigste geval is die van ewewig-statistiese meganika en die ooreenkomstige fundamentele aanname van ewekansige toestande. Hera eiding van die standaard formulering lei ons tot die bevraagtekening van die aanname van logiese onafhanklikheid en spesi ek die onmoontlikheid van opdatering van waarskynlikheid wanneer data beskikbaar raak. Gevolglik vervang ons die aanname van logiese onafhanklikheid met De Finetti se aanname van omruilbaarheid. Om die ooreenkomstige voorstelling stellings te gebruik moet ons a priori verdelings konstrueer vir 'n paar algemene parameter-ruimtes. Ons stel voor dat stabiliteits-eienskappe gebruik moet word om geskikte a priori distribusies te identi seer. Die kombinase van omruilbare aanneemlikheids funksies en die ooreenkomstige a priori verdelings lei ons tot nuwe toekennings van getuienis-verdelings. Hierdie nuwe getuienesverdelings is n veralgemening van Shannon se entropie na ander entropie-maatstawwe. Die doel van hierdie entropie formalismes is om 'n raamwerk vir modelkonstruksie te verskaf.

A subfamília Mydinae (Insecta, Diptera, Mydidae) ocorre somente nas Américas e é composta por 12 gêneros e 84 espécies, sendo a grande maioria das espécies de Mydidae pertencentes a essa subfamília. Mydinae é atualmente dividida em quatro tribos: Dolichogastrini, Mydini, Phylomydini e Messiasiini. A monofilia da subfamília, assim como de suas tribos e gêneros, ainda não havia sido testada por análises filogenéticas, o que justifica os objetivos deste trabalho, que são: 1)testar a monofilia da subfamília Mydinae; 2)verificar o relacionamento filogenético dos Mydinae com outras subfamílias de Mydidae; 3)testar a monofilia das tribos, subtribos e gêneros de Mydinae, assim como a monofilia dos grupos de espécies do gênero Mydas; 4)propor uma nova classificação para a subfamília, baseada nos resultados filogenéticos. A partir de dados da morfologia externa de adultos, e também de sequência de DNA do gene COI, dois métodos de análise foram empregados: análises de parcimônia, com pesagem igual dos caracteres, e análises probabilísticas bayesianas. Para cada um dos métodos, foram analisados os dados morfológicos e moleculares separadamente, e também em conjunto. A monofilia de Mydinae, conforme delimitada na classificação vigente, não é corroborada no presente trabalho, em nenhuma das análises. Nas duas análises com dados morfológicos, e na análise bayesiana com dados morfológicos e moleculares, foi recuperado um clado formado por todos os Mydinae (exceto Messiasia wilcoxi) + Paramydas (\'Apiophorinae\'). Dentre as tribos de Mydinae, não foi recuperada a monifilia de Messiassiini e Mydini. Já os gêneros Ceriomydas, Stratiomydas, Phyllomydas e Protomydas foram reconhecidos como mofiléticos. Já os gêneros Baliomydas, Gauromydas, Messiasia e Mydas, não formaram grupos monofiléticos em nenhuma das análises. Neste trabalho, puderam ser testadas as monofilias de quatro dos cinco grupos de espécies de Mydas: clavatus, fulvifrons, interruptus e xanthopterus, sendo o grupo hardyi monotípico. Apenas o grupo interruptus foi recuperado como monofilético, embora seja reconhecido aqui que os caracteres de coloração tradicionalmente utilizados para a separação dos grupos não foram utilizados. A subfamília Apiophorinae, com amostragem de quatro espécies, não foi recuperada como monofilética, com o gênero Eumydas agrupando-se aos Rhopaliinae. A classificação de Mydinae é aqui revisada, porém devido à incerteza razoável quanto ao relacionamento entre alguns grupos, alguns táxons da classificação tradicional foram mantidos, apesar de não serem monofiléticos / The Mydinae (Insecta, Diptera, Mydidae) occur only in the Americas and comprise 12 genera and 84 species, of which the vast majority of mydids occurring in Brazil belonging to this subfamily. Mydinae is currently divided into four tribes: Dolichogastrini, Messiasiini, Mydini and Phylomydini. The monophyly of the subfamily, as well as the monophyly of their tribes and genera, had not yet been tested by phylogenetic analysis. Concerning this fact, the objectives of this work are: 1) test the monophyly of the subfamily Mydinae, 2) check the phylogenetic relationship between Mydinae and other subfamilies of Mydidae, 3) test the monophyly of the tribes, subtribes and genera of Mydinae, as well as the monophyly of the species-groups of the genus Mydas; 4) propose a new classification of the subfamily based on phylogenetic results. The data from the external morphology of adults, and also DNA sequence of the COI gene, two methods of analysis were used: parsimony analysis with equal weighting of characters, and Bayesian probabilistic analysis. For each method, morphological and molecular data were analyzed separately and also in combination. The monophyly of Mydinae, as defined in the current classification, is not borne out in the present study. In both analyzes with morphological data, and Bayesian analysis with morphological and molecular data, a clade formed by all Mydinae (except Messiasia wilcoxi) + Paramydas (\'Apiophorinae\') was recovered. Among the tribes of Mydinae, the monophylies of Messiassiini and Mydini were not recovered. The genera Ceriomydas, Stratiomydas, Phyllomydas and Protomydas are recognized as natural groups. In the other hand, the genera Baliomydas, Gauromydas, Messiasia and Mydas did not form monophyletic groups in any of the conducted analyzes. Concerning the Mydas species-groups, only the interruptus group was recovered as monophyletic, although it is recognized here that color based characters traditionally used for separating the groups were not used in the present work. The subfamily Apiophorinae, with four species sampled, was not recovered as monophyletic, with genus Eumydas grouping to Rhopaliinae. The classification of Mydinae is reviewed here, but due to reasonable uncertainty as to the relationships between some groups, some taxa of the traditional classification were kept, although not recognized as monophyletic

<p>The main idea of our work is the calibration parameters for the Heston stochastic volatility model. We make this procedure by using the OMXS30 index from the NASDAQ OMX Nordic Exchange Market. We separate our data into the stable period and high-volatility period on this Nordic Market. Deviation detection problem are solved using the Bayesian analysis of change-points. We estimate parameters of the Heston model for each of periods and make some conclusions.</p>

The main idea of our work is the calibration parameters for the Heston stochastic volatility model. We make this procedure by using the OMXS30 index from the NASDAQ OMX Nordic Exchange Market. We separate our data into the stable period and high-volatility period on this Nordic Market. Deviation detection problem are solved using the Bayesian analysis of change-points. We estimate parameters of the Heston model for each of periods and make some conclusions.