Search

This project introduces a flexible univariate probability model referred to as the q-analogue of the Extended Generalized Gamma (or q-EGG) distribution, which encompasses the majority of the most frequently used continuous distributions, including the gamma, Weibull, logistic, type-1 and type-2 beta, Gaussian, Cauchy, Student-t and F. Closed form representations of its moments and cumulative distribution function are provided. Additionally, computational techniques are proposed for determining estimates of its parameters. Both the method of moments and the maximum likelihood approach are utilized. The effect of each parameter is also graphically illustrated. Certain data sets are modeled with q-EGG distributions; goodness of fit is assessed by making use of the Anderson–Darling and Cram´er–von Mises criteria, among others. Improved approximations to the distribution of quadratic forms are considered as well. Since much effort was expended to develop the code required to implement the various methodologie

Maintaining an adequate level of earthquake take-up rate could protect the insurance industry from systemic failure. Past research has shown that British Columbia and Quebec have significant differences in earthquake insurance take-up rate. This report investigates key factors from the structure (default options and various types) of the insurance plan and personal characteristics along with socioeconomic/demographic profiles that affect the demand for earthquake protection in the form of insurance. The report also provides a prediction model for earthquake insurance take-up rate. The results show an importance ranking of key factors of earthquake insurance take up, the most important three are "annual expected loss ratio", “age” and “average household size”. An optimal prediction model constructed by random forest with 15 predictors provides 69.4% testing accuracy. An important finding is that there exist cognitive biases among participants. Possible explanations of this finding are discussed.

This study is on the topic of financial literacy, with the data source containing information on clients' demographic information and self-evaluation, change in account value, and trade record, three major problems were investigated: first, whether a client's demographic traits are related to his/her self-evaluation of financial knowledge level; second, does the trading behaviour differ for clients who self-identified as in different financial knowledge groups; and third, do people who self-identified as financially knowledgeable have better investment result. Data manipulation was done using SQL and R. Exploratory analysis including multiple types of plots and proportion tables was used to derive the hypothesis of the potential relationship between variables, and hypothesis tests, contingency tables were used to prove the significance of the relationship. It is observed that demographic traits including marital status, gender, maximum age attained, the residence of living, income and net worth are related to a client's evaluation of his/her financial knowledge level, but the relationship was not strong enough to make predictions based on available information. Investors who think of themselves as more financially knowledgeable tend to choose a more risky portfolio, and they trade more frequently with a clear preference for agent operations -- this type of trade is also commonly used for the group of investors who believe that they lack enough knowledge in this field; while investors in between prefer principal operations. For the actual investment performance, investors who self-identified as equipped with more financial knowledge do have better performance on average, with the internal rate of return used as the standard of evaluation, it is also observed that the investors who see themselves as having an excellent amount of financial knowledge also have the largest diversity in terms of their performance.

In this paper, we recommend a mechanism for determining whether to logit or not to logit data in the unit interval which is based on quantile estimation of data between 0 and 1. By using a simulated dataset generated from a Beta regression model, the estimated quantile for this model perform better than those based on the linear quantile regression with logit transformation. Further, we investigate the performance of the quantile regression estimators based on the LQR and we conclude that it is better than those based on the Beta regression when the distribution is contaminated with 10% uniform numbers between 0 and 1. The proposed recommendation is that we can use logit transformation LQR if (1) we are dealing with quantile estimation in data between 0 and 1 (2) we ascertain that the data fit well to the contemplated bounded data regressions (whether Beta Regression or otherwise) and (3) if the fit of the model is suspected.

Quantum computing has been an emerging technology in the past few decades. It utilizes the power of programmable quantum devices to perform computation, which can solve complex problems in a feasible time that is impossible with classical computers. Simulating quantum chemical systems using quantum computers is one of the most active research fields in quantum computing. However, due to the novelty of the technology and concept, most materials in the literature are not accessible for newbies in the field and sometimes can cause ambiguity for practitioners due to missing details. This report provides a rigorous derivation of simulating quantum chemistry systems using quantum computers. The Hydrogen molecule is used as an example throughout the process to make it readable to a broader audience. Specifically, the ground state energies and the first-excited energies of the Hydrogen molecule, as well as the ground state energies of the Lithium Hydride molecule at different bond lengths under the governing of their corresponding Hamiltonians are explored through the Schrodinger’s equation, the Phase Estimation Algorithm (PEA), the second quantization, the Bravyi-Kitaev transformation (BKT), and the Hamiltonian establishment. Then, a quantum circuit is built from scratch based on the second-quantization and BKT Hamiltonian to demonstrate the process of quantum circuit derivation for quantum chemistry system. Lastly, Simulations on both the ground and excited state energies of the Hydrogen molecule and the ground state energies of the Lithium Hydride molecule are carried out based on the design of the circuits with Google’s Cirq quantum simulator. Finally, some quantitative and qualitative comparisons and analysis are conducted with the results.

Epidemiological modelling, most recently disseminated widely in the case of COVID-19, is a useful tool to simulate the future course of an epidemic. Unfortunately, such modelling is complex, as it is based on multiple assumptions regarding the relevant variables that may affect how an epidemic progresses. Such complexity oftentimes leads to the models not being understood by non-experts, and may even be kept from the public eye (e.g. modelling by Health Authorities). Notwithstanding this, the public is made aware of results either in a biased manner by experts and academics, and oftentimes portrayed in a alarmist manner, especially by the press. A underlying risk of such modelling is that it may also be resistant to falsification, as it can always be argued that if observed data do not fit the prediction, it is due to the predicted scenario nor playing out as simulated. To better close the gap between expert modelling and current epidemiological evolution, one possibility is to describe the latter using a simpler approach based on descriptive statistics (namely, percentiles). A trial of such approach on COVID-19 data from New Zealand and the United Kingdom shows that the approach seems adequate for conveying both the potential spread of the epidemic and the current location of the epidemic within such potential spread. Thus far, the model is descriptive of past data. But, inherent within the model, it is its capability to set the range for the next measuring period (say, the next day, if summarizing daily performance, the next week, if summarizing weekly data, or next month, if summarizing monthly data). Because such range act as an expectation, we could call it expectative modelling (a.k.a., it goes beyond mere description, as it has an element of future expectation, but it does not cross into simulation or prediction). Expectative modelling has very few assumptions, and the focus on percentiles allows to set the minimum and maximum bounds for our description at, say the 5th and 95th percentile (instead of at the minimum and maximum observed values). This range-based modelling has two main properties: On the one hand, to describe with Severity (Mayo), so that we may contain within the range highly informative (observed) behaviour by eliminating extreme data with a high probability of being exceptional, a fluke or a reporting error. On the other hand, to be attentive to Black Swans (Taleb), as the range itself tells us which (future) behaviours should not really surprise us (as opposed to those which fall outside the range). It is this expectative property of the approach that merits a preregistration, if only to mark a definite break between past data (already released) and current/future data (yet to be released).

Data on insemination records of Holstein Friesian (HF) purebred (n=45,497) and crossbred (n=58,497) collected from the BAIF Research Foundation were utilized. The conception rate was modeled as a binary trait, using linear repeatability models. Random regression models (RRM) were used to obtain the trajectory of variance components across age of the bulls. Legendre Polynomials up to order of fit of 4 were used for the random effects of additive genetic and permanent environmental effects. 200,000 Gibbs samples were generated with a burn-in of 20,000 and thinning interval of 50 using the THRGIBBS1F90 program. Heritability estimates were very low (0.1) in both breeds but peaked at the extreme ages. Heritability and repeatability estimates ranged between 0.038 (8 years) to 0.627 (10 years) and 0.060 to 0.809 respectively in purebreds. Narrower ranges of 0.010 (4 years) to 0.087 (11 years) and 0.532 to 0.832 for heritability and repeatability respectively, were obtained in crossbreds. Effect of permanent environment was low in purebreds compared to the crossbreds. The study using RRM was able to provide genetic parameter estimates of fertility for all ages throughout the productive lifespan of bulls.

Regulators’ early intervention is crucial when the financial system is experiencing difficulties. Financial stability must be preserved to avert banks’ bailouts, which hugely drain government's financial resources. Detecting in advance periods of financial crisis entails the development and customisation of accurate and robust quantitative techniques. The goal of this thesis is to construct automated systems via the interplay of various mathematical and statistical methodologies to signal financial instability episodes in the near-term horizon. These signal alerts could provide regulatory bodies with the capacity to initiate appropriate response that will thwart or at least minimise the occurrence of a financial crisis. This thesis presents three self-contained but related research undertakings on the subject of inventing early-warning alert systems described as follows. Our first research study puts forward a generalised multivariate version of a hidden Markov model (HMM) that modulates the regime-switching framework. In particular, the bivariate dynamics of the Financial Stability Index (FSI) and Industrial Production Index (IPI) exhibiting salient features of stochasticity, mean reversion, seasonality, spikes and memory are accurately and simultaneously captured by the resulting HMM filters. An integrated early-warning device is constructed, where the FSI and IPI are taken as inputs, to capture both the financial and business cycles. In our second research investigation, two different stochastic models are fused together to describe adequately the behaviours of four financial-market indices: Treasury bill yield-Eurodollar spread (TED), US Dollar Index (DXY), Volatility Index (VIX) and S&P 500 bid-ask spread, which are all deemed to mirror the liquidity levels in the financial markets. A blended multivariate HMM, which drives the regime-switching characteristics of market liquidity risk, is proposed to capture the dynamics of four time series. An early-warning signal extraction method along with its validation diagnostics is devised to generate alerts prior to or at a relatively early stage of the crisis events. The third research work in this thesis focuses on the determination of signs for possible crisis episodes that may wreak havoc to financial market or economic stability. Synthesising stochastic-process modelling, hidden Markov filtering, Random Forest and XGBoost, we create a hybrid supervised-learning system to detect anomalies in a multivariate time-series index data. Our methodology is capable of efficiently and accurately tracing concomitantly the FSIs of multiple countries and more importantly detecting anomalous FSIs’ behaviour portending a possible financial instability. Our proposed model is able to generate dynamically 6-step-ahead binary anomalous-normal classification predictions in a probabilistic sense. Two projected anomaly-warning signals are constructed to forecast two types of extremely anomalous events in the near future with a good accuracy.

This thesis proposes three contributing manuscripts related to patient flow management, server decision-making, and ventilation time in the intensive care and step-down units system. First, a Markov decision process (MDP) model with a Monte Carlo simulation was performed to compare two patient flow policies: prioritizing premature step-down and prioritizing rejection of patients when the intensive care unit is congested. The optimal decisions were obtained under the two strategies. The simulation results based on these optimal decisions show that a premature step-down strategy contributes to higher congestion downstream. Counter-intuitively, premature step-down should be discouraged, and patient rejection or divergence actions should be further explored as a viable alternative for congested intensive care units (ICUs). Secondly, an investigation of the length of stay (LOS) competition between the intensive care unit (ICU) and the step-down unit (SDU), two servers in tandem without a buffer between them was proposed using queuing games. Analysis of the competition was done under four different scenarios: (i) both servers cooperate; (ii) the servers do not cooperate and make decisions simultaneously; (iii) the servers do not cooperate but the first server, the ICU is the leader; (iv) the servers do not cooperate, the second server the SDU is the leader. Finally, a numerical analysis was performed. The results show that the length of stay decisions of each server depends critically on the payoff function’s form and the exogenous demand. Secondly, with a linear payoff function, the SDU is only beneficial to the system if the unit cost is greater than its unit reward at the ICU. Perhaps most importantly, the critical care pathway performs better under coordination and or leadership at the ICU level. Finally, first-day ventilated patients' ventilation time was analyzed using survival analysis. The probabilistic behaviour of the ventilation time duration was analyzed and the predictors of the ventilation time duration were determined based on available first-day covariates. Data were obtained from the Critical Care Information System (CCIS) about patients admitted to the ICUs in Ontario between July 2015 and December 2016. The log-logistic AFT model was found to be the best to relate the association between first-day covariates and the ventilation time.

This book has attempted to propose a modern innovative Practical Guide to Applied Research & Data Analysis with the view that research, statistics, and Islam are basically compatible. A glance at this book entitled "A Practical Guide to Applied Research & Data Analysis " should confirm the applied coverage to research. Applied Research is like flying an airplane, you learn more by doing (practice) than by reading. After more than 30 years of teaching Applied Statistics, Applied Econometrics, Research Methods and advising graduate students on their theses and dissertations, the major author of this book, Professor Abdulrazzak Charbaji; has found that “practice makes perfect” (i.e., the more you practice research the more you become proficient in it). In order to provide the best possible Applied Research Book, Professor Abdulrazzak Charbaji has decided to partner with his wife. What’s more, every member of this family has his / her own stake in this book. On the one hand, Ghada Bakir Charbaji provided an Islamic perspective on research and statistics and gave a brief description of the importance and origin of research and statistical concepts in Islam. On the other hand, Rima, Suzanne, Amer, and Samer provided rich and supportive learning examples. Turning family relations into a partnership was made easy in this book because we shared the same goal of making this book a continuous charity (Sadaqah Jariyah صدقة جارية ) and knowledge that others benefited from وعلم ينتفع به ( as was recommended by our Prophet Mohammad (peace be upon him)

Poster presented at ICTMC 2022 Calculating the sample size for cluster-randomised controlled trials (cRCTs) requires an inflation factor to account for the intra-cluster correlation coefficient (ICC), a value that quantifies the degree of dependence within clusters. Estimates of the ICC are often taken from pilot or preliminary trials and are estimated with uncertainty. This uncertainty can have a marked impact on the resulting power of the trial being designed. We aimed to develop an approach to account for the uncertainty in the ICC estimate when calculating the sample size for a cRCT with a continuous outcome. This was a methodological study using simulated data. We developed an approach to account for the imprecision in the ICC estimate using numerical methods to integrate the sample size for a cRCT over plausible values of the ICC. This gives a sample size which is the average over all these plausible values. We simulated 4 hypothetical scenarios which take an ICC estimate from pilot cRCTs of differing sizes. For each, we generated distributions of plausible values for the ICC estimated using Searle’s, Swiger’s and Fisher’s methods. Finally, we calculated the sample size for a main cRCT using our integrative adjustment over the plausible ICC values provided by the three different methods. We compared these with two other common approaches. A sensitivity analysis explored the impact of this approach on the main trial power in a realistic scenario. In each case the main trial sample size using our integrative adjustment was greater than using the point estimate for the ICC which does not account for its imprecision. The overall sample size also depended on the number of clusters in the main trial. We found that this approach consistently preserved main trial power at 10% or more above using a simple ICC point estimate for realistic conservative scenarios. The proposed method estimates the sample size for a cRCT that accounts for the imprecision in the ICC and thus can help mitigate potential power loss that can result from using an uncertain point ICC estimate. This method can be used with any means of estimating distributions of plausible values for the ICC, allowing broad applicability. This work has been published in Statistical Methods in Medical Research and R code for the calculation of the adjusted cRCT sample size is available.

In this work, we mainly focus on the topic related to dimension reduction, operator learning and uncertainty quantification for problems of differential equations. The supervised machine learning methods introduced here belong to a newly booming field compared to traditional numerical methods. The building blocks for our works are mainly Gaussian process and neural network. The first work focuses on supervised dimension reduction problems. A new framework based on rotated multi-fidelity Gaussian process regression is introduced. It can effectively solve high-dimensional problems while the data are insufficient for traditional methods. Moreover, an accurate surrogate Gaussian process model of original problem can be formulated. The second one we would like to introduce is a physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equations(PDEs). In this work, Gaussian process regression model is incorporated with given physical information to find solutions or discover unknown coefficients of given PDEs. Three different models are introduce and their performance are compared and discussed. Lastly, we propose attention based MultiAuto-DeepONet for operator learning of stochastic problems. The target of this work is to solve operator learning problems related to time-dependent stochastic differential equations(SDEs). The work is built on MultiAuto-DeepONet and attention mechanism is applied to improve the model performance in specific type of problems. Three different types of attention mechanism are presented and compared. Numerical experiments are provided to illustrate the effectiveness of our proposed models.

The Gulf of Maine haddock population is assessed in three ways. The first considers the haddock in this area to be an isolated stock. The other two incorporate movement into that area, either permanent or temporary, by haddock from Georges Bank. The evidence for such movement from these analyses alone is sufficient to point to scenarios involving limited movement being of similar plausibility to that of an isolated stock. Catch projections under constant fishing mortality are found to be sensitive, in particular, to this possibility of limited movement for the case where the movement is permanent. Assessment results for the most recent recruitment are sensitive to the procedure used to shrink this estimate to the mean.

Poster presented at the International Clinical Trials Methodology Conference (ICTMC) 2022. Our aim was to calculate the intra-cluster correction (ICC) from a number of individually randomised trials that had a patient reported outcome measure (PROM) as an outcome and clustering in the trial design. This analysis aims to inform ICC assumptions in the design of individually randomised cluster trials in the absence of trial specific outcome data. Ethics approval for the secondary analysis of data was obtained through the University of Sheffield School of Health and Related Research (ScHARR) Ethics Committee (Reference: 034554).

This report reflects a series of Panel reviews and recommendations relating to analyses of west coast rock lobster poaching data. Panel recommendations are indicated to have been satisfactorily implemented.

The TAC for Tristan da Cunha island rock lobster for the 2014 season as calculated using the current OMP.

This document presents responses to a number of comments made in an analysis of gannet data by Gremillet et al., questioning the defensibility of a number of them and in particular those related to suggested additional restrictions on South African purse-seine fisheries.

In this paper, a simulation study was conducted to assess whether it is ideal to address the issue of non-detects in data using a traditional substitution approach for non-detects, imputation, or a non-imputation based approach. Simulated data used were simple nested designs motivated by a real-life data in a study of bumble bee activity in a commercial cherry orchard by Kuivila et al. (2021). The simulated data were generated at different thresholds or censoring levels and at different effect sizes. For each simulated data, seven popular existing techniques to handle non-detects were applied: (i) Zero substitution, (ii) Substitution with half Limit of Detection (LOD/2), (iii) Substitution with LOD/√ 2, (iv) Multiple Imputation (MI), (v) Regression on Order Statistics (ROS) (Imputation approach), and (vi) Maximum Likelihood Estimation (MLE) (likelihood estimation approach) and (vii) Kaplan-Meier (KM). Multiple Imputation (MI) was not applicable as the design of the simulated data violated the assumption of having a multivariate distribution. By comparative analysis of the simulated data, substituting with LOD/2 seemed appropriate for the design simulated, as it outperformed the other techniques (i.e ROS, MLE, KM, LOD/√ 2, and zero substitution) by yielding a lower Type I error, lower bias, and a better power across increasing effect sizes.

This document presents some preliminary Operational Management Procedures (OMP) - 2014 results for the south coast rock lobster fishery. The operating model which has been used to test alternative OMPs is model RC1 reported in Johnston (2013). The current OMP (OMP-2010) is described in the Appendix for reference to aid comparison. Note that the OMP-2010 has as its management target Bsp(2025/2006)=1.20 (in median terms).

A final set of results for the South Coast rock lobster fishery for three different Operational Management Procedures (OMPs) is provided. Results are also compared for three different scenarios relating to constraints for future Total Allowable Catch (TAC).

This dissertation address two significant challenges in the causal inference workflow for Big Observational Data. The first is designing Big Observational Data with high-dimensional and heterogeneous covariates. The second is performing uncertainty quantification for estimates of causal estimands that are obtained from the application of black box machine learning algorithms on the designed Big Observational Data. The methodologies developed by addressing these challenges are applied for the design and analysis of Big Observational Data from a large public university in the United States. Distributed Design A fundamental issue in causal inference for Big Observational Data is confounding due to covariate imbalances between treatment groups. This can be addressed by designing the study prior to analysis. The design ensures that subjects in the different treatment groups that have comparable covariates are subclassified or matched together. Analyzing such a designed study helps to reduce biases arising from the confounding of covariates with treatment. Existing design methods, developed for traditional observational studies consisting of a single designer, can yield unsatisfactory designs with sub-optimum covariate balance for Big Observational Data due to their inability to accommodate the massive dimensionality, heterogeneity, and volume of the Big Data. We propose a new framework for the distributed design of Big Observational Data amongst collaborative designers. Our framework first assigns subsets of the high-dimensional and heterogeneous covariates to multiple designers. The designers then summarize their covariates into lower-dimensional quantities, share their summaries with the others, and design the study in parallel based on their assigned covariates and the summaries they receive. The final design is selected by comparing balance measures for all covariates across the candidates and identifying the best amongst the candidates. We perform simulation studies and analyze datasets from the 2016 Atlantic Causal Inference Conference Data Challenge to demonstrate the flexibility and power of our framework for constructing designs with good covariate balance from Big Observational Data. Designed Bootstrap The combination of modern machine learning algorithms with the nonparametric bootstrap can enable effective predictions and inferences on Big Observational Data. An increasingly prominent and critical objective in such analyses is to draw causal inferences from the Big Observational Data. A fundamental step in addressing this objective is to design the observational study prior to the application of machine learning algorithms. However, the application of the traditional nonparametric bootstrap on Big Observational Data requires excessive computational efforts. This is because every bootstrap sample would need to be re-designed under the traditional approach, which can be prohibitive in practice. We propose a design-based bootstrap for deriving causal inferences with reduced bias from the application of machine learning algorithms on Big Observational Data. Our bootstrap procedure operates by resampling from the original designed observational study. It eliminates the need for additional, costly design steps on each bootstrap sample that are performed under the standard nonparametric bootstrap. We demonstrate the computational efficiency of this procedure compared to the traditional nonparametric bootstrap, and its equivalency in terms of confidence interval coverage rates for the average treatment effects, by means of simulation studies and a real-life case study. Case Study We apply the distributed design and designed bootstrap methodologies in a case study involving institutional data from a large public university in the United States. The institutional data contains comprehensive information about the undergraduate students in the university, ranging from their academic records to on-campus activities. We study the causal effects of undergraduate students’ attempted course load on their academic performance based on a selection of covariates from these data. Ultimately, our real-life case study demonstrates how our methodologies enable researchers to effectively use straightforward design procedures to obtain valid causal inferences with reduced computational efforts from the application of machine learning algorithms on Big Observational Data.

I use two examples to illustrate three methods for model averaging: using AIC weights, using BIC weights, and fully Bayesian analyses. The first example is a capture-recapture study that estimates the population size by averaging over 4 models for capture probabilities. The second is an analysis of a study of logging impacts on Curculionid weevils using a before-after-control-impact (BACI) study design. The estimated impact is averaged over 4 ecologically relevant models. Both examples demonstrate the sensitivity of model weights, or posterior model probabilities, to the choice of prior model probabilities and prior distributions for parameters. The model averaged estimates and their confidence intervals are less influenced by those choices. The BACI-design example also demonstrates the need to carefully choose the model parameterization so that the parameter of interest, the interaction, has the same interpretation for all models in the model set. I also briefly discuss three other frequentist approaches to model averaging: bagging, stacking, and model-averaged-tail-area confidence intervals.

Principal response curve (PRC) analysis was applied to an assessment of the ecological impact of the genetically-modified (GM), insect-resistant, cotton MON 88702 on predatory Hemiptera communities in the field. The field community was represented by ten taxa collected ten times across the season at six sites, in which individual taxa were not observed in at least 25% of the time (unique site x collection combinations). These complete absences and those nearly so, called sparse subsets of the data in this investigation, were the result of geoclimatic and seasonal variations, which are both independent of the treatment effect for which the PRC analysis is intended. If the sparse subsets were included in the analysis, the treatment effect would be underestimated. Here, a modified analysis is proposed to remove those sparse subsets and to be performed on the incomplete data. In the application to MON 88702, four components (PRC1-4) were significant at the 5% level by the modified method, when more than 50% of the data were excluded due to no- or low responses, and five (PRC1-5) by the classical method. While PRC1-2 was highly consistent between two methods, PRC3-5 was largely different because of sparse subsets of the data. Differences in results between two methods demonstrate that excluding sparse subsets prevented the bias in the estimation of the treatment effect and the relationship with the community from confounding with the environmental variation that caused the sparse data. In this regard, the modification should be considered as a supplement of the classical PRC analysis and recommended when abundance data have sparse subsets.

Comments in the form of embellishments and caveats are added to the information and suggestions provided in PEL/102. The relative power of alternative future closure patterns should be evaluated by simulation before any choice might be made. Clarification of what future monitoring data are planned to be collected is important. Discussion to clarify different hypotheses on the manner in which closure impacts penguins is required, as this is pertinent to assessing the possible impact of recent MPA declarations on analyses of the impact of closures. In summarizing results for decision makers, benefits for and costs to both penguins and industries need to be quantified; this exercise will need to distinguish (possibly defensibly differing) expert judgements from individual preferences regarding risk, as eventual decisions related to the latter are the responsibility of the decision maker.