Understanding that large earthquakes can be violent to human beings, a wide variety of seismicity forecasting models are proposed. To perform useful comparisons among these point process models, graphical residual methods are proposed because they visualize and highlight when and where a given model does not agree closely with either the observed seismicity or another model. In this paper, we work with the one-day observational and forecasting earthquake data from Southern California in the entire year of 2017. Our goal is to utilized Voronoi analysis and Super-thinned analysis to evaluate and compare the Epidemic- Type Aftershock Sequence model (ETAS) and the Modified Nonparametric Hawkes Point Process model (Modified MISD). Essentially, our results suggest that the Modified MISD Model returns comparatively better predictions and better goodness of fit.

Nowadays distance measures techniques have been quickly developed and widely used to the real application. The main objective of this thesis is to make a brief introduction of different distance measures methods, especially spike-time distance and its application to point pattern prototypes and Multi-Dimensional Scaling (MDS) methods. Meantime, R programming packages for spike-time distance, prototype and Multi-Dimensional Scaling have also been introduced in order to make these methods more practical and convenient to the real world. And, their packages are used to a real dataset as an application.

MyTherapistMatch.com seeks to match visiting patients with suitable therapists after patients fill out the online questionnaire which consists of many psychological questions. However, a problem with this website is that many patients in fact do not end up scheduling a session with a therapist. The website founder believes that one of the major reasons is the length of the questionnaire. Therefore, to reduce annoyance for users, the task becomes selecting a subset of necessary questions from the questionnaire. The website provides patient selection data and patient action data which records how a patient interacts with a matched therapist. This thesis tries to implement hierarchical clustering method on both the question responses and the questions themselves, in order to find a reasonable way to pick the necessary questions. Correlation coefficients and Pearson's chi-squared test are used to define the metrics in hierarchical clustering. Satisfiable results are obtained. A linear model is also used to find the relationship between question responses and patient actions.

We investigate the properties of a weighted analogue of Ripley’s K-function which was first introduced by Baddeley, Møller, and Waagepetersen. This sta- tistic, called the weighted or inhomogeneous K-function, is useful for assessing the fit of point process models. The advantage of this measure of goodness- of-fit is that it can be used in situations where the null hypothesis is not a stationary Poisson model. We note a correspondence between the weighted K- function and thinned residuals, and derive the asymptotic distribution of the weighted K-function for a spatial inhomogeneous Poisson process. We then present an application of the use of the weighted K-function to assess the goodness-of-fit of a class of point process models for the spatial distribution of earthquakes in Southern California.

Guidelines for Assessment and Instruction in Statistics Education (GAISE)

provide a framework for revising introductory statistics courses. GAISE promotes statistical literacy and statistical thinking, where students not only understand concepts but are able to critically evaluate and make arguments based on quantitative information.

There are multiple definitions of statistical literacy and statistical thinking in

the literature. In this thesis we are interested in the aspect of statistical literacy

that aims for an educated consumer, one who can process everyday statistical

information. Further, Statistical thinking is present when students can apply the statistical information learned to situations such as: 1) using statistics to solve real world problems, 2) critique and interpretation of statistical information reported in the mass media, and 3) interpretation and communication of statistical findings within context .

Despite this growing consensus that students must acquire higher-order think-

iing and performance skills in order to apply statistical reasoning and thinking

to their research problems successfully, a gap still exists between course objectives and student outcomes. After completion of the coursework, students are more likely to forget the materials learned in course and continue to struggle with applying statistical reasoning and thinking. The type of assessment used in statistics courses provides one explanation for this gap. With the increase number of students enrolled in introductory courses, instructors rely heavily on multiple choice questions to evaluate students0undesrtanding of course materials and principles. Furthermore, in subjects such as mathematics, statistics, chemistry, biology, and physics, research has shown that about 70% of the questions are at the recall or comprehension level with very little attention paid to the questions

that target application, analysis, synthesis, and evaluation. Therefore, and based on Bloom's taxonomy, the student outcomes focus on lower level thinking skills (knowledge and comprehension), whereas the course objectives and expectations involve higher level of thinking skills (application, analysis, synthesis, and evaluation). In order to bridge the gap between objectives and outcomes, tests must provide students opportunities to employ higher order thinking.

The objectives of this thesis include:

1. Comparison of students'responses to open-ended questions on condence

interval and P-value.

2. Prediction of the students' final scores from their scores on "upper level

thinking", "application", "lower level computation and "upper level computation".

3. Pinpoint the students'misconceptions of the P-value by comparing the pro-

portion of correct answers under two conditions including: a) deciding about

the null hypothesis by comparison of the P-value Vs. level of signicance

or alpha, and b) deciding about the null hypothesis by examination of the

condence interval and the interpretation of the P-vlaue.

This paper examines the transmission properties of the COVID-19 virus in Taipei from May 2021 to April 2022. Taipei, being a densely populated city, is an easy target for a highly transmissible virus such as COVID-19. However, the Taiwanese government set up strict public health policies that include a monitoring system and quarantine to prevent the outbreak that was effective in controlling the virus during the peak of infection. Incorporating data collected and maintained by the g0v community, this study dive into the temporal and spatial properties of the virus in Taipei by utilizing the Hawkes Process model. Three variations of the models are fitted in an attempt to find out the most fitting model for the virus data. In conclusion, we found out that using a normal distribution in modeling time and exponential distribution in distance of event occurrence is a suitable way of modeling the COVID-19 spread in Taipei.