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BACKGROUND: Following the first locally transmitted case in Sukhbaatar soum, Selenge Province, we aimed to investigate the ultimate scale of the epidemic in the scenario of uninterrupted transmission. METHODS: This was a prospective case study following the locally modified WHO FFX cases generic protocol. A rapid response team collected data from November 14 to 29, 2020. We created a stochastic process to draw many transmission chains from this greater distribution to better understand and make inferences regarding the outbreak under investigation. RESULTS: The majority of the cases involved household transmissions (35, 52.2%), work transmissions (20, 29.9%), index (5, 7.5%), same apartment transmissions (2, 3.0%), school transmissions (2, 3.0%), and random contacts between individuals transmissions (1, 1.5%). The posterior means of the basic reproduction number of both the asymptomatic cases R 0 Asy $$ {R}_0^{Asy} $$ and the presymptomatic cases R 0 Pre $$ {R}_0^{Pre} $$ (1.35 [95% CrI 0.88-1.86] and 1.29 [95% CrI 0.67-2.10], respectively) were lower than that of the symptomatic cases (2.00 [95% Crl 1.38-2.76]). CONCLUSION: Our study highlights the heterogeneity of COVID-19 transmission across different symptom statuses and underscores the importance of early identification and isolation of symptomatic cases in disease control. Our approach, which combines detailed contact tracing data with advanced statistical methods, can be applied to other infectious diseases, facilitating a more nuanced understanding of disease transmission dynamics.

Statistical classification of texts often use dimension-reduction techniques to reduce the number of features in the classification model. However, this often has the consequences of making inputs difficult for humans to decipher. In this thesis, I propose and algorithm using topic modeling as an interpretable dimension-reduction technique for text classification. I apply the algorithm in the context of nationalized campaign rhetoric amongst gubernatorial candidates in U.S. politics, finding such candidates largely speak about issues germane to their jurisdictions.

The short satellite-observed period from 1979 to 2023 has seen the Antarctic sea ice changedramatically. The sea ice generally increased until 2014 then precipitously decreased from 2014 to 2017. Record lows were then observed in February 2022 and February 2023. To evaluate these recent changes in the context of anthropogenic climate change requires information on Antarctic sea ice variability over the full 20th century. However, only temporally and spatially sparse data are available before 1979, creating a need for statistical reconstructions. We create a stochastic ensemble reconstruction of monthly Antarctic sea ice extent from 1900-1979 using a novel Bayesian spatio-temporal model. This model produces a set of 2500 plausible reconstructions of sea ice extent by sector. These reconstructions improve on prior approaches with realistic month-to-month changes and interdecadal trends as well as plausible interactions between the sectors. These unique features allow the direct computation of extreme event probabilities for the pre-satellite period of the 20th century. For example, we compute a 0.44% probability of reconstructing a decline in total Antarctic sea ice extent as extreme or more extreme than the 2014-2017 decline. We compute a 16% probability of observing a sea ice minimum as low or lower than the February 2022 minimum in total sea ice extent of 2.22 mio. km2, and a probability of 4% for the February 2023 minimum of 2.04 mio. km2. We also propose a novel approach to modeling the Antarctic sea ice edge using a functional regression model. The sea ice edge on a given day is treated as a continuous set of points circling the South Pole and the latitudes of these points are modeled as a function of their longitude. This enables the estimation and visualization of a circumpolar annual cycle and interannual development of the sea ice, providing novel insight into the regionality of sea ice variability. We develop statistical techniques for reconstructing 1966-1

Networked populations consist of inhomogeneous individuals connected via relational ties. The individuals typically vary in multivariate attributes. In some cases primary interest focuses on individual attributes and in others the understanding of the social structure of the ties. In many circumstances both are of interest, as is their relationship. In this paper we consider this last, most general, case. We model the joint distribution of social ties and individual attributes when the population is only partially observed. Of central interest is when the population is surveyed using a network sampling design. A second situation is when data about a subset of the ties and/or the individual attributes is unintentionally missing. Exponential-family random network models (ERNM)s are capable of specifying a joint statistical representation of both the ties of a network and individual attributes. This class of models allow the nodal attributes to be modeled as stochastic processes, expanding the range and realism of exponential-family approaches to network modeling. In this paper we develop a theory of inference for ERNMs when only part of the network is observed, as well as specific methodology for partially observed networks, including non-ignorable mechanisms for network-based sampling designs. In particular, we consider data collected via contact tracing, of considerable importance to infectious disease epidemiology and public health.

Relative Distributions and Optimal Transport are versatile and widely used tools across various industries and fields. Relative Distributions are adept at gauging the disparities in ratios between two distributions. At the same time, Optimal Transport provides a deep understanding of the differences between distributions based on the amount of mass required to equalize them. Individuals have made past efforts to incorporate specific techniques into already established models for Statistics, Machine Learning, and Artificial Intelligence. Thus far, there has been an absence of any conclusive correlation between these two domains despite multiple individual endeavors. We have linked Relative Distributions with Optimal Transport, using various distributions to analyze distribution variation precisely. When dealing with Relative Distributions, our one-to-one distributions become Uniform, and the Optimal Transport method generates a Matrix that indicates how these inequalities should be adjusted. Our research indicates that our model may surpass other commonly used models, potentially promoting the implementation of similar approaches across multiple fields.

The structure of many complex social networks is determined by nodal and dyadic covariates that are endogenous to the tie variables. While exponential-family random graph models (ERGMs) have been very successful in modeling social networks with exogenous covariates, they are often misspecified for networks where some covariates are stochastic. Exponential-family random network models (ERNMs) are an extension of ERGM that retain the desirable properties of ERGM, but allow the joint modeling of tie variables and covariates. We compare ERGM to ERNM to show how conclusions of ERGM modeling are improved by consideration of the ERNM framework. In particular, ERNM simultaneously represents the effects of social influence and social selection processes while commonly used models do not. We also look into the latent class models for group clustering problems in social network. The random nodal attributes can be observed or latent in ERNM. When the attributes is treated as latent, we can investigate the probability of cluster group. Stochastic Block Models are a well-known statistical models for group classification, however, they rely on the relational data and omit the nodal characteristics. We compare these two models and provide a case study to illustrate the main points.

We introduce the relative distribution as a tool in Bayesian analysis to compare the posteriorto the prior distribution. Two interpretations are given: one as a density ratio, and another as a reparametrized likelihood. Several important properties are reviewed, as well as notes on usage and connections to information theory and relative surprise inference. Explicit examples and derivations for several common models are given. The relative distribution focuses on the effect of the data and the resulting differences between the posterior and prior, emphasizing the role of the likelihood in connecting the two.

PURPOSE: Digital methods to augment traditional contact tracing approaches were developed and deployed globally during the COVID-19 pandemic. These Exposure Notification (EN) systems present new opportunities to support public health interventions. To date, there have been attempts to model the impact of such systems, yet no reports have explored the value of real-time system data for predictive epidemiological modeling. METHODS: We investigated the potential to short-term forecast COVID-19 caseloads using data from Californias implementation of the Google Apple Exposure Notification (GAEN) platform, branded as CA Notify. CA Notify is a digital public health intervention leveraging residents smartphones for anonymous EN. We extended a published statistical model that uses prior case counts to investigate the possibility of predicting short-term future case counts and then added EN activity to test for improved forecast performance. Additional predictive value was assessed by comparing the pandemic forecasting models with and without EN activity to the actual reported caseloads from 1-7 days in the future. RESULTS: Observation of time series presents noticeable evidence for temporal association of system activity and caseloads. Incorporating earlier ENs in our model improved prediction of the caseload counts. Using Bayesian inference, we found nonzero influence of EN terms with probability one. Furthermore, we found a reduction in both the mean absolute percentage error and the mean squared prediction error, the latter of at least 5% and up to 32% when using ENs over the model without. CONCLUSIONS: This preliminary investigation suggests smartphone based ENs can significantly improve the accuracy of short-term forecasting. These predictive models can be readily deployed as local early warning systems to triage resources and interventions.

In this thesis, we aimed to obtain a better understanding of the public and private Twitter/Xpersonas of a professional basketball team (the 2022-2023 NBA Spurs). We used the data to form a social network and utilized statistical network analysis methodology to study our data. We studied this network to understand how an average NBA team’s players represent themselves to the public as opposed to studying the top teams/players in the NBA. We found that stochastic block models group the players correctly into two groups but mishandles the classification of some players due to their network structure. Analysis with Exponential- family random graph models (ERGMs) reinforce the idea that players often tend to keep their social media presence professional. Players also rated higher on an ESPN metric of performance tended to be more involved with social media.

Many social processes studied by demographers can be viewed as two-sided matching markets. For example, heterosexual marriages, job searching, and residency assignments for medical school graduates all require members of two disjoint groups to mutually consent to form a relationship, or ``match.'' Yet the underlying mechanisms dictating such processes are often opaque. Demographers require statistical models for partnership formation that separate the underlying preferences individuals have for various types of partners from the availability of such partners.To address this need, in my dissertation I develop a revealed preferences model (RPM) which captures the complex interplay between discrete characteristics, both observed and unobserved, of individuals and the availabilities of potential partners to form a stable set of partnerships in networks of different sizes. The major contribution of this work is the introduction of a model that not only estimates partnership outcomes in a two-sided matching market, but also is flexible enough to handle realistic data drawn from various sampling schemes and population types.Contextualizing the problem in the heterosexual marriage market setting, in the first two chapters I present background information on the two-sided matching market problem and and introduce the revealed preferences model novel statistical methodology to compute point estimates for preferences parameters. I validate the approaches with multiple simulation studies and demonstrate RPM’s key novel contribution, the ability to recover societal preferences for partners independent of the types of partners available. I additionally use these simulation studies to conduct a comprehensive study of model performance under different conditions, such as varying population and sample sizes and different sampling schemes. To facilitate the use of the model in practical settings, I propose additional novel tools such as bootstrap procedures for bias-correcting parame

The rapid rate of improvement of natural language processing (NLP) systems and large language models (LLMs) begets a wide array of applications in the field of education and classroom instruction. The possibility of individualized practice and immediate student feedback from a low-cost and widely-available service has an enormous capacity to change modes of student instruction. In this review, we discuss the current state of research into the applications of LLMs for science and mathematics classroom education, calling particular attention to concerns surrounding overreliance and equity, as well as suggesting specific directions for future study. We conclude by considering the CourseKata interactive textbook as an illustration of how AI tools may begin to reshape traditional methods of content delivery.

We revisit a novel causal model published in Demography by Hicks et al. (2018), designed to assess whether exposure to neighborhood disadvantage over time affects children's reading and math skills. Here, we provide corrected and new results. Reconsideration of the model in the original article raised concerns about bias due to exposure-induced confounding (i.e., past exposures directly affecting future exposures) and true state dependence (i.e., past exposures affecting confounders of future exposures). Through simulation, we show that our originally proposed propensity function approach displays modest bias due to exposure-induced confounding but no bias from true state dependence. We suggest a correction based on residualized values and show that this new approach corrects for the observed bias. We contrast this revised method with other causal modeling approaches using simulation. Finally, we reproduce the substantive models from Hicks et al. (2018) using the new residuals-based adjustment procedure. With the correction, our findings are essentially identical to those reported originally. We end with some conclusions regarding approaches to causal modeling.

We revisit a novel causal model published in Demography by Hicks et al. (2018), designed to assess whether exposure to neighborhood disadvantage over time affects children's reading and math skills. Here, we provide corrected and new results. Reconsideration of the model in the original article raised concerns about bias due to exposure-induced confounding (i.e., past exposures directly affecting future exposures) and true state dependence (i.e., past exposures affecting confounders of future exposures). Through simulation, we show that our originally proposed propensity function approach displays modest bias due to exposure-induced confounding but no bias from true state dependence. We suggest a correction based on residualized values and show that this new approach corrects for the observed bias. We contrast this revised method with other causal modeling approaches using simulation. Finally, we reproduce the substantive models from Hicks et al. (2018) using the new residuals-based adjustment procedure. With the correction, our findings are essentially identical to those reported originally. We end with some conclusions regarding approaches to causal modeling.

The total Antarctic sea ice extent (SIE) experiences a distinct annual cycle, peaking in September and reaching its minimum in February. In this paper we propose a mathematical and statistical decomposition of this temporal variation in SIE. Each component is interpretable and, when combined, gives a complete picture of the variation in the sea ice. We consider timescales varying from the instantaneous and not previously defined to the multi-decadal curvilinear trend, the longest. Because our representation is daily, these timescales of variability give precise information about the timing and rates of advance and retreat of the ice and may be used to diagnose physical contributors to variability in the sea ice. We define a number of annual cycles each capturing different components of variation, especially the yearly amplitude and phase that are major contributors to SIE variation. Using daily sea ice concentration data, we show that our proposed invariant annual cycle explains 29 % more of the variation in daily SIE than the traditional method. The proposed annual cycle that incorporates amplitude and phase variation explains 77 % more variation than the traditional method. The variation in phase explains more of the variability in SIE than the amplitude. Using our methodology, we show that the anomalous decay of sea ice in 2016 was associated largely with a change of phase rather than amplitude. We show that the long term trend in Antarctic sea ice extent is strongly curvilinear and the reported positive linear trend is small and dependent strongly on a positive trend that began around 2011 and continued until 2016.

Building an intelligent robot that is capable of collaborating with humans in daily tasks is a challenging problem. Although recent artificial intelligence research shows remarkable results in classical tasks, there is still a long way to achieve human-level intelligent robots. We need to start developing methods in terms of perception, learning, reasoning, and planning. In this dissertation, we study multi-modal robotic learning, reasoning, and planning from three different perspectives: (i) robot imitation learning: we first introduce a series of works including hardware prototype, data collection, modeling human demonstration, and planning for robot imitation learning. (ii) multi-modal reasoning: we study multi-modal reasoning in two different tasks. We develop a dataset and models for visual abstraction reasoning with human IQ test. Additionally, we propose a visual language reasoning method for outside knowledge visual question answering. (iii) robot planning: we show our attempts in robot planning. We introduce a physically realistic virtual testbed where robots can interact with humans. In addition, we show a hierarchical reinforcement learning method for robot planning.

In demographic studies, the latent preferences for partners during a partnership formation process has long been a crucial problem. However, in practical setting, individuals are usu- ally only aware of a certain subset of potential partners, and these should be separated from preferences when modelling this matching process. In this thesis, we address this issue by constructing an awareness model for matching where individuals are aware of a subset of po- tential partners, and have nontransferable utilities for them based on certain characteristics. We extend Goyal et al.’s framework (2022) to estimate preference and awareness parame- ters, where awareness parameters are estimated based on continuous covariates. We conduct simulation studies in multiple theoretical scenarios to show that under various settings, the model accurately recovers preference and awareness parameters. We also conduct a case study based on recent marriages observed in the 2019 American Community Survey (ACS) data.

Prior research in the area of housing policy has shown that rental prices collected from the US government surveys do not reflect the market rental prices that are paid by new rent seekers. This paper is motivated by previous studies, where researchers have particularly criticized the American Community Survey (ACS) conducted by the US Census Bureau for heavily underestimating the market price of rental housing units. It collects rental data for Los Angeles County web scraped from Craigslist, a popular online marketplace, as an estimate for the current rental market. It then compares the distribution of that data with rental prices collected by the ACS. The results confirm previous findings since rental prices collected from the ACS are significantly lower than Craigslist. In addition, the rental data from Craigslist show a clear effect caused by the COVID-19 pandemic, which is not present in the ACS data.

This dissertation considers credible models for social network data. In the classical socialnetwork analysis setting, nodes are connected to each other with the connections between the nodes stochastic and interdependent. As a result social network modeling has a sample size of one, where each network observed must be regarded as a single realization of a stochastic process. I consider three distinct but related topics in this field in each of the chapters.I first consider the Latent Order Logistic (LOLOG) model, a recently proposed model classfor social network modeling. I take the data centric viewpoint, that is, how does the LOLOG model perform in terms of fit, qualitative interpretation and scientific conclusions on data that practitioners fit with commonly used exponential-family random graph models (ERGM).I also propose a method for Bayesian inference for the LOLOG model. This method alsoyields insight into the posterior distribution of the latent edge ordering, which is fundamental to the LOLOG model. This approach allows for deeper insight into the LOLOG process, as well as insight into the reasons for LOLOG’s desirable properties for social network analysis.The final chapter of the thesis considers a separate topic. I consider an approach for causalinference with observational data in a network setting. Current approaches assume the network is observed and exogenous. The main contribution of this chapter is to regard the edges and nodal covariates as jointly distributed in a causal model. We consider the causal structure of this problem, and provide an extension to current approaches to account for this . Throughout this dissertation, I use real-data networks to demonstrate the ideas and methodology. Examples include the National Longitudinal Study of Adolescent to Adult Health and a well known network of New England Lawyers.

This dissertation considers credible models for social network data. In the classical socialnetwork analysis setting, nodes are connected to each other with the connections between the nodes stochastic and interdependent. As a result social network modeling has a sample size of one, where each network observed must be regarded as a single realization of a stochastic process. I consider three distinct but related topics in this field in each of the chapters.I first consider the Latent Order Logistic (LOLOG) model, a recently proposed model classfor social network modeling. I take the data centric viewpoint, that is, how does the LOLOG model perform in terms of fit, qualitative interpretation and scientific conclusions on data that practitioners fit with commonly used exponential-family random graph models (ERGM).I also propose a method for Bayesian inference for the LOLOG model. This method alsoyields insight into the posterior distribution of the latent edge ordering, which is fundamental to the LOLOG model. This approach allows for deeper insight into the LOLOG process, as well as insight into the reasons for LOLOG’s desirable properties for social network analysis.The final chapter of the thesis considers a separate topic. I consider an approach for causalinference with observational data in a network setting. Current approaches assume the network is observed and exogenous. The main contribution of this chapter is to regard the edges and nodal covariates as jointly distributed in a causal model. We consider the causal structure of this problem, and provide an extension to current approaches to account for this . Throughout this dissertation, I use real-data networks to demonstrate the ideas and methodology. Examples include the National Longitudinal Study of Adolescent to Adult Health and a well known network of New England Lawyers.

Prior research in the area of housing policy has shown that rental prices collected from the US government surveys do not reflect the market rental prices that are paid by new rent seekers. This paper is motivated by previous studies, where researchers have particularly criticized the American Community Survey (ACS) conducted by the US Census Bureau for heavily underestimating the market price of rental housing units. It collects rental data for Los Angeles County web scraped from Craigslist, a popular online marketplace, as an estimate for the current rental market. It then compares the distribution of that data with rental prices collected by the ACS. The results confirm previous findings since rental prices collected from the ACS are significantly lower than Craigslist. In addition, the rental data from Craigslist show a clear effect caused by the COVID-19 pandemic, which is not present in the ACS data.

In demographic studies, the latent preferences for partners during a partnership formation process has long been a crucial problem. However, in practical setting, individuals are usu- ally only aware of a certain subset of potential partners, and these should be separated from preferences when modelling this matching process. In this thesis, we address this issue by constructing an awareness model for matching where individuals are aware of a subset of po- tential partners, and have nontransferable utilities for them based on certain characteristics. We extend Goyal et al.’s framework (2022) to estimate preference and awareness parame- ters, where awareness parameters are estimated based on continuous covariates. We conduct simulation studies in multiple theoretical scenarios to show that under various settings, the model accurately recovers preference and awareness parameters. We also conduct a case study based on recent marriages observed in the 2019 American Community Survey (ACS) data.

ProblemQuantifying mortality from coronavirus disease (COVID-19) is difficult, especially in countries with limited resources. Comparing mortality data between countries is also challenging, owing to differences in methods for reporting mortality.ContextTracking all-cause mortality (ACM) and comparing it with expected ACM from pre-pandemic data can provide an estimate of the overall burden of mortality related to the COVID-19 pandemic and support public health decision-making. This study validated an ACM calculator to estimate excess mortality during the COVID-19 pandemic.ActionThe ACM calculator was developed as a tool for computing expected ACM and excess mortality at national and subnational levels. It was developed using R statistical software, was based on a previously described model that used non-parametric negative binomial regression and was piloted in several countries. Goodness-of-fit was validated by forecasting 2019 mortality from 2015-2018 data.OutcomeThree key lessons were identified from piloting the tool: using the calculator to compare reported provisional ACM with expected ACM can avoid potential false conclusions from comparing with historical averages alone; using disaggregated data at the subnational level can detect excess mortality by avoiding dilution of total numbers at the national level; and interpretation of results should consider system-related performance indicators.DiscussionTimely tracking of ACM to estimate excess mortality is important for the response to COVID-19. The calculator can provide countries with a way to analyse and visualize ACM and excess mortality at national and subnational levels.

Exponential-family Random Graph models (ERGM) are widely used in social network analysis when modelling data on the relations between actors. ERGMs are typically interpreted as a snapshot of a network at a given point in time or in a final state. The recently proposed Latent Order Logistic model (LOLOG) directly allows for a latent network formation process. We assess the real-world performance of these models when applied to typical networks modelled by researchers. Specifically, we model data from an ensemble of articles in the journal Social Networks with published ERGM fits, and compare the ERGM fit to a comparable LOLOG fit. We demonstrate that the LOLOG models are, in general, in qualitative agreement with the ERGM models, and provide at least as good a model fit. In addition they are typically faster and easier to fit to data, without the tendency for degeneracy that plagues ERGMs. Our results support the general use of LOLOG models in circumstances where ERGMs are considered.

Building an intelligent robot that is capable of collaborating with humans in daily tasks is a challenging problem. Although recent artificial intelligence research shows remarkable results in classical tasks, there is still a long way to achieve human-level intelligent robots. We need to start developing methods in terms of perception, learning, reasoning, and planning. In this dissertation, we study multi-modal robotic learning, reasoning, and planning from three different perspectives: (i) robot imitation learning: we first introduce a series of works including hardware prototype, data collection, modeling human demonstration, and planning for robot imitation learning. (ii) multi-modal reasoning: we study multi-modal reasoning in two different tasks. We develop a dataset and models for visual abstraction reasoning with human IQ test. Additionally, we propose a visual language reasoning method for outside knowledge visual question answering. (iii) robot planning: we show our attempts in robot planning. We introduce a physically realistic virtual testbed where robots can interact with humans. In addition, we show a hierarchical reinforcement learning method for robot planning.

The total Antarctic sea ice extent (SIE) experiences a distinct annual cycle, peaking in September and troughing in March. In this paper we propose a mathematical and statistical decomposition of this temporal variation in SIE. Each component is interpretable and, when combined, give a complete picture of the variation of the sea ice. We consider time scales varying from the instantaneous, and not previously defined, to the multidecadal curvilinear trend, the longest. Because our representation is daily, these timescales of variability give precise information about the timing and rates of advance and retreat of the ice and may be used to diagnose physical contributors to variability in the sea ice. We define a number of annual cycles each capturing different components of variation, especially the yearly amplitude and phase that are major contributors to SIE variation. Using daily sea ice concentration data, we show that our proposed invariant annual cycle explains 29 % more of the variation of daily SIE than the traditional method. The proposed annual cycle that incorporates amplitude and phase variation explains 77 % more variation than the traditional method. The variation in phase explains more of the variability in SIE than the amplitude. Using our methodology, we show that the anomalous decay of sea ice in 2016 was associated largely with a change of phase rather than amplitude. We show that the long term trend in Antarctic sea ice extent is strongly curvilinear and the reported positive linear trend is small and dependent strongly on a positive trend that began around 2011 and continued until 2016.

The total Antarctic sea ice extent (SIE) experiences a distinct annual cycle, peaking in September and troughing in March. In this paper we propose a mathematical and statistical decomposition of this temporal variation in SIE. Each component is interpretable and, when combined, give a complete picture of the variation of the sea ice. We consider time scales varying from the instantaneous, and not previously defined, to the multidecadal curvilinear trend, the longest. Because our representation is daily, these timescales of variability give precise information about the timing and rates of advance and retreat of the ice and may be used to diagnose physical contributors to variability in the sea ice. We define a number of annual cycles each capturing different components of variation, especially the yearly amplitude and phase that are major contributors to SIE variation. Using daily sea ice concentration data, we show that our proposed invariant annual cycle explains 29 % more of the variation of daily SIE than the traditional method. The proposed annual cycle that incorporates amplitude and phase variation explains 77 % more variation than the traditional method. The variation in phase explains more of the variability in SIE than the amplitude. Using our methodology, we show that the anomalous decay of sea ice in 2016 was associated largely with a change of phase rather than amplitude. We show that the long term trend in Antarctic sea ice extent is strongly curvilinear and the reported positive linear trend is small and dependent strongly on a positive trend that began around 2011 and continued until 2016.

As a result of today's massive information overload, the exploration and development of recommender systems is burgeoning. This paper consists of a comprehensive literature review in which the current knowledge surrounding statistical methods for recommender systems is outlined and evaluated. For each method, the theoretical premise and application-related aspects such as optimal use cases and common research problems are described. To round out the literature review, an implementation of several collaborative filtering techniques is conducted in order to apply the discussed theory and identify some advantages and disadvantages of the methods.

To justify the credibility of their causal designs, researchers are increasingly reporting the results of falsification analyses on the observable implications of their necessary causal assumptions. Traditional hypothesis testing procedures for these purposes are improperly formulated, therefore this work contributes to the growing body of research promoting equivalence-based tests for the falsification of causal assumptions (e.g. Hartman and Hidalgo, 2018; Hartman, 2020; Bilinski and Hatfield, 2018). To this end, I first present an empirical application with an emphasis on falsification testing (Chapter 2). In this chapter, augmented synthetic control methods are used to estimate the causal effect of a Los Angeles police reform policy, supplemented with falsification analyses to both strengthen the credibility of the design decisions and contextualize the significance of the results in context.The remainder of this work proposes equivalence-based tests. Chapter 3 develops an equivalence test for conditional independence hypotheses, paying particular attention to the interpretability and specification of the necessary equivalence range. Many causal designs require the conditional ignorability assumption, and thus balance testing is proposed as an application of this method. Chapter 4 takes a broader view of causal assumption evaluation. For a suite of common causal designs (selection on observables, mediation, difference-in-differences, regression discontinuity, synthetic control, and instrumental variables), I map the necessary causal assumptions to the testable observable implications, ultimately contrasting traditional falsification approaches to proposed equivalence-based alternatives. To conclude, Chapter 5 discusses the implications and limitations of this work with an emphasis on open questions in causal assumption evaluation.

Landfast sea ice (fast ice) is an important though poorly-understood component of the cryosphere on the Antarctic continental shelf, where it plays a key role in atmosphere-ocean-ice sheet interaction and coupled ecological and biogeochemical processes. Here, we present a first in-depth baseline analysis of variability and change in circum-Antarctic fast-ice distribution (including its relationship to bathymetry), based on a new high-resolution satellite-derived time series for the period 2000 to 2018. This reveals a) an overall trend of −882 ± 824 km²/y (−0.19 ± 0.18 %/y); and b) eight distinct regions in terms of fast-ice coverage and modes of formation. Of these, four exhibit positive trends over the 18 y period and four negative. Positive trends are seen in East Antarctica and in the Bellingshausen sea, with this region claiming the largest positive trend of +1,198 ± 359 km²/y (+1.10 ± 0.35 %/y). The four negative trends predominantly occur in West Antarctica, with the largest negative trend of −1,206 ± 277 km²/y (−1.78 ± 0.41 %/y) occurring in the Victoria and Oates Lands region in the eastern Ross Sea. All trends are significant. This new baseline analysis represents a significant advance in our knowledge of the current state of both the global cryosphere and the complex Antarctic coastal system that is vulnerable to climate variability and change. It will also inform a wide range of other studies.

Landfast sea ice (fast ice) is an important though poorly understood component of the cryosphere on the Antarctic continental shelf, where it plays a key role in atmosphere–ocean–ice-sheet interaction and coupled ecological and biogeochemical processes. Here, we present a first in-depth baseline analysis of variability and change in circum-Antarctic fast-ice distribution (including its relationship to bathymetry), based on a new high-resolution satellite-derived time series for the period 2000 to 2018. This reveals (a) an overall trend of -882±824 km2 yr−1 (-0.19±0.18 % yr−1) and (b) eight distinct regions in terms of fast-ice coverage and modes of formation. Of these, four exhibit positive trends over the 18-year period and four negative. Positive trends are seen in East Antarctica and in the Bellingshausen Sea, with this region claiming the largest positive trend of +1198±359 km2 yr−1 (+1.10±0.35 % yr−1). The four negative trends predominantly occur in West Antarctica, with the largest negative trend of -1206±277 km2 yr−1 (-1.78±0.41 % yr−1) occurring in the Victoria and Oates Land region in the western Ross Sea. All trends are significant. This new baseline analysis represents a significant advance in our knowledge of the current state of both the global cryosphere and the complex Antarctic coastal system, which are vulnerable to climate variability and change. It will also inform a wide range of other studies.

As a result of today's massive information overload, the exploration and development of recommender systems is burgeoning. This paper consists of a comprehensive literature review in which the current knowledge surrounding statistical methods for recommender systems is outlined and evaluated. For each method, the theoretical premise and application-related aspects such as optimal use cases and common research problems are described. To round out the literature review, an implementation of several collaborative filtering techniques is conducted in order to apply the discussed theory and identify some advantages and disadvantages of the methods.

To justify the credibility of their causal designs, researchers are increasingly reporting the results of falsification analyses on the observable implications of their necessary causal assumptions. Traditional hypothesis testing procedures for these purposes are improperly formulated, therefore this work contributes to the growing body of research promoting equivalence-based tests for the falsification of causal assumptions (e.g. Hartman and Hidalgo, 2018; Hartman, 2020; Bilinski and Hatfield, 2018). To this end, I first present an empirical application with an emphasis on falsification testing (Chapter 2). In this chapter, augmented synthetic control methods are used to estimate the causal effect of a Los Angeles police reform policy, supplemented with falsification analyses to both strengthen the credibility of the design decisions and contextualize the significance of the results in context.The remainder of this work proposes equivalence-based tests. Chapter 3 develops an equivalence test for conditional independence hypotheses, paying particular attention to the interpretability and specification of the necessary equivalence range. Many causal designs require the conditional ignorability assumption, and thus balance testing is proposed as an application of this method. Chapter 4 takes a broader view of causal assumption evaluation. For a suite of common causal designs (selection on observables, mediation, difference-in-differences, regression discontinuity, synthetic control, and instrumental variables), I map the necessary causal assumptions to the testable observable implications, ultimately contrasting traditional falsification approaches to proposed equivalence-based alternatives. To conclude, Chapter 5 discusses the implications and limitations of this work with an emphasis on open questions in causal assumption evaluation.

Landfast sea ice (fast ice) is an important though poorly-understood component of the cryosphere on the Antarctic continental shelf, where it plays a key role in atmosphere-ocean-ice sheet interaction and coupled ecological and biogeochemical processes. Here, we present a first in-depth baseline analysis of variability and change in circum-Antarctic fast-ice distribution (including its relationship to bathymetry), based on a new high-resolution satellite-derived time series for the period 2000 to 2018. This reveals a) an overall trend of −882 ± 824 km²/y (−0.19 ± 0.18 %/y); and b) eight distinct regions in terms of fast-ice coverage and modes of formation. Of these, four exhibit positive trends over the 18 y period and four negative. Positive trends are seen in East Antarctica and in the Bellingshausen sea, with this region claiming the largest positive trend of +1,198 ± 359 km²/y (+1.10 ± 0.35 %/y). The four negative trends predominantly occur in West Antarctica, with the largest negative trend of −1,206 ± 277 km²/y (−1.78 ± 0.41 %/y) occurring in the Victoria and Oates Lands region in the eastern Ross Sea. All trends are significant. This new baseline analysis represents a significant advance in our knowledge of the current state of both the global cryosphere and the complex Antarctic coastal system that is vulnerable to climate variability and change. It will also inform a wide range of other studies.

As technology advances, the manner in which humans communicate and collaborate becomes increasingly intricate and the study of complex networks becomes ever important. Exponential-family Random Graph Models (ERGMs) have long been at the forefront of the analysis of relational data due to their interpretability, flexibility, and strong theoretical foundation. However, ERGMs sometimes suffer from a serious condition known as degeneracy, in which the model exhibits unrealistic behavior or a severe lack-of-fit to the observed data if it can even be fit at all.In an effort to overcome the issue of degeneracy, we take a variety of new approaches to network modeling and also build on the existing work of Fellows and Handcock (2017). We first consider several alternative models motivated by the maximization of various entropies or minimization of different divergence measures, as well as hierarchical models which expand on the ERG model. We derive their degenerate-inhibiting properties, but our analysis shows them ineffective for many purposes. Next, we provide an in-depth investigation of the Tapered ERGM and offer solutions to some related open questions, such as which terms to taper and how much. Several case studies are presented showing the effectiveness of the Tapered model and we derive some theoretical results. We also show, both theoretically and empirically, that the natural parameter estimates are largely numerically unaffected by the amount of tapering. We then extend the ideas behind the Tapered ERGM and generalize it as member of a class of so-called Restorative Force Models (RFMs), which disallow degeneracy through various constraints. A treatment of this general class of models is conducted, and we examine the properties of several types of RFMs such as the Stereo ERGM, MAD ERGM, and LogCosh ERGM.

International political relations are hard to characterize, as they depend on the network of state relationships. Important political alliances between two countries are often made with the help of other countries, international conflicts often require mediation, efforts of countries to tackle complex issues often require coordination of many states. Hence, it is important to gauge the network structure of international relations when accessing relation between any pair of countries. Many current approaches rely on existing alliances or conflicts to characterize government-to-government interactions at a given point in time, but these are often the outcomes of ongoing negotiations or mounting conflicts, and thus are more likely to characterize past relations, rather than relations of the current period. In recent years, the availability of data capturing day-to-day interactions of countries has increased dramatically, greatly increasing the number of dimensions to be captured, and providing scholars with an opportunity to explore the network of smaller-scale country-to-country interactions. This thesis proposes a way to characterise state-to-state relations in a context of the whole network of international relations in a given year applying latent network approach proposed by Hoff, Raftery and Handcock (2002) to summarized Integrated Crisis Early Warning System (ICEWS) events dataset. Under the latent space framework the probability (magnitude) of a relation between countries depends on the positions of countries in an unobserved "social space." These positions are estimated within a Bayesian framework, using Markov chain Monte Carlo procedures to infer latent positions. I validate the resulting measure of government-to-government relations by demonstrating that they are strong predictors of international trade, outperforming the most commonly used measured of state relations, known as the S-Score.

The exponential random graph models are a family of statistical models that are often used for analyzing networks. The most common method of simulating networks from these models is using the Metropolis-Hastings algorithm. However, the Metropolis-Hastings algorithm has certain disadvantages such as long mixing times and issues of degeneracy. As a result, the goal of this paper is to look for an alternative method of simulating networks from exponential random graph models that can improve upon the drawbacks of the Metropolis-Hastings algorithm. The three alternative methods explored in this paper are the Swendsen-Wang algorithm, the Gibbs sampler with Swendsen-Wang algorithm, and the iterative sampling with spectral clustering algorithm. Out of these three, the iterative sampling with spectral clustering ultimately proved to be the most viable algorithm. The rest of the paper focuses on analyzing the network simulations generated using this method.