This thesis studies four independent resource allocation problems with different assumptions on information available to the central planner, and strategic considerations of the agents present in the system. We start off with an online, non-strategic agents setting in Chapter 1, where we study the dynamic pricing and learning problem under the Bass demand model. The main objective in the field of dynamic pricing and learning is to study how a seller can maximize revenue by adjusting price over time based on sequentially realized demand. Unlike most existing literature on dynamic pricing and learning, where the price only affects the demand in the current period, under the Bass model, price also influences the future evolution of demand. Finding arevenue-maximizing dynamic pricing policy in this model is non-trivial even in the full information case, where model parameters are known. We consider the more challenging incomplete information problem where dynamic pricing is applied in conjunction with learning the unknown model parameters, with the objective of optimizing the cumulative revenues over a given selling horizon of length 𝑻. Our main contribution is an algorithm that satisfies a high probability regret guarantee of order 𝑚²/³; where the market size 𝑚 is known a priori. Moreover, we show that no algorithm can incur smaller order of loss by deriving a matching lower bound. We then switch our attention to a single round, strategic agents setting in Chapter 2, where we study a multi-resource allocation problem with heterogeneous demands and Leontief utilities. Leontief utility function captures the idea that for certain resource allocation settings, the utility of marginal increase in one resource depends on the availabilities of other resources. We generalize the existing literature on this model formulation to incorporate more constraints faced in real applications, which in turn requires new algorithm design and analysis techniques. The main contribution of this chapter is an allocation algorithm that satisfies Pareto optimality, envy-freenss, strategy-proofness, and a notion of sharing incentive. In Chapter 3, we study a single round, non-strategic agent setting, where the central planner tries to allocate a pool of items to a set of agents who each has to receive a prespecified fraction of all items. Additionally, we want to ensure fairness by controlling the amount of envy that agents have with the final allocations. We make the observation that this resource allocation setting can be formulated as an Optimal Transport problem, and that the solution structure displays a surprisingly simple structure. Using this insight, we are able to design an allocation algorithm that achieves the optimal trade-off between efficiency and envy. Finally, in Chapter 4 we study an online, strategic agent setting, where similar to the previous chapter, the central planner needs to allocate a pool of items to a set of agents who each has to receive a prespecified fraction of all items. Unlike in the previous chapter, the central planner has no a priori information on the distribution of items. Instead, the central planner needs to implicitly learn these distributions from the observed values in order to pick a good allocation policy. Additionally, an added challenge here is that the agents are strategic with incentives to misreport their valuations in order to receive better allocations. This sets our work apart both from the online auction mechanism design settings which typically assume known valuation distributions and/or involve payments, and from the online learning settings that do not consider strategic agents. To that end, our main contribution is an online learning based allocation mechanism that is approximately Bayesian incentive compatible, and when all agents are truthful, guarantees a sublinear regret for individual agents' utility compared to that under the optimal offline allocation policy.

This thesis considers two related problems that has application in the field of experimental design for clinical trials: • fixed sample size determination for parallel arm, double-blind survival data analysis to test the hypothesis of no difference in survival functions, and • blinded sample size re-estimation for the same. For the first problem of fixed sample size determination, a method is developed generally for testing of hypothesis, then applied particularly to survival analysis; for the second problem of blinded sample size re-estimation, a method is developed specifically for survival analysis. In both problems, the exponential survival model is assumed. The approach we propose for sample size determination is Bayesian decision theoretical, using explicitly a loss function and a prior distribution. The loss function used is the intrinsic discrepancy loss function introduced by Bernardo and Rueda (2002), and further expounded upon in Bernardo (2011). We use a conjugate prior, and investigate the sensitivity of the calculated sample sizes to specification of the hyper-parameters. For the second problem of blinded sample size re-estimation, we use prior predictive distributions to facilitate calculation of the interim test statistic in a blinded manner while controlling the Type I error. The determination of the test statistic in a blinded manner continues to be nettling problem for researchers. The first problem is typical of traditional experimental designs, while the second problem extends into the realm of adaptive designs. To the best of our knowledge, the approaches we suggest for both problems have never been done hitherto, and extend the current research on both topics. The advantages of our approach, as far as we see it, are unity and coherence of statistical procedures, systematic and methodical incorporation of prior knowledge, and ease of calculation and interpretation. / Statistics

A model was developed to incorporate the major forces impacting upon a school superintendent and the descriptors, stability measures, intentions and processes of those forces. Tenure was determined to be the best outcome measure, thus the model became a quantitative method for predicting tenure. A survey measuring characteristics of the community, School Board, and the superintendent was sent to superintendents nationwide who had left a superintendency between 1983 and 1985. Usable forms were returned by 835 persons. The regression analysis was significant (p ≤ .0000) and accounted for 40% of the variance in superintendent tenure. In developing the equation, statistical applications included Mallows C_P for subset selection, Rousseeuw’s Least Median of Squares for outlier diagnostics, and the PRESS statistic for validation. The survey also included 24 hypothetical situations randomly selected out of a set of 290 items with four optional courses of action. The answers were weighted by the tenure groups of the superintendents. and the responses analyzed using a Bayesian joint probability formula. Predictions of the most probable tenure based on these items were accurate for only 18% of the superintendents. Variables found to contribute significantly in every candidate equation included per pupil expenditure, recent board member defeat, years in the contract, use of a formal interview format, age, being in the same etlmic group as the community, intention to move to another superintendency, orienting new Board members, salary, enrollment, and Board stability. Variables which were significant in some equations were region of the country, state turnover rate, proportion of Board support, whether changes were expected, use of a regular written evaluation, community power structure, number of Board members, grade levels in the district, gender, and having worked in the same school district. Variables which did not contribute were per capita income, whether the board was elected or appointed, educational degree and type of community. / Ph. D. / incomplete_metadata

This dissertation addresses high-level path planning and cooperative control for autonomous vehicles. The objective of our work is to closely and rigorously incorporate classication and detection performance into path planning algorithms, which is not addressed with typical approaches found in literature. We present novel path planning algorithms for two different applications in which autonomous vehicles are tasked with engaging targets within a stochastic environment. In the first application an autonomous underwater vehicle (AUV) must reacquire and identify clusters of discrete underwater objects. Our planning algorithm ensures that mission objectives are met with a desired probability of success. The utility of our approach is verified through field trials. In the second application, a team of vehicles must intercept mobile targets before the targets enter a specified area. We provide a formal framework for solving the second problem by jointly minimizing a cost function utilizing Bayes risk. / Ph. D.

Financial incentives offered by payers to health care providers and patients have been identified as a key mechanism to lower costs while improving quality of care. How to effectively design incentive programs that can align the varying objectives of health care stakeholders, as well as predict programs' performance and stakeholders' decision response is an unresolved research challenge. The objective of this study is to establish a novel approach based on multiscale decision theory (MSDT) that can effectively model and efficiently analyze such incentive programs, and the complex health care system in general. The MSDT model captures the interdependencies of stakeholders, their decision processes, uncertainties, and how incentives impact decisions and outcomes at the payer, hospital, physician, and patient level. In the first part of this thesis, we study the decision processes of agents pertaining to the investment and utilization of imaging technologies. We analyze the payer-hospital-physician relationships and later extend the model to include radiologist and patient as major stakeholders in the second part of this thesis. We focus on a specific incentive program, the Medicare Shared Savings Program (MSSP) for Accountable Care Organizations (ACOs). The multi-level interactions between agents are mathematically formulated as a sequential non-cooperative game. We derive the equilibrium solutions using the subgame perfect Nash equilibrium (SPNE) concept and the backward induction principle, and determine the conditions under which the MSSP incentive leads to the desired outcomes of cost reduction and quality of care improvements. In the third part of this thesis, we study the multi-level decision making in chronic disease management. We model and analyze patients' and physicians' decision processes as a general-sum stochastic game with perfect information and switching control structure. We incorporate the Health Belief Model (HBM) as the theoretical foundation to capture the behavioral aspect of agents. We analyze how incentives and interdependencies affect patients' engagement in health-promoting activities and physicians' delivery of primary care services. We show that a re-alignment of incentives can improve the effectiveness of chronic disease management. / Ph. D.

One aspect of the algorithmic lens in theoretical computer science is a view on other scientific disciplines that focuses on satisfactory solutions that adhere to real-world constraints, as opposed to solutions that would be optimal ignoring such constraints. The algorithmic lens has provided a unique and important perspective on many academic fields, including molecular biology, ecology, neuroscience, quantum physics, economics, and social science. This thesis applies the algorithmic lens to Bayesian epistemology. Traditional Bayesian epistemology provides a comprehensive framework for how an individual's beliefs should evolve upon receiving new information. However, these methods typically assume an exhaustive model of such information, including the correlation structure between different pieces of evidence. In reality, individuals might lack such an exhaustive model, while still needing to form beliefs. Beyond such informational constraints, an individual may be bounded by limited computation, or by limited communication with agents that have access to information, or by the strategic behavior of such agents. Even when these restrictions prevent the formation of a *perfectly* accurate belief, arriving at a *reasonably* accurate belief remains crucial. In this thesis, we establish fundamental possibility and impossibility results about belief formation under a variety of restrictions, and lay the groundwork for further exploration.

This dissertation studies three models of sequential social learning, each of which has implications for the impact of the internet and social media on political discourse. I take three features of online political discussion, and consider in what ways they interfere with or assist learning.In Chapter 1, I consider agents who engage in motivated reasoning, which is a belief-formation procedure in which agents trade-off a desire to form accurate beliefs against a desire to hold ideologically congenial beliefs. Taking a model of motivated reasoning in which agents can reject social signals that provide too strong evidence against their preferred state, I analyse under which conditions we can expect asymptotic consensus, where all agents choose the same action, and learning, in which Bayesian agents choose the correct state with probability 1. I find that learning requires much more connected observation networks than is the case with Bayesian agents. Furthermore, I find that increasing the precision of agents’ private signals can actually break consensus, providing an explanation for the advance of factual polarisation despite the greater access to information that the internet provides. In Chapter 2, I evalute the importance of timidity. In the presence of agents who prefer not to be caught in error publicly, and can choose to keep their views to themselves given this, insufficiently confident individuals may choose not to participate in online debate. Studying social learning in this setting, I discover an unravelling mechanism by which non-partisan agents drop out of online political discourse. This leads to an exaggerated online presence for partisans, which can cause even more Bayesian agents to drop out. I consider the possibility of introducing partially anonymous commenting, how this could prevent such unravelling, and what restrictions on such commenting would be desirable. In Chapter 3, my focus moves on to considering rational inattention, and how this interacts with the glut of information the internet has produced. I set out a model that incorporates the costly observation of private and social information, and derive conditions under which we should expect learning to obtain despite these costs. I find that expanding access to cheap information can actually damage learning: giving all agents Blackwell-preferred signals or cheaper observations of all their neighbors can reduce the asymptotic probability with which they match the state. Furthermore, the highly connected networks social media produces can generate a public good problem in investigate journalism, damaging the ‘information ecosystem’ further still.

This dissertation used synthetic datasets, semi-synthetic datasets, and a real-world dataset from an educational intervention to compare the performance of 15 machine learning and multiple imputation methods to estimate the individual treatment effect (ITE). In addition, it examined the performance of five evaluation metrics that can be used to identify the best ITE estimation method when conducting research with real-world data. Among the ITE estimation methods that were analyzed, the S-learner, the Bayesian Causal Forest (BCF), the Causal Forest, and the X-learner exhibited the best performance. In general, the meta-learners with BART and tree-based direct estimation methods performed better than the representation learning methods and the multiple imputation methods. As for the evaluation metrics, τ_(risk_R ) and the Switch Doubly Robust MSE (SDR-MSE) performed the best in identifying the best ITE estimation method when the true treatment effect was unknown. This dissertation contributes to a small but growing body of research on ITE estimation which is gaining popularity in various fields due to its potential for tailoring interventions to meet the needs of individuals and targeting programs at those who would benefit the most from those interventions.

This dissertation examines the integration of expert datasets to enhance the data efficiency of online Deep Reinforcement Learning (DRL) algorithms in large state and action space problems. The focus is on effectively integrating real-world data, including data from biological systems, to accelerate the learning process within the online DRL pipeline. The motivation for this work is twofold. First, the internet provides access to a vast amount of data, such as videos, that demonstrate various tasks of interest but are not necessarily designed for use in the DRL framework. Leveraging these data to enhance DRL algorithms presents an exciting and challenging opportunity. Second, biological systems exhibit numerous inductive biases in their behavior that enable them to be highly efficient and adaptable learners. Incorporating these mechanisms for efficient learning remains an open question in DRL, and this work considers the use of human and animal data as a possible solution to this problem. Throughout this dissertation, important questions are addressed, such as how prior knowledge can be distilled into RL agents, the benefits of leveraging offline datasets for online RL, and the algorithmic challenges involved. Five original works are presented that investigate the use of animal videos to enhance RL learning performance, develop a framework to learn bio-inspired foraging policies using human data, propose an online algorithm for performing hierarchical imitation learning in the options framework, and formulate and theoretically motivate novel algorithms for imitation from videos in the presence of visual mismatch. This research demonstrates the effectiveness of utilizing offline datasets to improve the efficiency and performance of online DRL algorithms, providing valuable insights into accelerating the learning process for complex tasks.

With the increasing availability of large multivariate datasets, modern parametric statisticalmodels makes increasing use of high-dimensional parameter spaces to flexibly represent complex data generating mechanisms. Yet, ceteris paribus, increases in dimensionality often carry drawbacks across the various sub-problems of data analysis, posing challenges for the data analyst who must balance model plausibility against the practical considerations of implementation. We focus here on challenges to three components of data analysis: computation, inference, and model checking. In the computational domain, we are concerned with achieving reasonable scaling of the computational complexity with the parameter dimension without sacrificing the trustworthiness of our computation. Here, we study a particular class of algorithms - the vectorized approximate message passing (VAMP) iterations - which offer the possibility of linear per-iteration scaling with dimension. These iterations perform approximate inference for a class of Bayesian generalized linear regression models, and we demonstrate that under flexible distributional conditions, the estimation performance of these VAMP iterations can be predicted to high accuracy with probability decaying exponentially fast in the size of the regression problem. In the realm of statistical inference, we investigate the relationship between parameter dimension and identification. We develop formal notions of weak identification and model expansion in the Bayesian setting and use this to argue for a very general tendency for dimensionality-increasing model expansion to weaken the identification of model parameters. We draw two substantive conclusions from this formalism. First, the negative association between dimensionality and identification can be weakened or reversed when we construct prior distributions that encode sufficiently strong dependence between parameters. Absent such prior information, we derive bounds which indicate that decreasing identification is usually unavoidable with sufficient inflation of the dimension without increasing the severity of the third challenge we consider: that of dimensionality to model checking. We divide the topic of model checking into two sub-problems: fitness testing and correctness testing. Using our model expansion formalism, we show again that both of these problems tend to become more difficult as the model dimension grows. We propose two extensions of the posterior predictive 𝑝-value - certain conditional and joint 𝑝-values, which are designed to address these challenges for fitness and correctness testing respectively. We demonstrate the potential of these 𝑝-values to allow successful model checking that scales with dimensionality theoretically and with examples.