Browsing by Subject "Forecasting"

This dissertation discusses model and forecast comparison, calibration, and combination from a foundational perspective. For nearly five decades, the field of forecast combination has grown exponentially. Its practicality and effectiveness in important real world problems concerning forecasting, uncertainty, and decisions propels this. Ample research-- theoretical and empirical-- into new methods and justifications have been produced. However, its foundations-- the philosophical/theoretical underpinnings on which methods and strategies are built upon-- have been unexplored in recent literature. Bayesian predictive synthesis (BPS) defines a coherent theoretical basis for combining multiple forecast densities, whether from models, individuals, or other sources, and generalizes existing forecast pooling and Bayesian model mixing methods. By understanding the underlying foundation that defines the combination of forecasts, multiple extensions are revealed, resulting in significant advances in the understanding and efficacy of the methods for decision making in multiple fields.

The extensions discussed in this dissertation are into the temporal domain. Many important decision problems are time series, including policy decisions in macroeconomics and investment decisions in finance, where decisions are sequentially updated over time. Time series extensions of BPS are implicit dynamic latent factor models, allowing adaptation to time-varying biases, mis-calibration, and dependencies among models or forecasters. Multiple studies using different data and different decision problems are presented, demonstrating the effectiveness of dynamic BPS, in terms of forecast accuracy and improved decision making, and highlighting the unique insight it provides.

Using the wisdom of crowds---combining many individual forecasts to obtain an aggregate estimate---can be an effective technique for improving forecast accuracy. When individual forecasts are drawn from independent and identical information sources, a simple average provides the optimal crowd forecast. However, correlated forecast errors greatly limit the ability of the wisdom of crowds to recover the truth. In practice, this dependence often emerges because information is shared: forecasters may to a large extent draw on the same data when formulating their responses.

To address this problem, I propose an elicitation procedure in which each respondent is asked to provide both their own best forecast and a guess of the average forecast that will be given by all other respondents. I study optimal responses in a stylized information setting and develop an aggregation method, called pivoting, which separates individual forecasts into shared and private information and then recombines these results in the optimal manner. I develop a tailored pivoting procedure for each of three information models, and introduce a simple and robust variant that outperforms the simple average across a variety of settings.

In three experiments, I investigate the method and the accuracy of the crowd forecasts. In the first study, I vary the shared and private information in a controlled environment, while the latter two studies examine forecasts in real-world contexts. Overall, the data suggest that a simple minimal pivoting procedure provides an effective aggregation technique that can significantly outperform the crowd average.

In this thesis, we consider two classes of problems where algorithms are increasingly used to make, or assist in making, a wide range of decisions. The first class of problems we consider is the allocation of jointly owned resources among a group of agents, and the second is the elicitation and aggregation of probabilistic forecasts from agents regarding future events. Solutions to these problems must trade off between many competing objectives including economic efficiency, fairness between participants, and strategic concerns.

In the first part of the thesis, we consider shared resource allocation, where we relax two common assumptions in the fair divison literature. Firstly, we relax the assumption that goods are private, meaning that they must be allocated to only a single agent, and introduce a more general public decision making model. This allows us to incorporate ideas and techniques from fair division to define novel fairness notions in the public decisions setting. Second, we relax the assumption that decisions are made offline, and instead consider online decisions. In this setting, we are forced to make decisions based on limited information, while seeking to retain fairness and game-theoretic desiderata.

In the second part of the thesis, we consider the design of mechanisms for forecasting. We first consider a tradeoff between several desirable properties for wagering mechanisms, showing that the properties of Pareto efficiency, incentive compatibility, budget balance, and individual rationality are incompatible with one another. We propose two compromise solutions by relaxing either Pareto efficiency or incentive compatibility. Next, we consider the design of decentralized prediction markets, which are defined by the lack of any single trusted authority. As a consequence, markets must be closed by popular vote amongst a group of anonymous, untrusted arbiters. We design a mechanism that incentivizes arbiters to truthfully report their information even when they have a (possibly conflicting) stake in the market themselves.

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