Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics without spatial modeling. We propose Deep Spatiotemporal Point Process (DeepSTPP), a deep dynamics model that integrates spatiotemporal point processes. Our method is flexible, efficient, and can accurately forecast irregularly sampled events over space and time. The key construction of our approach is the nonparametric space-time intensity function, governed by a latent process. The intensity function enjoys closed form integration for the density. The latent process captures the uncertainty of the event sequence. We use amortized variational inference to infer the latent process with deep networks. Using synthetic datasets, we validate our model can accurately learn the true intensity function. On real-world benchmark datasets, our model demonstrates superior performance over state-of-the-art baselines.

In three essays, I present my work that uses mathematical modelling to analyse real-world problems in marketing. In the first chapter, I model the design of referral programmes and offer normative advice about improving the cost-effectiveness of a referral programme. The second chapter is joint work with my co-advisor, Yuichiro Kamada. In this work, we construct a tractable game-theoretic model for multiple-priority queue management. Lastly, the third chapter analyses the incentives of online bloggers that post product reviews to subscribers when the reviews may be sponsored.

Customer referrals have become an increasingly important way for firms to grow their customer base. Likely thanks to improvements to customer relationship management software as well as growing awareness of the potential of word-of-mouth marketing, referral programmes are becoming increasingly popular among firms. In the first chapter, I study the design of customer referral programmes by constructing a stylized static principal-agent model with hidden actions, in which a firm designs a referral programme to incentivize an existing customer to exert costly efforts to refer the customer's friends to the firm. In the baseline model, I find it optimal for the firm to pay the customer if and only if every friend of the customer is successfully referred. In a number of extensions that are important and relevant to referral programmes, although the optimal referral contract is no longer a threshold contract, this class of contracts still plays an important role in the optimal referral programme design. Overall, my work shows that it is cost-effective to use or include threshold contracts to incentivize efforts.

When access to a service facility is congested, service providers commonly implement a special type of queue called priority queue, where each person/entity in the queue has an associated priority such that those with a higher priority will be ahead of those with a lower priority in the queue. Previous studies into second-degree price discrimination and queue management suggest that the firm that manages the firm that manages the park should set a large number of different priorities in order to improve price discrimination. In the second chapter, my co-author and I construct a model in which an amusement park sells different priority passes to customers in a queue whose utilities depend on positions in the queue. A customer's valuation of a priority pass depends on the distribution of customers buying each priority pass, and hence other customers' purchase decisions have an externality on the customer's valuation, which differentiates our model from the standard screening models. Through the model, we discuss the implementability of selling multiple passes for different patterns of customer utility functions. The main result of our work is that the externality makes the implementation of multi-pass schemes difficult, an issue that persists even when customers have heterogeneous utilities of positions in a queue.

Thanks to the popularity of internet platforms such as YouTube and TikTok, more and more customers are turning to their favourite internet bloggers for product reviews. That the bloggers have many subscribers that rely on their reviews for purchase decision makes bloggers a potential sales channel. This type of marketing is often called influencer marketing. To incentivize the bloggers to help promote a firm's product, one common incentive is for the firm to sponsor a blogger's product review by offering sales commissions for purchases by the blogger's subscribers. In a sponsored review, since the blogger now benefits from higher sales, the blogger has a bigger incentive to review the product favourably, even though the blogger's own private signal about the product's quality says otherwise. On the other hand, the blogger cares about the accuracy of the review because accurate reviews attract viewership. In the third chapter, I construct a stylized model that analyses the incentives of a blogger posting reviews of products with uncertain quality on an internet platform to the blogger's subscribers. Specifically, the blogger receives a costless private signal about the quality of the product and then sends a review message to the subscribers. On the one hand, the platform rewards the blogger for posting accurate reviews. On the other hand, higher sales of the product lead to higher sales commission offered by the firm manufacturing the product. I find that the blogger has an incentive to truthfully communicate the received signal when the signal is informative; otherwise, the blogger has an incentive to pretend to receive a favourable signal even when the realized signal is unfavourable to the product. Under a symmetric signal structure, my model shows that the blogger has an incentive for an honest review when the product is perceived to be mid-end.