We consider the problem of modeling temporal textual data taking endogenous and exogenous processes into account. Such text documents arise in real world applications, including job advertisements and economic news articles, which are influenced by the fluctuations of the general economy. We propose a hierarchical Bayesian topic model which imposes a "group-correlated" hierarchical structure on the evolution of topics over time incorporating both processes, and show that this model can be estimated from Markov chain Monte Carlo sampling methods. We further demonstrate that this model captures the intrinsic relationships between the topic distribution and the time-dependent factors, and compare its performance with latent Dirichlet allocation (LDA) and two other related models. The model is applied to two collections of documents to illustrate its empirical performance: online job advertisements from DirectEmployers Association and journalists' postings on BusinessInsider.com.
Understanding how housing values evolve over time is important to policy makers, consumers and real estate professionals. Existing methods for constructing housing indices are computed at a coarse spatial granularity, such as metropolitan regions, which can mask or distort price dynamics apparent in local markets, such as neighborhoods and census tracts. A challenge in moving to estimates at, for example, the census tract level is the sparsity of spatiotemporally localized house sales observations. Our work aims at addressing this challenge by leveraging observations from multiple census tracts discovered to have correlated valuation dynamics. Our proposed Bayesian nonparametric approach builds on the framework of latent factor models to enable a flexible, data-driven method for inferring the clustering of correlated census tracts. We explore methods for scalability and parallelizability of computations, yielding a housing valuation index at the level of census tract rather than zip code, and on a monthly basis rather than quarterly. Our analysis is provided on a large Seattle metropolitan housing dataset.
We describe algorithms for use by prediction markets in forming a crowd consensus joint probability distribution over thousands of related events. Equivalently, we describe market mechanisms to efficiently crowdsource both structure and parameters of a Bayesian network. Prediction markets are among the most accurate methods to combine forecasts; forecasters form a consensus probability distribution by trading contingent securities. A combinatorial prediction market forms a consensus joint distribution over many related events by allowing conditional trades or trades on Boolean combinations of events. Explicitly representing the joint distribution is infeasible, but standard inference algorithms for graphical probability models render it tractable for large numbers of base events. We show how to adapt these algorithms to compute expected assets conditional on a prospective trade, and to find the conditional state where a trader has minimum assets, allowing full asset reuse. We compare the performance of three algorithms: the straightforward algorithm from the DAGGRE (Decomposition-Based Aggregation) prediction market for geopolitical events, the simple block-merge model from the SciCast market for science and technology forecasting, and a more sophisticated algorithm we developed for future markets.
Discrete-time hidden Markov models are a broadly useful class of latent-variable models with applications in areas such as speech recognition, bioinformatics, and climate data analysis. It is common in practice to introduce temporal non-homogeneity into such models by making the transition probabilities dependent on time-varying exogenous input variables via a multinomial logistic parametrization. We extend such models to introduce additional non-homogeneity into the emission distribution using a generalized linear model (GLM), with data augmentation for sampling-based inference. However, the presence of the logistic function in the state transition model significantly complicates parameter inference for the overall model, particularly in a Bayesian context. To address this we extend the recently-proposed Polya-Gamma data augmentation approach to handle non-homogeneous hidden Markov models (NHMMs), allowing the development of an efficient Markov chain Monte Carlo (MCMC) sampling scheme. We apply our model and inference scheme to 30 years of daily rainfall in India, leading to a number of insights into rainfall-related phenomena in the region. Our proposed approach allows for fully Bayesian analysis of relatively complex NHMMs on a scale that was not possible with previous methods. Software implementing the methods described in the paper is available via the R package NHMM.
Alpha signals for statistical arbitrage strategies are often driven by latent factors. This paper analyses how to optimally trade with latent factors that cause prices to jump and diffuse. Moreover, we account for the effect of the trader's actions on quoted prices and the prices they receive from trading. Under fairly general assumptions, we demonstrate how the trader can learn the posterior distribution over the latent states, and explicitly solve the latent optimal trading problem. We provide a verification theorem, and a methodology for calibrating the model by deriving a variation of the expectation-maximization algorithm. To illustrate the efficacy of the optimal strategy, we demonstrate its performance through simulations and compare it to strategies which ignore learning in the latent factors. We also provide calibration results for a particular model using Intel Corporation stock as an example.