Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions

Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn't yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative Marketing and Economics vol 4 (2006), no. 2, 173--20

Interdependent Infrastructure as Linked Social, Ecological, and Technological Systems (SETSs) to Address Lock‐in and Enhance Resilience

Traditional infrastructure adaptation to extreme weather events (and now climate change) has typically been techno‐centric and heavily grounded in robustness—the capacity to prevent or minimize disruptions via a risk‐based approach that emphasizes control, armoring, and strengthening (e.g., raising the height of levees). However, climate and nonclimate challenges facing infrastructure are not purely technological. Ecological and social systems also warrant consideration to manage issues of overconfidence, inflexibility, interdependence, and resource utilization—among others. As a result, techno‐centric adaptation strategies can result in unwanted tradeoffs, unintended consequences, and underaddressed vulnerabilities. Techno‐centric strategies that lock‐in today\u27s infrastructure systems to vulnerable future design, management, and regulatory practices may be particularly problematic by exacerbating these ecological and social issues rather than ameliorating them. Given these challenges, we develop a conceptual model and infrastructure adaptation case studies to argue the following: (1) infrastructure systems are not simply technological and should be understood as complex and interconnected social, ecological, and technological systems (SETSs); (2) infrastructure challenges, like lock‐in, stem from SETS interactions that are often overlooked and underappreciated; (3) framing infrastructure with a SETS lens can help identify and prevent maladaptive issues like lock‐in; and (4) a SETS lens can also highlight effective infrastructure adaptation strategies that may not traditionally be considered. Ultimately, we find that treating infrastructure as SETS shows promise for increasing the adaptive capacity of infrastructure systems by highlighting how lock‐in and vulnerabilities evolve and how multidisciplinary strategies can be deployed to address these challenges by broadening the options for adaptation

A practitioner's guide to Bayesian estimation of discrete choice dynamic programming models

This paper provides a step-by-step guide to estimating infinite horizon discrete choice dynamic programming (DDP) models using a new Bayesian estimation algorithm (Imai et al., Econometrica 77:1865–1899, 2009a) (IJC). In the conventional nested fixed point algorithm, most of the information obtained in the past iterations remains unused in the current iteration. In contrast, the IJC algorithm extensively uses the computational results obtained from the past iterations to help solve the DDP model at the current iterated parameter values. Consequently, it has the potential to significantly alleviate the computational burden of estimating DDP models. To illustrate this new estimation method, we use a simple dynamic store choice model where stores offer “frequent-buyer” type rewards programs. Our Monte Carlo results demonstrate that the IJC method is able to recover the true parameter values of this model quite precisely. We also show that the IJC method could reduce the estimation time significantly when estimating DDP models with unobserved heterogeneity, especially when the discount factor is close to 1

Role of retinoic receptors in lung carcinogenesis

Several in vitro and in vivo studies have examined the positive and negative effects of retinoids (vitamin A analogs) in premalignant and malignant lesions. Retinoids have been used as chemopreventive and anticancer agents because of their pleiotropic regulator function in cell differentiation, growth, proliferation and apoptosis through interaction with two types of nuclear receptors: retinoic acid receptors and retinoid X receptors. Recent investigations have gradually elucidated the function of retinoids and their signaling pathways and may explain the failure of earlier chemopreventive studies

A Survey of Bayesian Statistical Approaches for Big Data

The modern era is characterised as an era of information or Big Data. This has motivated a huge literature on new methods for extracting information and insights from these data. A natural question is how these approaches differ from those that were available prior to the advent of Big Data. We present a review of published studies that present Bayesian statistical approaches specifically for Big Data and discuss the reported and perceived benefits of these approaches. We conclude by addressing the question of whether focusing only on improving computational algorithms and infrastructure will be enough to face the challenges of Big Data