Gourab Mukherjee

We investigate the problem of compound estimation of normal means while accounting for the presence of side information. Leveraging the empirical Bayes framework, we develop a nonparametric integrative Tweedie (NIT) approach that incorporates structural knowledge encoded in multivariate auxiliary data to enhance the precision of compound estimation. Our approach employs convex optimization tools to estimate the gradient of the log-density directly, enabling the incorporation of structural constraints. We conduct theoretical analyses of the asymptotic risk of NIT and establish the rate at which NIT converges to the oracle estimator. As the dimension of the auxiliary data increases, we accurately quantify the improvements in estimation risk and the associated deterioration in convergence rate. The numerical performance of NIT is illustrated through the analysis of both simulated and real data, demonstrating its superiority over existing methods.

Amid increasing awareness regarding opioid addiction, medical marijuana has emerged as a substitute to opioids for pain management. Concurrently, opioid manufacturers are putting significant research into making opioids safer yet effective. Interactions between these manufacturers and physicians are critical to advance existing pain management protocols. Direct payments from opioid manufacturers to physicians are established practices that often moderates such interactions. We study the effects of passage of a medical marijuana law (MML) on these direct payments to physicians. To draw causal conclusions, we develop a novel penalized synthetic control (SC) method that accommodates zero-payment related latent structures inherent in these payments. Under a truncated flexible additive mixture model, we show that the SC method has uncontrolled maximal risk without the penalty; by contrast, the proposed penalized method provides efficient estimates. Our analysis finds a significant decrease in direct payments from opioid manufacturers to pain medicine physicians as an effect of MML passage. We provide evidence that this decrease is due to medical marijuana becoming available as a substitute. Finally, our heterogeneity analyses indicate that the decrease in direct payments is comparatively higher for physicians practicing in localities with higher white populations, lower affluence, and a larger proportion of working-age residents. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Should one teach coding in a required introductory statistics and data science class for non-major students? Many professors advise against it, considering it a distraction from the important and challenging statistical topics that need to be covered. By contrast, other professors argue that the ability to interact flexibly with data will inspire students with a lasting love of the subject and a continued commitment to the material beyond the introductory course. With the release of large language models that write code, we saw an opportunity for a middle ground, which we tried in Fall 2023 in a required introductory data science course in our school's full-time MBA program. We taught students how to write English prompts to the artificial intelligence tool Github Copilot that could be turned into R code and executed. In this short article, we report on our experience using this new approach.

We analyze consumer adoption of hybrid cars using automobile transaction data from the Sacramento market during the first half of $2007$, a critical period in the lifecycle of hybrid technology. Modeling demand for durable goods such as automobiles is made more difficult by the absence of repeat purchase data and pooling information across similar consumers is one way to address this data scarcity. We propose a new multinomial spatial probit model that connects different consumers using multiple weighted networks, which are based on different similarity structures. Unlike in the traditional multinomial spatial probit, different subsets of the parameter vector, i.e., the preference and marketing coefficients can be correlated in their own unique ways.

Parameter estimation is carried out via a novel Monte-Carlo Expectation-Maximization (MCEM) based approach, which enables the model to be used with a significantly greater number of consumers and choice alternatives than is possible with the standard model. The approach substitutes the computationally expensive E-step in the classical EM algorithm by an efficient Gibbs sampling-based evaluation and, additionally, implements the M-step using a fast back-fitting method that iteratively fits weighted regressions based on the associated similarity matrix for each coefficient subset. We establish the convergence properties of the proposed MCEM algorithm, present computational perspectives on the scalability of the proposed method, and provide a distributed computing-based implementation that yields parameter estimates and their standard errors.

We apply the model to sales data for compact cars from the Sacramento market and find that the best fitting version of our model is one in which the intercepts are based on the geographical closeness between consumers and the slope coefficients on the similarity of their previously owned vehicles. We summarize the cross-price elasticity matrices to produce clout and vulnerability measures for each vehicle and to produce competitive maps of the product category. We show how the multiple network weights explain the changes in price sensitivity of consumers across geographic locations, captures the variation in brand preferences among consumers and together deliver more accurate estimates of a consumer's hybrid purchase probability. Finally, we demonstrate how an automobile manufacturer can leverage the estimated heterogeneous spatial contiguity effects to improve the effectiveness of targeted promotions that are designed to accelerate the consumer adoption of the Toyota hybrid.