Robert E. McCulloch

Overview

Robert E. McCulloch is a Bayesian statistician (University of Chicago Graduate School of Business at the time of the 1993 papers; later University of Arizona and Texas A&M). He is known for applying Gibbs sampling to AR time series with random mean and variance shifts, and for co-developing Stochastic Search Variable Selection (SSVS) with Edward George.

Key Contributions

McCulloch, Polson, and Rossi (2000): ID prior for the MNP model — places the prior directly on the identified parameter space (σ₁₁ = 1 with probability 1) via Σ = [[1, γ'], [γ, Φ+γγ']] with γ ~ N, Φ⁻¹ ~ Wishart; four-block conjugate Gibbs with no tuning parameters. Key result: the NID marginal prior on β is √χ² × Normal — heavy-tailed and hard to assess informatively; ID prior gives straightforward N(β̄, D⁻¹) directly on identified coefficients. Analytical results for prior assessment (Results 1–3). Cost: higher autocorrelation than NID. Journal of Econometrics 99: 173–193. See Multinomial Probit and McCulloch-Polson-Rossi (2000).
Rossi, McCulloch, and Allenby (1996): Hierarchical MNP with demographic regression mean βₕ = Δzₕ + vₕ; five information sets; target couponing revenue framework: full info 2.55× blanket, one observation 1.56×; Bayesian coupon optimization vs. plug-in; continuous normal heterogeneity beats finite mixture by ~100% log-likelihood. See Rossi-McCulloch-Allenby (1996).
McCulloch and Rossi (1994): Foundational Gibbs sampler for the multinomial probit model; exact likelihood analysis via data augmentation over latent utility vectors; all Gibbs blocks conjugate; avoids the $(m-1)T_h$ -dimensional integral of classical MNP MLE; extended by Allenby-Rossi (1999) to the hierarchical random-coefficient setting. Journal of Econometrics 64: 207–240. See Multinomial Probit.
George-McCulloch (1997) — Approaches For Bayesian Variable Selection: Extended SSVS within a unified hierarchical framework. Co-developed conjugate prior $\pi(\beta|\sigma,\gamma)=\mathcal{N}_p(0,\sigma^2 D^*_\gamma R_\gamma D^*_\gamma)$ ; analytical integration of $(\beta,\sigma^2)$ ; Chambers-based fast updating; Gray Code exhaustive enumeration for $p \leq 25$ ; three-algorithm comparison (NG/CG/CM); stuck- $\gamma$ failure mode analysis; two-phase S&P 500 application ( $p=200 \to 50 \to 21$ variables, $R^2=95.6\%$ ). Statistica Sinica 7 (1997): 339–373.
RLAR and RVAR models (with Tsay 1993): Developed the random level-shift AR (RLAR) and random variance-shift AR (RVAR) models with Gibbs sampler inference. Each time point has an independent Bernoulli shift indicator; a probit extension links shift probability to exogenous variables for shift prediction. Published in JASA 88(423): 968–978. See Structural Break Testing and Gibbs Sampler.
Stochastic Search Variable Selection (with George 1993): SSVS — three-block Gibbs sampler over $(\beta, \sigma^2, \gamma)$ with spike-and-slab mixture prior. The latent binary indicators $\gamma \in \{0,1\}^p$ are drawn Bernoulli from the ratio of spike/slab Normal densities evaluated at the current $\beta$ draw; the $\gamma$ block does not depend on $Y$ directly. High-frequency $\gamma$ patterns across all post-burn-in output identify high-posterior-probability subsets across $2^p$ models without enumeration. Published in JASA 88(423): 881–889.
Bayesian AR time series (with Tsay, in press 1993): Prior companion paper extending Gibbs sampling to AR time series with additive outliers and missing values.
Markov switching inference (with Tsay 1991): Technical report on Gibbs sampling for Markov-switching AR models; companion to the RLAR/RVAR work.
Allenby, Rossi, and McCulloch (2005): Practitioners guide to hierarchical Bayes models in marketing; develops four-block Gibbs for random-effects logit conjoint ( $\beta_h = \Gamma z_h + \xi_h$ , $V_\beta$ free); credit card study (N=946); demonstrates that $V_\beta$ off-diagonal structure determines tail-area targeting advantages. See Conjoint Analysis.

Robert E. McCulloch

Overview

Key Contributions

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