James H. Albert

Overview

James H. Albert is a statistician at Bowling Green State University. His research focuses on Bayesian computation, MCMC methods, and their applications to time series models with regime changes and latent variables.

Key Contributions / Features

• Albert (1996): Bayesian selection of log-linear models for contingency tables; Poisson likelihood with block-diagonal precision prior $\Sigma^{-1}=\text{diag}(0I_{p_0},P_1I_{p_1},\ldots,P_sI_{p_s})$; Gamma($\nu_j/2$,$b_j^2\nu_j/2$) hyperprior on group precisions $P_j$ → Cauchy marginals at $\nu_j=1$ for robustness; Laplace approximation with IWLS mode-finder for posterior model probabilities; Gibbs sampler over $(\{\beta_j\},Z,P^*)$; BMA inflates posterior SEs nearly 2× vs. MAP model; Fienberg (1980) and Shapiro et al. (1979) applications.
• Albert and Chib (1997): MCMC-based model diagnostics for the conditionally independent hierarchical model (CIHM); three perturbation diagnostics — scale-inflated outlier mixture $\pi(\theta_i)=(1-p_i)N(\mu,\tau^2)+p_i N(\mu,K\tau^2)$, partial exchangeability via $G$ latent groups, and Aranda-Ordaz mixture link functions — each implemented by adding one discrete Bernoulli block to the base CIHM Gibbs sampler; MCMC-grid BF for fixed vs. random effects; cancer mortality (84 Missouri cities, BF=32.4 for random effects; one outlier; logit link confirmed) and math placement (32 items, 2-group partial exchangeability) applications.
• Albert and Chib (1993): Data augmentation approach to Bayesian estimation of Markov-switching AR models; treats latent state sequence $S_n$ as missing data; Gibbs sampler with closed-form conditionals for states (backward binary draws), regression coefficients (truncated Normal), variances (Inverse-Gamma), and transition probabilities (Beta); foundational univariate precursor to the MS-VAR literature.
• Albert and Chib (1993b): Data augmentation for binary and polychotomous probit models; latent $Z_i \sim \mathcal{N}(x_i'\beta, 1)$ converts truncated-likelihood probit into a two-block Normal/truncated-Normal Gibbs sampler; extensions to t-link scale mixtures, hierarchical priors, ordered multinomial, and unordered multinomial probit; validated on Finney (1947) toxicity data, 1976 US election data, and Daganzo trivariate probit.
• Albert and Chib (1995): Bayesian residual analysis for binary regression; defines parametric residual $r_i = y_i - p_i(\beta)$ and latent data residual $\varepsilon_i = Z_i - x_i^T\beta$ (a priori $\mathcal{N}(0,1)$ in the probit case); both emerge free from the Gibbs run; Rao-Blackwellised density estimates for smoother summaries; extensions to logistic link and longitudinal random effects probit; illustrated on Brown (1980) prostate cancer and Kenward-Jones (1987) crossover datasets.
• Albert and Chib (1997b): Unified Bayesian MCMC framework for fitting and comparing three non-nested ordinal models — cumulative probit, sequential probit, and two-step compound; log-spacing reparameterization $\alpha_j = \log(\gamma_j - \gamma_{j-1})$ lifts ordered cut-points to an unrestricted real vector enabling a tuned multivariate-$t$ MH step; Bayes factors via Chib (1995) marginal likelihoods; three prior elicitation methods (training sample, imaginary prior, Dirichlet-on-multinomial) for valid non-nested comparison; NLSY educational attainment (cumulative wins, log BF=3.15) and Canada GSS physician visits (two-step wins, log BF=−10.7) applications. See Ordinal Regression.
• Albert and Chib (1998): Working paper version of Albert-Chib (2001); adds hierarchical sequential model (Algorithm 2) that shrinks free cutpoints $\{\gamma_j\}$ toward a quadratic polynomial surface via variance hyperparameter $\tau^2$; 6-model comparison table (cumulative, basic sequential, sequential+interaction, sequential+quadratic, Weibull, log-logistic) with different training/evaluation split from published paper; log-spacing cut-point reparameterization in Algorithm 3 consistent with Albert-Chib (1997b).
• Albert and Chib (2001): Bayesian framework for the sequential ordinal model; ordinal response $Y_i\in\{1,\ldots,J\}$ generated by $J-1$ independent binary hazard decisions; data augmentation with truncated normals; unordered cutpoints absorbed into unrestricted $\boldsymbol{\beta}$; right censoring handled natively; marginal likelihood via Chib (1995); hospital length-of-stay application ($N=1000$, $J=12$) decisively favours sequential model over cumulative probit and parametric survival alternatives. See Sequential Ordinal Model.

Related

• Siddhartha Chib
• Markov-Switching VAR
• Binary Probit
• Sequential Ordinal Model
• Ordinal Regression
• Bayesian Residual Analysis
• Gibbs Sampler
• James D. Hamilton