In recent years, there has been an avalanche of new data in observational high-energy astrophysics. Recently launched or soon-to-be launched space-based telescopes that are designed to detect and map ultra-violet, X-ray, and $\gamma$-ray electromagnetic emission are opening a whole new window to study the cosmos. Because the production of high-energy electromagnetic emission requires temperatures of millions of degrees and is an indication of the release of vast quantities of stored energy, these instruments give a completely new perspective on the hot and turbulent regions of the universe. The new instrumentation allows for very high resolution imaging, spectral analysis, and time series analysis; the Chandra X-ray Observatory, for example, produces images at least thirty times sharper than any previous X-ray telescope. The complexity of the instruments, of the astronomical sources, and of the scientific questions leads to a subtle inference problem that requires sophisticated statistical tools. For example, data are subject to non-uniform stochastic censoring, heteroscedastic errors in measurement, and background contamination. Astronomical sources exhibit complex and irregular spatial structure. Scientists wish to draw conclusions as to the physical environment and structure of the source, the processes and laws which govern the birth and death of planets, stars, and galaxies, and ultimately the structure and evolution of the universe.

The California-Harvard Astrostatistics Collaboration is a group of astrophysicists and statisticians working together to develop statistical methods, computational techniques, and freely available software to address outstanding inferential problems in high-energy astrophysics. We emphasize fully model-based statistical inference; we explicitly model the complexities of both astronomical sources and the data generation mechanisms inherent in new high-tech instruments, and fully utilize the resulting highly structured models in learning about the underlying astronomical and physical processes. Using these models requires sophisticated scientific computation, advanced methods for statistical inference, and careful model checking procedures.

Here we discuss the broad scientific goals of observation high-energy astrophysics, the specifics of the data collection mechanism involved with the Chandra X-ray Observatory, current statistical methods, and the Bayesian models and methods that we propose. We illustrate our statistical strategy in the context of several applied examples, including the estimation of hardness ratios, spectral analysis, multiscale image analysis, and reconstruction of the distribution of the temperature of hot plasma in a stellar corona. This paper was presented at the Case Studies in Bayesian Statistics Workshop 7 held at Carnegie Mellon University in September 2003.

A beam of protons is produced by a linear charged particle accelerator, then focused through the use of successive quadrupoles. The initial state of the beam is unknown, in terms of particle position and momentum. Wire scans provide the only available data on the current state of the beam as it passes through and beyond the focusing region; the goal is to infer the initial state from these position histograms. This setup is that of an inverse problem, in which a computer simulator is used to link an initial state configuration to observable values (wire scans), and then inference is performed for the distribution of the initial state. Our Bayesian approach allows estimation of uncertainty in our initial distributions and beam predictions.

The process of calibrating radiocarbon determinations onto the calendar scale involves, as a first stage, the estimation of the relationship between calendar and radiocarbon ages (the radiocarbon calibration curve) from a set of available high-precision calibration data. Traditionally the radiocarbon calibration curve has been constructed by forming a weighted average of the data, and then taking the curve as the piece-wise linear function joining the resulting calibration data points. Alternative proposals for creating a calibration curve from the averaged data involve a spline or cubic interpolation, or the use of Fourier transformation and other filtering techniques, in order to obtain a smooth calibration curve. Between the various approaches, there is no consensus as to how to make use of the data in order to solve the problems related to the calibration of radiocarbon determinations.

We propose a nonparametric Bayesian solution to the problem of the estimation of the radiocarbon calibration curve, based on a Gaussian process prior structure on the space of possible functions. Our approach is model-based, taking into account specific characteristics of the dating method, and provides a generic solution to the problem of estimating calibration curves for chronology building.

We apply our method to the 1998 international high-precision calibration dataset, and demonstrate that our model predictions are well calibrated and have smaller variances than other methods. These data have deficiencies and complications that will only be unravelled with the publication of new data, expected in early 2005, but this analysis suggests that the nonparametric Bayesian model will allow more precise calibration of radiocarbon ages for archaeological specimens.

In his campaign for the U.S. presidency from 1975 to 1979, Ronald Reagan delivered over 1000 radio broadcasts. For over 600 of these we have direct evidence of Reagan's authorship. The aim of this study was to determine the authorship of 312 of the broadcasts for which no direct evidence is available. We addressed the prediction problem for speeches delivered in different epochs and we explored a wide range of off-the-shelf classification methods and fully Bayesian generative models. Eventually we produced separate sets of predictions using the most accurate classifiers, based on non-contextual words as well as on semantic features, for the 312 speeches of uncertain authorship. All the predictions agree on 135 of the "unknown" speeches, whereas the fully Bayesian models agree on an additional 154 of them.

The magnitude of the posterior odds of authorship led us to conclude that Ronald Reagan drafted 167 speeches and was aided in the preparation of the remaining 145. Our inferences were not sensitive to "reasonable" variations in the sets of constants underlying the prior distributions, and the cross-validated accuracy of our best fully Bayesian model was above 90 percent in all cases. The agreement of multiple methods for predicting the authorship for the "unknown" speeches reinforced our confidence in the accuracy of our classifications.

We discuss a model-based approach to identifying clusters of objects based on subsets of attributes, so that the attributes that distinguish a cluster from the rest of the population may depend on the cluster being considered. The method is based on a Pólya urn cluster model for multivariate means and variances, resulting in a multivariate Dirichlet process mixture model. This particular model-based approach accommodates outliers and allows for the incorporation of application-specific data features into the clustering scheme. For example, in an analysis of genetic CGH array data we are able to design a clustering method that accounts for spatial dependence of chromosomal abnormalities.

For Bayesian analysis of massive data, Markov chain Monte Carlo (MCMC) techniques often prove infeasible due to computational resource constraints. Standard MCMC methods generally require a complete scan of the dataset for each iteration. Ridgeway and Madigan (2002) and Chopin (2002b) recently presented importance sampling algorithms that combined simulations from a posterior distribution conditioned on a small portion of the dataset with a reweighting of those simulations to condition on the remainder of the dataset. While these algorithms drastically reduce the number of data accesses as compared to traditional MCMC, they still require substantially more than a single pass over the dataset. In this paper, we present "1PFS," an efficient, one-pass algorithm. The algorithm employs a simple modification of the Ridgeway and Madigan (2002) particle filtering algorithm that replaces the MCMC based "rejuvenation" step with a more efficient "shrinkage" kernel smoothing based step. To show proof-of-concept and to enable a direct comparison, we demonstrate 1PFS on the same examples presented in Ridgeway and Madigan (2002), namely a mixture model for Markov chains and Bayesian logistic regression. Our results indicate the proposed scheme delivers accurate parameter estimates while employing only a single pass through the data.

This article explores a Bayesian analysis of a generalization of the Poisson distribution. By choice of a second parameter $\nu$, both under-dispersed and over-dispersed data can be modeled. The Conway-Maxwell-Poisson distribution forms an exponential family of distributions, so it has sufficient statistics of fixed dimension as the sample size varies, and a conjugate family of prior distributions. The article displays and proves a necessary and sufficient condition on the hyperparameters of the conjugate family for the prior to be proper, and it discusses methods of sampling from the conjugate distribution. An elicitation program to find the hyperparameters from the predictive distribution is also discussed.

In the conjugate prior for the normal linear model, the prior variance for the coefficients is a multiple of the error variance parameter. However, if the prior mean for the coefficients is poorly chosen, the posterior distribution of the model can be seriously distorted because of prior dependence between the coefficients and error variance. In particular, the error variance will be overestimated, as will the posterior variance of the coefficients. This occurs because the prior mean, which can be thought of as a weighted pseudo-observation, is an outlier with respect to the real observations. While this situation will be easily noticed and avoided in simple models, in more complicated models, the effect can be easily overlooked. The issue arises in the unit information (UI) prior, a conjugate prior in which the prior contributes information equal to that in one observation. In particular, a successful Bayesian nonparametric regression model — Bayesian Adaptive Regression Splines (BARS) — that relies on the UI prior for its model selection step suffers from this problem, and addressing the problem within the Bayesian paradigm alters the penalty on model dimensionality.