On the equivalence of posterior inference based on retrospective and prospective likelihoods: application to a case-control study of colorectal cancer.

The paper develops a class of priors that leads to equivalent posterior inference for odds ratio parameters based on prospective and retrospective models for categorical response data. The results are applicable to both unmatched and matched case-control studies. The results hold for a general class of link functions for categorical response. The proposed method can accommodate multiple and possibly ordered disease states. The results are applied to the analysis of discrete subtypes in an ongoing case-control study of colorectal cancer. A simulation study illustrates the need for carefully considering prior choices in Bayesian analysis of data collected under retrospective design.

Response to best-frequency tone bursts in the ventral cochlear nucleus is governed by ordered inter-spike interval statistics.

The spike trains generated by short constant-amplitude constant-frequency tone bursts in the ventral cochlear nucleus of the anaesthetised guinea pig are examined. Spikes are grouped according to the order in which they occur following the onset of the stimulus. It is found that successive inter-spike intervals have low statistical dependence according to information-theoretic measures. This is in contrast to previous observations with long-duration tone bursts in the cat dorsal and posteroventral cochlear nuclei and lateral superior olive, where it was found that long intervals tended to be followed by shorter ones and vice versa. The interval distributions can also be reasonably modelled by a shifted Gamma distribution parameterised by the dead-time and the mean and coefficient of variation of the dead-time corrected ISI distribution. Knowledge of those three parameters for each interval is sufficient to determine the peri-stimulus time histogram and the regularity measures used to classify these neurons.

Exact tests of goodness of fit of log-linear models for rates.

We propose Metropolis-Hastings sampling methods for estimating the exact conditional p-value for tests of goodness of fit of log-linear models for mortality rates and standardized mortality ratios. We focus on two-way tables, where the required conditional distribution is a multivariate noncentral hypergeometric distribution with known noncentrality parameter. Two examples are presented: a 2 x 3 table, where the exact results, obtained by enumeration, are available for comparison, and a 9 x 7 table, where Monte Carlo methods provide the only feasible approach for exact inference.

Monte Carlo exact methods used for analysing interethnic unions in Great Britain.

The value of using exact rather than asymptotic tests to measure intermarriage in the United Kingdom is examined. "We develop Markov chain Monte Carlo methods for estimating the exact conditional p-value and the exact distribution of the residuals, for quasi-independence and quasi-symmetry. These methods are used to analyse a sparse 10 x 10 symmetric table of interethnic unions, extracted from the 1% household sample of anonymized records from the 1991 U.K. census. With the exception of Pakistani/White and Other Asian/White unions, there is no evidence against quasi-symmetry. We conclude that, with these exceptions, there are no gender differences in the affinities between ethnic groups."