Experiment-dependent priors in psychology and physics

Sometimes conducting an experiment to ascertain the state of a system changes the state of the system being measured. Kahneman & Tversky modelled this effect with support theory. Quantum physics models this effect with probability amplitude mechanics. As this paper shows, probability amplitude mechanics is similar to support theory. Additionally, Viscusi's proposed generalized expected utility model has an analogy in quantum mechanics.     

Optimal Bayesian Randomization

Randomization is a puzzle for Bayesians. The intuitive need for randomization is clear, but there is a standard result that Bayesians need not randomize. In this paper we propose a model in which randomization is a strictly optimal procedure. The most important aspect of our model is that there are several parties who make different decisions and observe different data. The result also sheds light on the ethical considerations involving randomization in a clinical trial.     

Bayesian phylogenetic inference from animal mitochondrial genome arrangements

Summary. The determination of evolutionary relationships is a fundamental problem in evolutionary biology. Genome arrangement data are potentially more informative than deoxyribonucleic acid sequence data for inferring evolutionary relationships between distantly related taxa. We describe a Bayesian framework for phylogenetic inference from mitochondrial genome arrangement data using Markov chain Monte Carlo methods. We apply the method to assess evolutionary relationships between eight animal phyla.     

Stockouts and Restocking: Monitoring the Retailer from the Supplier’s Perspective

Suppliers and retailers typically do not have identical incentives to avoid stockouts (lost sales due to the lack of product availability on the shelf). Thus, the supplier needs to monitor the retailer’s restocking efforts with the available data. We empirically assess stockout levels using only shipment and sales data that is readily available to the supplier. The model distinguishes between store stockouts (zero inventory in the store) and shelf stockouts (an empty shelf but some inventory in other parts of the store), thereby identifying the cause of the stockout to be either a supply chain or a restocking issue. We find that, as suspected by the supplier, the average stockout rate is much higher than published averages. In addition, stockout rates vary widely between stores. Moreover, almost all stockouts are shelf stockouts. The model identifies stores that may have restocking issues.     

Bayesian demography: projecting the Iraqi Kurdish population, 1977-1990

"Projecting populations that have sparse or unreliable data, such as those of many developing countries, presents a challenge to demographers. The assumptions that they make to project data-poor populations frequently fall into the realm of ?educated guesses', and the resulting projections, often regarded as forecasts, are valid only to the extent that the assumptions on which they are based reasonably represent the past or future, as the case may be. These traditional projection techniques do not incorporate a demographer's assessment of uncertainty in the assumptions. Addressing the challenges of forecasting a data-poor population, we project the Iraqi Kurdish population using a Bayesian approach. This approach incorporates a demographer's uncertainty about past and future characteristics of the population in the form of elicited prior distributions."     

A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution

Summary.  A useful discrete distribution (the Conway–Maxwell–Poisson distribution) is revived and its statistical and probabilistic properties are introduced and explored. This distribution is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric). It also leads to the generalization of distributions derived from these discrete distributions (i.e. the binomial and negative binomial distributions). We describe three methods for estimating the parameters of the Conway–Maxwell–Poisson distribution. The first is a fast simple weighted least squares method, which leads to estimates that are sufficiently accurate for practical purposes. The second method, using maximum likelihood, can be used to refine the initial estimates. This method requires iterations and is more computationally intensive. The third estimation method is Bayesian. Using the conjugate prior, the posterior density of the parameters of the Conway–Maxwell–Poisson distribution is easily computed. It is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data. We also explore two sets of real world data demonstrating the flexibility and elegance of the Conway–Maxwell–Poisson distribution in fitting count data which do not seem to follow the Poisson distribution.     

Laplace approximations to posterior moments and marginal distributions on circles,spheres, and cylinders

We extend recent work on Laplace approximations (Tierney and Kadane 1986; Tierney, Kass, and Kadane 1989) from parameter spaces that are subspaces of R^k to those that are on circles, spheres, and cylinders. While such distributions can be mapped onto the real line (for example, a distribution on the circle can be thought of as a function of an angle θ, 0 ? 0 ? 2π), that the end points coincide is not a feature of the real line, and requires special treatment. Laplace approximations on the real line make essential use of the normal integral in both the numerator and the denominator. Here that role is played by the von Mises integral on the circle, by the Bingham integrals on the spheres and hyperspheres, and by the normal-von Mises and normal-Bingham integrals on the cylinders and hypercylinders, respectively. We begin with a brief introduction to Laplace approximations and to previous Bayesian work on circles, spheres, and cylinders. We then develop the theory for parameter spaces that are hypercylinders, since all other shapes considered here are special cases. We compute some examples, which show reasonable accuracy even for small samples.     

Using administrative lists to estimate census omissions

"We present a method for estimating omission rates from censuses. Our method is based on the merger of administrative lists, sampling from these lists, and matching against census rolls. We describe the method, present the results of a test in New York City...in 1980, and evalute the results. We compare our proposed method to other procedures for estimating omission rates."     

Hybrid methods for calculating optimal few-stage sequential strategies: Data monitoring for a clinical trial

Optimal batch-sequential designs are difficult to compute, even when sufficient statistics and relatively uncomplicated loss functions simplify the calculations required. While backward induction applies, its difficulty grows exponentially in the number of stages, while a recently developed forward algorithm grows only linearly, but involves a maximization over a rather flat surface. This paper explores a hybrid algorithm, partially backward induction, partially forward, that has some of the advantages of each.