Bayesian analysis of elapsed times in continuous‐time Markov chains

The authors consider Bayesian analysis for continuous‐time Markov chain models based on a conditional reference prior. For such models, inference of the elapsed time between chain observations depends heavily on the rate of decay of the prior as the elapsed time increases. Moreover, improper priors on the elapsed time may lead to improper posterior distributions. In addition, an infinitesimal rate matrix also characterizes this class of models. Experts often have good prior knowledge about the parameters of this matrix. The authors show that the use of a proper prior for the rate matrix parameters together with the conditional reference prior for the elapsed time yields a proper posterior distribution. The authors also demonstrate that, when compared to analyses based on priors previously proposed in the literature, a Bayesian analysis on the elapsed time based on the conditional reference prior possesses better frequentist properties. The type of prior thus represents a better default prior choice for estimation software.     

Quantifying uncertainty in the biospheric carbon flux for England and Wales

Summary.  A crucial issue in the current global warming debate is the effect of vegetation and soils on carbon dioxide (CO₂) concentrations in the atmosphere. Vegetation can extract CO₂ through photosynthesis, but respiration, decay of soil organic matter and disturbance effects such as fire return it to the atmosphere. The balance of these processes is the net carbon flux. To estimate the biospheric carbon flux for England and Wales, we address the statistical problem of inference for the sum of multiple outputs from a complex deterministic computer code whose input parameters are uncertain. The code is a process model which simulates the carbon dynamics of vegetation and soils, including the amount of carbon that is stored as a result of photosynthesis and the amount that is returned to the atmosphere through respiration. The aggregation of outputs corresponding to multiple sites and types of vegetation in a region gives an estimate of the total carbon flux for that region over a period of time. Expert prior opinions are elicited for marginal uncertainty about the relevant input parameters and for correlations of inputs between sites. A Gaussian process model is used to build emulators of the multiple code outputs and Bayesian uncertainty analysis is then used to propagate uncertainty in the input parameters through to uncertainty on the aggregated output. Numerical results are presented for England and Wales in the year 2000. It is estimated that vegetation and soils in England and Wales constituted a net sink of 7.55 Mt C (1 Mt C = 10¹² g of carbon) in 2000, with standard deviation 0.56 Mt C resulting from the sources of uncertainty that are considered.     

Backward Induction Is Not Robust: The Parity Problem and the Uncertainty Problem

A cornerstone of game theory is backward induction, whereby players reason backward from the end of a game in extensive form to the beginning in order to determine what choices are rational at each stage of play. Truels, or three-person duels, are used to illustrate how the outcome can depend on (1) the evenness/oddness of the number of rounds (the parity problem) and (2) uncertainty about the endpoint of the game (the uncertainty problem). Since there is no known endpoint in the latter case, an extension of the idea of backward induction is used to determine the possible outcomes. The parity problem highlights the lack of robustness of backward induction, but it poses no conflict between foundational principles. On the other hand, two conflicting views of the future underlie the uncertainty problem, depending on whether the number of rounds is bounded (the players invariably shoot from the start) or unbounded (they may all cooperate and never shoot, despite the fact that the truel will end with certainty and therefore be effectively bounded). Some real-life examples, in which destructive behavior sometimes occurred and sometimes did not, are used to illustrate these differences, and some ethical implications of the analysis are discussed.     

Deconstructing maternal sensitivity: Predictive relations to mother‐child attachment in home and laboratory settings

Despite the well‐documented importance of parental sensitivity for child development, there is a lack of consensus regarding how best to assess it. We investigated the factor structure of maternal caregiving behavior as assessed at 12 months by the Maternal Behavior Q‐Sort (Pederson & Moran) with 274 mother‐infant dyads. Subsequently, we examined associations between these empirically‐derived dimensions and child attachment, assessed in the home and laboratory (final N = 157). Three dimensions of maternal behavior were identified, corresponding fairly closely to Ainsworth's original scales. They were labeled Cooperation/Attunement, Positivity, and Accessibility/Availability. Only Cooperation/Attunement consistently predicted home‐based attachment at 15 months and 2 years, and at comparable strength to the overall sensitivity score, suggesting that this construct may be central to sensitivity. At 18 months, compared to their primarily secure counterparts, different types of laboratory‐assessed insecure attachment were associated with different patterns of maternal behavior. Mothers in avoidant relationships (n = 18) were low on Cooperation/Attunement and Accessibility/Availability, but fairly high on Positivity. Mothers of disorganized infants (n = 11) were Cooperative/Attuned but somewhat less Positive toward, and less Accessible/Available to, their infants. A multidimensional approach to parental behavior may facilitate the identification of parenting precursors of insecure parent‐child relationships.     

Daubert v. Merrell Dow pharmaceuticals: Toward a better relationship between law and science

[Scientists] are neither Gods nor charlatans; they are merely experts, like every other expert on the political stage. They have, of course, their special area of expertise, the physical world, but their knowledge is no more immaculate than that of economists, health policy makers, police officers, legal advocates, weather forecasters, travel agents, car mechanics, or plumbers. The expertise that we need to deal with them is the well‐developed expertise of everyday life; it is what we use when we deal with plumbers and the rest. Plumbers are not perfect-far from it‐but society is not beset with anti‐plumbers because being anti-plumbing is not a choice available to us.1     

Consumer racial discrimination: A reassessment of the market for baseball cards

Research on the presence of consumer racial discrimination in the baseball labor and memorabilia markets has produced contradictory empirical results. While studies of baseball salaries find no evidence of discrimination, Nardinelli and Simon (1990) and Andersen and La Croix (1991) use data from the baseball card market to show that the price that consumers pay for a card depends on the player’s race. In this paper, we reconsider the evidence of consumer discrimination in the baseball card market. Our study improves on previous research by applying more appropriate econometric methods and using a data set in which card supply is constant and incentives for speculative demand are weaker. In contradiction to the aforementioned studies, we find little evidence of racial discrimination. This result proves robust across variable specifications and econometric models. The authors thank Tyler Cowen, Kevin Grier, David Levy, Barb McKiernan, Don Palmer, Dan Sutler, and Bob Tollison for helpful suggestions on an earlier draft.     

5‐Month‐Olds’ Categorization of Novel Objects: Task and Measure Dependence

To examine key parameters of the initial conditions in early category learning, two studies compared 5‐month‐olds’ object categorization between tasks involving previously unseen novel objects, and between measures within tasks. Infants in Experiment 1 participated in a visual familiarization–novelty preference (VFNP) task with two‐dimensional (2D) stimulus images. Infants provided no evidence of categorization by either their looking or their examining even though infants in previous research systematically categorized the same objects by examining when they could handle them directly. Infants in Experiment 2 participated in a VFNP task with 3D stimulus objects that allowed visual examination of objects’ 3D instantiation while denying manual contact with the objects. Under these conditions, infants demonstrated categorization by examining but not by looking. Focused examination appears to be a key component of young infants’ ability to form category representations of novel objects, and 3D instantiation appears to better engage such examining.