Search Results

This introductory chapter provides an overview of the main questions examined in this book. It argues that there are three sets of questions which demarcate the so-called ‘trade and environment’ nexus: The first set of questions concerns the relationship between WTO law, multilateral environmental agreements, and non-WTO law more generally. This brings into play the issue of conflict of norms, the legal status of the lex specialis principle and similar legal maxims, and the concepts jurisdiction and applicable law in WTO dispute settlement. A second set of questions is related to the disputed concepts of extraterritorial jurisdiction and unilateral state action. A third group of issues concerns the scope and contents of relevant WTO disciplines. In this respect, this book examines the basic principles governing the General Agreement on Tariffs and Trade (GATT) and the Agreement on Technical Barriers to Trade (TBT Agreement).

This chapter is about Bayesian decision theory. It explains why game theorists model players' beliefs using subjective probability distributions, and how these beliefs are updated using Bayes' rule as further information is received during the play of a game. A skeptical assessment of Bayesian decision theory as a solution to the general problem of scientific induction is then offered, suggesting that we stick to Leonard Savage's view that his theory properly applies only in the context of a small world. The chapter ends with a brief review of the common prior assumption and the idea of subjective equilibria.

This chapter provides solutions to the problems presented in the preceding chapter. It presents the diagrams for each problem as well as some explanations on how the solutions are arrived at. As has been advised in the previous chapter, each solution is best referred to individually, as each problem in the preceding chapter has been solved. The problems this chapter addresses involve the mean number of ticks per sheep assuming the counts are distributed as a Poisson random variable, the portrayal of light limitation for a single tree species, the landscape occupancy of Swiss breeding birds, the allometry of savanna trees, and the movement of seals in the North Atlantic.

Objective statistical induction may be behavioural, instantial, or pro-subjective (Bayesian), depending on the form of judging inferential uncertainty. In the behavioral case, the unknown parameters are fixed and uncertainty is judged by measures of procedural trustworthiness (like significance and confidence levels, power and risk functions), interpreted through repeated conceptual experimentation. Various principles are invoked for optimizing the procedure in different problems. The instantial approach (likelihood inference, P-value testing, and fiducial inference) remains pegged to the instance at hand without visualizing repetition, and weighs uncertainty in non-standard ways, although often like the behavioural approach, it also has to appeal to sampling theory. In the pro-subjective Bayesian approach, the unknown parameters are subjectively random with a known prior distribution, and inference is based on their posterior distribution. Various kinds of priors (improper/proper, impersonal/personal) fit in different tastes and situations. The subjective approach, based on a fully known subjective probability model, ‘previses’ about future observables, conditionally fixing the observations, often assuming exchangeability to simplify the process. Comparison of the different approaches shows that each has a natural setting in which it is advantageous.

Around the middle of the 18th century, Bayes conceived the idea of treating an unknown parameter as a subjective random variable distributed according to a prior, and inferring about it from its conditional (posterior) distribution given the observations. He considered the particular case of a binomial parameter subject to a uniform prior, and following the pro-subjective approach used the posterior to derive an interval estimate. Later, Laplace stated the result in its general form and employed it extensively for pro-subjective inference of various types in different situations, often basing his computation on the asymptotic normality of the posterior distribution. In a novel application, Laplace used pro-subjective reasoning and the data from a sample survey to estimate the size of the population of France.

This chapter seeks to explain hierarchical models and how they differ from simple Bayesian models and to illustrate building hierarchical models using mathematically correct expressions. It begins with the definition of hierarchical models. Next, the chapter introduces four general classes of hierarchical models that have broad application in ecology. These classes can be used individually or in combination to attack virtually any research problem. Examples are used to show how to draw Bayesian networks that portray stochastic relationships between observed and unobserved quantities. The chapter furthermore shows how to use network drawings as a guide for writing posterior and joint distributions.

This chapter explains how to implement Bayesian analyses using the Markov chain Monte Carlo (MCMC) algorithm, a set of methods for Bayesian analysis made popular by the seminal paper of Gelfand and Smith (1990). It begins with an explanation of MCMC with a heuristic, high-level treatment of the algorithm, describing its operation in simple terms with a minimum of formalism. In this first part, the chapter explains the algorithm so that all readers can gain an intuitive understanding of how to find the posterior distribution by sampling from it. Next, the chapter offers a somewhat more formal treatment of how MCMC is implemented mathematically. Finally, this chapter discusses implementation of Bayesian models via two routes—by using software and by writing one's own algorithm.

This chapter shows how to make inferences using MCMC samples. Here, the process of inference begins on the assumption that a single model is being analyzed. The objective is to estimate parameters, latent states, and derived quantities based on that model and the data. These estimates are conditioned on the single model being analyzed. The chapter also returns to an example advanced in the first chapter, to illustrate choices on specific distributions needed to implement the model, to show how informative priors can be useful, and to illustrate some of the inferential procedures described in this chapter—posterior predictive checks, marginal posterior distributions, estimates of derived quantities, and forecasting.

This chapter describes how to evaluate alternative models with data. There are two broad ways to formally use multiple models: model selection and model averaging. In model selection, models are evaluated based on some criterion. In model averaging, inferences are made using all models in the set, or a subset of them, using a weighted average of posterior distributions of individual models. This chapter first discusses model selection before turning to model averaging in turn, before detailing some general considerations which might help the researcher's selection of a particular model, given that both methods have their own strengths and shortcomings.

This chapter provides a set of structured problems to hone the reader's skills in model building. Each problem requires the reader to draw a Bayesian network and write the posterior and joint distributions. Computational syntax is de-emphasized because there are many sources that teach the details of writing code for MCMC software using ecological examples and a few that show how to construct one's own MCMC algorithms. The examples offered in this chapter are drawn from several ecological sub-disciplines, though the intent of these problems is to be instructive regardless of the reader's focus of research. The chapter also offers some pointers for approaching these problems and how to apply their lessons to one's own research.

The posterior femoral cutaneous nerve is also referred to as the lesser sciatic nerve. It originates from the S1 to S3 roots. It exits from the pelvis by passing anterior to the piriformis muscle and posteromedial to the sciatic nerve, innervating the perineum and inferior gluteal skin. Its course is then in the muscular groove between the medial and lateral hamstring muscles. It passes distally through the popliteal fossa, innervating the posterior thigh, and extends distally, innervating the posterior calf with the lateral sural and saphenous nerves. The sacral region is difficult to evaluate. In the male, the dorsal nerve of the penis is the terminal branch of the pudendal nerve and serves as the sensory supply for most of the penis. It is also the afferent arc of the bulbocavernosus reflex entering through the S1 through S3 roots. These studies are useful in evaluating patients with abnormalities of sexual, bowel, or bladder function.

This chapter presents evidence that supports the idea that activity in the interoceptive cortex in the posterior insula is re-represented, integrated, and transformed in the middle and anterior portions of human insular cortex to generate the feelings that one experiences. It also explains how vivid feelings are generated in a model of interoceptive integration that engenders homeostatic sentience. The emergence of bodily feelings provides the foundation for the generation of emotional feelings in the anterior insular cortex as if they are feelings from the body. The chapter then describes the evidence for the embodiment of emotional feelings, including the recent use of Botox to elucidate central mechanisms for the facial feedback hypothesis.

The intent of a statistically-based phylogenetic method is to estimate tree topologies and values of possibly relevant parameters, as well as the uncertainty inherent in those estimations. A method that could do that with reasonable accuracy would be attractive indeed. It is often claimed that it is advantageous for a method to be based on a specific evolutionary model, because that allows incorporating into the analysis the ‘knowledge’ of the real world embodied in the model. Bayesian methods have become very prominent among model-based methods, in part because of computational advantages, and in part because they estimate the probability that a given hypothesis is true, given the observations and model assumptions. Through simulation studies, this chapter finds that even if there is the potential for Bayesian estimations of monophyly to provide correct topological estimations for infinite numbers of characters, the resulting claims to measure degrees of support for conclusions — in a statistical sense — are unfounded. Additionally, for large numbers of terminals, it is argued to be extremely unlikely that a search via Markov Monte Carlo techniques would ever pass through the optimal tree(s), let alone pass through the optimal tree(s) enough times to estimate their posterior probability with any accuracy.

This chapter describes a simple model of the “percolation” of information of common interest through an over-the-counter market with many agents. It also includes an explicit solution for the cross-sectional distribution of posterior beliefs at each time. It begins with the basic information structure for the economy and the setting for search and random matching. It then shows how to solve the model for the dynamics of the cross-sectional distribution of information. The remainder of the chapter is devoted to market settings and to extensions of the model that handle public releases of information, the receipt of new private information over time, and the release of information among groups of more than two agents at a time.

This chapter begins with a historical account of the study of the internal capsule. It then discusses the results of the investigation of the internal capsule of rhesus monkey brains. Topics covered include the anterior limb of the internal capsule, genu of the internal capsule, posterior limb of the internal capsule, internal capsule fibers from the posterior parietal cortex, and internal capsule fibers from the superior temporal region.

The authors recall the basic differences of view between classical and Bayesian analysis and note that the dispute among statisticians has not been exactly reflected in econometrics. Starting with a ‘falt prior’that is already contestable, Bayesian econometricians were happy to reproduce the results of their colleagues. This is now less the case and Bauwens and Lubrano suggest that Bayesian methods are more effective at detecting unit roots and avoiding spurious acceptance of integration of series.

In another area, that of computation, the authors suggest that there is more complementarity between classical and Bayesian econometrics and that the sort of tools used such as Gibbs sampling may be of general value. They conclude by suggesting that Bayesian methods will more than hold their own in cases where samples are small and extra information is necessary as is often the case.

This chapter presents what is known about the anatomy and function of the executive processes to provide a better understanding of them. The discussion covers the sensory and mnemonic representations that remain in posterior cortex, the ensemble of executive processes, the anatomy and physiology of the prefrontal cortex, whether active prefrontal connections necessary for posterior conscious states, access consciousness versus phenomenal consciousness, and bare consciousness.