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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.

Restructuring of the electricity industry is one of the important interventions which the Electricity Act envisages for bringing about competition and ensuring efficiency in the operation of the industry in the country. This chapter presents an overview of the restructuring system, discusses the status of unbundling of State Electricity Boards, and deals separately with the restructuring in generation, transmission, and distribution segments. The concept and issues around multiple distribution licensees in the same area of supply have been dealt with in this chapter. The vision of the Act in doing away with the single buyer model has been explained, and the present state of affairs in terms of implementation of this requirement has been examined with live examples from some states. The chapter reiterates the objectives of restructuring the electricity industry in terms of providing competition for the benefit of consumer, attracting private investment, and improving efficiency of operations. It also suggests the way forward for translating this vision of the Act into reality.

This chapter examines the application of the dynamic regression models for inference and prediction with dynamic econometric models. It shows how to extend to the dynamic case the notion of Bayesian cut seen in the static case to justify conditional inference. The chapter also explains how Bayesian inference can be used for single-equation dynamic models. It discusses the particular case of models with autoregressive errors, discusses the issues of moving average errors, and illustrates the empirical use of the error correction model by an analysis of a money demand function for Belgium.

This chapter obtains a Lifshitz-type formula for the atom-wall interaction considering one of the two walls as a rarefied medium. This formula is applied for various wall materials and various atoms. It is shown that the Casimir interaction between an atom and a metal wall does not depend on the model of the metal used. The respective Casimir entropy satisfies the Nernst heat theorem. In the case of an atom interacting with a dielectric wall, the Lifshitz theory is thermodynamically consistent if the dc conductivity of the dielectric material is neglected. If the dc conductivity of the dielectric wall is included in the model of the dielectric response, the Nernst heat theorem is violated. The atom-wall interaction is also considered when the wall material is magnetic, anisotropic and in the nonequilibrium case when the temperatures of the wall and of the environment are different.

This chapter discusses dynamical SUSY breaking. Topics covered include a rule of thumb for SUSY breaking, the 3-2 model, the SU(5) model, SUSY breaking and deformed moduli spaces, SUSY breaking from baryon runaways, direct gauge mediation, and single sector models. An exercise is given at the end of the chapter.

Integrated models of cognitive systems can be contrasted with the dominant variety of cognitive modeling that produces single-focus models of cognitive functions such as control of eye movements, visual attention, categorization, decision making, or memory. Such single-focus models are necessary but not sufficient for understanding human cognition. Although single-focused models are not usually created to be part of a larger, more integrated system, if cast in the right form, they can play strong roles in building integrated models of cognitive systems. Builders of integrated models need to explain what they mean by integration. This chapter proposes a new vocabulary that, if adopted, will clarify for the modeling community some of the issues in building integrated models. It may also lead to ways of separating the evaluation of integrated models from their component single-focus models. The heart of the chapter introduces and discusses three types of control and three types of components of integrated models of cognitive systems.

This chapter addresses the shortcomings that emerge in global climate models attributable to the interactions between resolved and parametized unresolved cloud-related processes (convection, turbulence, clouds and radiation). It also discusses alternative modeling techniques to study perturbed clouds, which include the numerical weather prediction model, large eddy simulation models, cloud-resolving models, and super-parameterized single column models.

Observer models specify computations that are sufficient to predict the behavior of an observer for many different input stimuli with a small number of parameters. Observer models specify the transformations leading to the relevant internal representations from the stimulus, and define the decision rules for particular tasks. These models have a remarkable ability to summarize compactly the behavioral outcomes in many conditions and provide a conceptual framework within which to understand the responses of the sensory system. In this chapter, we consider both modern single-channel and multichannel observer models. Each observer in a task can be described by a small number of parameters that fully specify how the stimulus is recoded in an internal response and then subjected to a task-relevant decision. Once these parameters have been estimated from specific experimental tests, it is possible to make predictions about an observer’s responses to a wide range of stimuli and paradigms.

This chapter highlights the importance of the revised analysis of electroencephalography (EEG) and magnetoencephalography (MEG) spike source estimation based on comprehensive case conference discussion. It discusses two typical cases of localization-related epilepsy: case 1 as a simple situation and case 2 as a complicated situation. No “gold standard” for epileptic spike analysis in EEG or MEG has been established, so several methods must be adopted to achieve the most reasonable interpretation. However, such intense and revisional analyses may be too time-consuming in clinical settings and result in arbitrary conclusions. Therefore, the authors currently use a simple method first, that is, a single dipole model for the peak or preceding upward slope of unaveraged single spikes. In the following case conference, EEG and MEG data are reviewed with seizure semiology, anatomical magnetic resonance imaging (MRI), and ¹⁸F-fluorodeoxyglucose positron emission tomography (FDG-PET). If all the findings almost agree, the clinical decision can be easily made. If not, revisional analysis of EEG/MEG is recommended using averaged spikes and principal component analysis models as well as distributed source models. In addition to EEG/MEG, the authors often order revisional analysis and additional MRI and FDG-PET studies after the conference. Even further history taking will be recommended if necessary.

This chapter focuses on the publication of information by public authorities in Scotland as a statutory obligation under the Freedom of Information (Scotland) Act 2002 (FOISA). FOISA requires each Scottissh authority to publish information in accordance with a publication scheme that it must adopt and maintain and has to be approved by the Scottish Information Commissioner. Authorities are free to publish as they see fit, tailored to their own circumstances, in recognition of their varying size and public-facing functions. Whatever they choose to do, the law requires that publication schemes must specify: classes of information which the authority publishes or intends to publish; the manner in which information of each class is, or is intended to be, published; and whether the published information is, or is intended to be, available to the public free of charge or on payment. In 2010, the Commissioner proposed a significant change in approach by introducing, among others, a single Model Publication Scheme, a generic set of classes of information, a standard charging policy for published information, a notification procedure, and a guide to information.

This chapter documents that ETFs can provide a broadly diversified investment tool for investors that is typically designed to mimic an underlying index. Index management may appear to be a simple type of investment management but in practice its implementation is not necessarily straightforward. Such factors as tracking error, liquidity, and the difference between the closing price and the NAV can influence the choice of a performance measure. However, other factors can lead to a divergence in ETFs’ performance from the underlying index. The chapter documents that international ETFs outperformed the market between 2001 and 2014 but failed to provide sufficient diversification. A single index model produces positive excess return and risk-adjusted performance as measured by the Sortino and Omega ratios. ETFs outperformance becomes less pronounced after the financial crisis of 2007–208.

Different types of global catastrophic risks (GCRs) are studied in various chapters of this book by direct analysis. In doing so, researchers benefit from a detailed understanding of the interplay of the underlying causal factors. However, the causal network is often excessively complex and difficult or impossible to disentangle. Here, we would like to consider limitations and theoretical constraints on the risk assessments which are provided by the general properties of the world in which we live, as well as its contingent history. There are only a few of these constraints, but they are important because they do not rely on making a lot of guesses about the details of future technological and social developments. The most important of these are observation selection effects. Physicists, astronomers, and biologists have been familiar with the observational selection effect for a long time, some aspects of them (e.g., Malmquist bias in astronomy or Signor-Lipps effect in paleontology) being the subject of detailed mathematical modelling. In particular, cosmology is fundamentally incomplete without taking into account the necessary ‘anthropic bias’: the conditions we observe in fundamental physics, as well as in the universe at large, seem atypical when judged against what one would expect as ‘natural’ according to our best theories, and require an explanation compatible with our existence as intelligent observers at this particular epoch in the history of the universe. In contrast, the observation selection effects are still often overlooked in philosophy and epistemology, and practically completely ignored in risk analysis, since they usually do not apply to conventional categories of risk (such as those used in insurance modelling). Recently, Bostrom (2002a) laid foundations for a detailed theory of observation selection effects, which has applications for both philosophy and several scientific areas including cosmology, evolution theory, thermodynamics, traffic analysis, game theory problems involving imperfect recall, astrobiology, and quantum physics. The theory of observation selection effects can tell us what we should expect to observe, given some hypothesis about the distribution of observers in the world. By comparing such predictions to our actual observations, we get probabilistic evidence for or against various hypotheses.