It is a relatively well-known fact that in problems of Bayesian model selection, improper priors should, in general, be avoided. In this paper we will derive and discuss a collection of four proper uniform priors which lie on an ascending scale of informativeness. It will turn out that these priors lead us to evidences that are closely associated with the implied evidence of the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC). All the discussed evidences are then used in two small Monte Carlo studies, wherein for different sample sizes and noise levels the evidences are used to select between competing C-spline regression models. Also, there is given, for illustrative purposes, an outline on how to construct simple trivariate C-spline regression models. In regards to the length of this paper, only one half of this paper consists of theory and derivations, the other half consists of graphs and outputs of the two Monte Carlo studies.@en

We present here a Bayesian framework of risk perception. This framework encompasses plausibility judgments, decision making, and question asking. Plausibility judgments are modeled by way of Bayesian probability theory, decision making is modeled by way of a Bayesian decision theory, and relevancy judgments are modeled by way of a Bayesian information theory. These theories are discussed in Parts I, II, and III, respectively, of this thesis. Bayesian probability theory is fairly well known and well established. Bayesian probability theory is not only a powerful tool of data analysis, but it also may function as a model for the way we (implicitly) do induction, that is, the way we make plausibility judgments on the basis of incomplete information. In Part I of this thesis we will make the case that Bayesian probability theory is nothing but common sense quantified. The Bayesian decision theory, as proposed in this thesis, derives directly from Bayesian probability theory. In this decision theory we compare utility probability distributions, which are constructed by way of assigning utilities, that is, subjective worths, to the objective outcomes of our outcome probability distributions, which are derived by way of Bayesian probability theory. When the outcomes under consideration are monetary, then we may use the Weber-Fechner law of psychophysics, or, equivalently, Bernoulli's utility function, to assign utilities to these outcomes. This mapping of outcomes to utilities, transforms our outcome probability distributions to their corresponding utility probability distributions. That utility probability distribution which is located more to the right on the utility axis will tend to be, depending on the context of our problem of choice, either more profitable or less disadvantageous than the utility probability distribution that is more to the left. So, we will tend to prefer that decision which `maximizes' our utility probability distributions. This then, in a nutshell, is the whole of our Bayesian decision theory. In Part~II of this thesis, we will apply the Bayesian decision theory to both investment and insurance problems. Not all questions are equal, some questions, when answered, may give us more information than others. Stated differently, questions may differ in their relevancy, in relation to some issue of interest we wish to see resolved. This is borne out by the well known adage that, 'to know the question, is to have gone half the journey'. Bayesian information theory, by way of a mathematical operationalization of the concept of a question, allows us to determine which question, when answered, will be the most informative in relation to some issue of interest. The Bayesian information theory does this by assigning relevancies to the questions under consideration. These relevancies are then operated upon, by way of the information theoretical product and sum rules, in order to determine the relevancy of some question in relation to the issue of interest. The Bayesian information theory constitutes an expansion of the 'canvas of rationality', and, consequently, of the range of psychological phenomena which are amenable to mathematical analysis. For example, we may assign relevancies not only to questions, but also to the messages that are communicated to us by some source of information. The relevancy of a message represents the usefulness of that message, when received, in determining some issue of interest. By assigning a relevancy to the message, we indirectly assign a relevancy to the sources of information itself; possible examples of sources of information being the media, scientists, and governmental institutions. In Part~III of this thesis, we will give an information theoretical analysis of a simple risk communication problem. Bayesian probability has its axiomatic roots in lattice theory, as the product and sum rule of Bayesian probability theory may be derived by way of consistency requirements on the lattice of statements. One may derive, likewise, by way of consistency requirements on the lattice of questions, the product and sum rules of Bayesian information theory. So, if we choose rationality, that is, consistency requirements on lattices, as our guiding principle in the derivation of our theories of inference, then we get on the one hand a Bayesian probability theory, with as its specific application a Bayesian decision theory, and on the other hand we get a Bayesian information theory. In doing so, we obtain a comprehensive, coherent, and powerful framework with which to model human reasoning, in the widest sense. @en

Because of the competing demands for scarce resources (funds, manpower, etc) national road owners are required to monitor the condition and performance of infrastructure elements through an effective inspection and assessment regime as part of an overall asset management strategy, the primary aim being to keep the asset in service at minimum cost. A considerable amount of information is then already available through existing databases and other information sources. Various analyzes have been carried out to identify the different forms of deterioration affecting infrastructures, to investigate the parameters controlling their susceptibility to, and rate of, deterioration. This paper proposes such an approach by building a transition matrix directly from the condition scores. The Markov assumption is used stating that the condition of a facility at one inspection only depends on the condition at the previous inspection. With this assumption, the present score is the only one which is taken into account to determine the future of the facility. The objective is then to combine nested sampling with a Markov-based estimation of the condition rating of infrastructure elements to put some confidence bounds on Markov transition matrices, and ultimately on corresponding maintenance costs.@en

In this paper, we will give the derivation of an inquiry calculus, or, equivalently, a Bayesian information theory. From simple ordering follow lattices, or, equivalently, algebras. Lattices admit a quantification, or, equivalently, algebras may be extended to calculi. The general rules of quantification are the sum and chain rules. Probability theory follows from a quantification on the specific lattice of statements that has an upper context. Inquiry calculus follows from a quantification on the specific lattice of questions that has a lower context. There will be given here a relevance measure and a product rule for relevances, which, taken together with the sum rule of relevances, will allow us to perform inquiry analyses in an algorithmic manner@en

We give here a comparison of the expected outcome theory, the expected utility theory, and the Bayesian decision theory, by way of a simple numerical toy problem in which we look at the investment willingness to avert a high impact low probability event. It will be found that for this toy problem the modeled investment willingness under the Bayesian decision theory is minimally three times higher compared to the investment willingness under either the expected outcome or the expected utility theories, where it is noted that the estimates of the latter two theories seem to be unrealistically low.@en

This paper presents an optimization framework for highway infrastructure elements that integrates risk profiles (for infrastructures) and economic aspects. One main goal is to assess the necessary additional effort to satisfy performance constraints under different scenarios of climate change. In order to be easily deployable by national road administrations (NRAs), this framework is built in such a way that it can be embedded into asset management systems that include an inventory of the asset, inspection strategies (to report element conditions and safety defects) and decision-making for funds allocation. Using the inventory of the asset and condition assessment as input, the method aims to determine some degradation profiles for bridge components, retaining walls and steep embankments. The method to determine the degradation process is detailed so that any infrastructure manager can determine their own deterioration processes based on the inventory and condition assessment of their stock. Combining degradation of highway infrastructures with a risk analysis, this paper presents an optimization framework to determine optimal management strategies.

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