4,017 research outputs found
An Outline of the Bayesian Decision Theory
In this paper we give an outline on the Bayesian Decision Theory.Comment: arXiv admin note: text overlap with arXiv:1409.826
Combinatorial Information Theory: I. Philosophical Basis of Cross-Entropy and Entropy
This study critically analyses the information-theoretic, axiomatic and
combinatorial philosophical bases of the entropy and cross-entropy concepts.
The combinatorial basis is shown to be the most fundamental (most primitive) of
these three bases, since it gives (i) a derivation for the Kullback-Leibler
cross-entropy and Shannon entropy functions, as simplified forms of the
multinomial distribution subject to the Stirling approximation; (ii) an
explanation for the need to maximize entropy (or minimize cross-entropy) to
find the most probable realization; and (iii) new, generalized definitions of
entropy and cross-entropy - supersets of the Boltzmann principle - applicable
to non-multinomial systems. The combinatorial basis is therefore of much
broader scope, with far greater power of application, than the
information-theoretic and axiomatic bases. The generalized definitions underpin
a new discipline of ``{\it combinatorial information theory}'', for the
analysis of probabilistic systems of any type.
Jaynes' generic formulation of statistical mechanics for multinomial systems
is re-examined in light of the combinatorial approach. (abbreviated abstract)Comment: 45 pp; 1 figure; REVTex; updated version 5 (incremental changes
Rigorous Bounds on Strong Interaction Coupling Constants
We investigate the problem of deriving bounds on strong interaction scattering amplitudes from the results of axiomatic field theory
How to Estimate Unbiased and Consistent input-output Multipliers on the Basis of use and Make Matrices
In the literature, the construction of technical coefficients is linked to flow data (use and make matrices), but stochastics are imposed on the coefficients when multipliers are calculated, by means of the Leontief inverse. Due the nonlinearity of this operation, the multiplier estimates are biased (it is generally argued that the Leontief inverse underestimates input-output multipliers). By going back to the flow data, this paper provides unbiased and consistent employment and output multipliers estimates for the Andalusian economy. Rectangular use and make matrices are accommodated and technical coefficients, the Leontief inverse, and associated problems (such as negative coefficients) are circumvented.Stochastic input-output analysis, employment multipliers, output multipliers, use and make matrices.
Utilitarian population ethics: a survey
This essay is a survey of utilitarian criteria aimed at guiding what Parfit (1984) called Different Number Choices (i.e. choices affecting both peopleâs number and identities). The emphasis is laid on two aspects of those criteria: their ethical foundations and their implications. Our analysis starts with total, average and critical-level utilitarianisms, against which numerous criticisms, such as Parfitâs Repugnant Conclusion and Mere Addition Paradox, were formulated, so that alternative social welfare criteria, as the ones developed by Hurka (1983) and Ng (1986), might seem appealing. However, those criteria are not fully satisfactory, and, as most criteria considered here, they do not stand up to Naversonâs (1967) critique, according to which social welfare cannot be increased or reduced if no existing person is affected. The difficulties resulting from taking Naversonâs critique into account â and thus from considering the Actual Problem rather than the Genesis Problem â are then discussed. It is concluded that utilitarian population ethics might reach an impasse, which might be regarded either as resulting from contradicting intuitions, or as an illustration of utilitarianismâs own limits. But those limits would be faced by any other consequences-based ethical theory in front of Different Number Choices.
A Process Modelling Framework Based on Point Interval Temporal Logic with an Application to Modelling Patient Flows
This thesis considers an application of a temporal theory to describe and model the patient journey in the hospital accident and emergency (A&E) department. The aim is to introduce a generic but dynamic method applied to any setting, including healthcare. Constructing a consistent process model can be instrumental in streamlining healthcare issues. Current process modelling techniques used in healthcare such as flowcharts, unified modelling language activity diagram (UML AD), and business process modelling notation (BPMN) are intuitive and imprecise. They cannot fully capture the complexities of the types of activities and the full extent of temporal constraints to an extent where one could reason about the flows. Formal approaches such as Petri have also been reviewed to investigate their applicability to the healthcare domain to model processes.
Additionally, to schedule patient flows, current modelling standards do not offer any formal mechanism, so healthcare relies on critical path method (CPM) and program evaluation review technique (PERT), that also have limitations, i.e. finish-start barrier. It is imperative to specify the temporal constraints between the start and/or end of a process, e.g., the beginning of a process A precedes the start (or end) of a process B. However, these approaches failed to provide us with a mechanism for handling these temporal situations. If provided, a formal representation can assist in effective knowledge representation and quality enhancement concerning a process. Also, it would help in uncovering complexities of a system and assist in modelling it in a consistent way which is not possible with the existing modelling techniques.
The above issues are addressed in this thesis by proposing a framework that would provide a knowledge base to model patient flows for accurate representation based on point interval temporal logic (PITL) that treats point and interval as primitives. These objects would constitute the knowledge base for the formal description of a system. With the aid of the inference mechanism of the temporal theory presented here, exhaustive temporal constraints derived from the proposed axiomatic systemâ components serves as a knowledge base.
The proposed methodological framework would adopt a model-theoretic approach in which a theory is developed and considered as a model while the corresponding instance is considered as its application. Using this approach would assist in identifying core components of the system and their precise operation representing a real-life domain deemed suitable to the process modelling issues specified in this thesis. Thus, I have evaluated the modelling standards for their most-used terminologies and constructs to identify their key components. It will also assist in the generalisation of the critical terms (of process modelling standards) based on their ontology. A set of generalised terms proposed would serve as an enumeration of the theory and subsume the core modelling elements of the process modelling standards. The catalogue presents a knowledge base for the business and healthcare domains, and its components are formally defined (semantics). Furthermore, a resolution theorem-proof is used to show the structural features of the theory (model) to establish it is sound and complete.
After establishing that the theory is sound and complete, the next step is to provide the instantiation of the theory. This is achieved by mapping the core components of the theory to their corresponding instances. Additionally, a formal graphical tool termed as point graph (PG) is used to visualise the cases of the proposed axiomatic system. PG facilitates in modelling, and scheduling patient flows and enables analysing existing models for possible inaccuracies and inconsistencies supported by a reasoning mechanism based on PITL. Following that, a transformation is developed to map the core modelling components of the standards into the extended PG (PG*) based on the semantics presented by the axiomatic system.
A real-life case (from the Kingâs College hospital accident and emergency (A&E) departmentâs trauma patient pathway) is considered to validate the framework. It is divided into three patient flows to depict the journey of a patient with significant trauma, arriving at A&E, undergoing a procedure and subsequently discharged. Their staff relied upon the UML-AD and BPMN to model the patient flows. An evaluation of their representation is presented to show the shortfalls of the modelling standards to model patient flows. The last step is to model these patient flows using the developed approach, which is supported by enhanced reasoning and scheduling
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