In Bayesian inference, the choice of prior has been of great interest. Subjective priors are ideal if sufficient information on priors is available. However, in practice, we cannot collect enough information on priors. Then objective priors are a good substitute for subjective priors. In this dissertation, an independent reference prior based on a class of objective priors is examined. It is a reference prior derived by assuming that the parameters are independent. The independent reference prior introduced by Sun and Berger (1998) is extended and generalized. We provide an iterative algorithm to derive the general independent reference prior. We also propose a sufficient condition under which a closed form of the independent reference prior is derived without going through the iterations in the iterative algorithm. The independent reference prior is then shown to be useful in respect of the invariance and the first order matching property. It is proven that the independent reference prior is invariant under a type of one-to-one transformation of the parameters. It is also seen that the independent reference prior is a first order probability matching prior under a sufficient condition. We derive the independent reference priors for various examples. It is observed that they are first order matching priors and the reference priors in most of the examples. We also study an independent reference prior in some types of non-regular cases considered by Ghosal (1997). / Ph. D.

published_or_final_version / Philosophy / Doctoral / Doctor of Philosophy

No description available.

12 pp. / This publication describes the procedure that is now recommended as a US standard for computing reference evapotranspiration. Included in the publication are: the rationale for developing the new procedure, the equations utilized in the new procedure, a discussion of how the new procedure differs from the established AZMET procedure, and tables to facilitate conversion between procedures (new and AZMET).

Switch-Reference (SR) is a phenomenon in which the coreferentiality of two (or more) subjects in a complex sentence is indicated by a morphological device. The purpose of this dissertation is to discuss recent work which deals with SR within the Government and Binding Theory, and propose an alternative analysis to it. The framework I will adopt for such an alternative analysis of SR is Categorial Grammar. A basic notion underlying Categorial Grammar is that an expression is divided into a functor and an argument, and each functor and argument are further divided into a functor and an argument until the division reaches to an undividable element. Given the assumptions that a functor and its argument must be compatible and that a functor has some subcategorization properties, I argue that "Agreement" phenomenon (subsuming agreement and disagreement) can be handled insightfully. Furthermore, I propose that such a treatment of "Agreement" can be extended to SR systems in general if we consider the "same subject" and "different subject" phenomena as cases of agreement and disagreement, respectively. I claim that a composite in which a SR morpheme appears forms a functor which takes another composite as its argument, and that the relation between the functor and its argument and the relation between some parts of the functor and its argument are characterized as "agreement" or "disagreement": The functor and the argument must be compatible as assumed above, and the nature of compatibility (whether "agreement" or "disagreement") is controlled by the subcategorization properties of the SR morpheme associated with the functor (i.e., if "same subject", the relation is agreement, and if "different subject", it is disagreement). By treating SR in this fashion, I intend to provide a unified analysis for apparently different SR systems in three diverse languages, namely, Tairora, Hopi, and Warlpiri.

No description available.

The purpose of this study was to investigate the effects of aspirational and dissociative reference group influence on consumer behavior. There are two ways in which behavior is influenced by reference groups. First, reference groups influence aspiration levels and therefore play a major role in producing satisfaction or frustration. Second, reference groups influence kinds of behavior, i.e., they establish approved patterns of behavior.

The main results of this thesis fall in to two areas, firstly quantum reference frames as a resource for quantum computations and secondly quantum algorithms. The results relating to quantum references consider their scaling with a requirements to perform measurements, operations and computations with a certain fidelity. For the case of a directional frame, the central question considered is of how many operations or measurements can be performed with it before its fidelity falls below some threshold. This is found to scale as the square of the size of the reference frame under for a range of physically interesting cases. To prove that result a new general form for any rotationally invariant map. This could have many applications is comparing and classifying rotationally invariant behaviour of quantum systems. Phase references are also considered for the case of performing quantum computations under an energy conservation law. The restriction that the expected energy be conserved for large quantum computations is shown to be manageable in many different potential architectures. In the case of completing computations is an energy conserving subspace, the requirements for ancillas are sublinear in the number of qubits, and even in a circuit model implementation, the errors due to phase reference imperfections are shown to not limit the apparent algorithmic improvements of quantum computing over classical computing. A quantum walk for the novel concept of two entangled walkers is proposed and analyzed. A modest improvement is found in the scaling of the expected separation of the walkers over the separable case. It illustrates the potential for making use of particle statistic behaviour in algorithms. Lastly, the relation between discrete and continuous time models of quantum computing is explored through the analysis of a new algorithm for simulating the Hamiltonian behaviour of a black box unitary operation. The scaling of the number of calls to the unitary required to obtain a simulation correct to within a parameter ϵ is found, as is a case where the efficiency of the algorithm is superior to directly applying the unitary repeatedly. Applications of the algorithm are considered.

The main results of this thesis fall in to two areas, firstly quantum reference frames as a resource for quantum computations and secondly quantum algorithms. The results relating to quantum references consider their scaling with a requirements to perform measurements, operations and computations with a certain fidelity. For the case of a directional frame, the central question considered is of how many operations or measurements can be performed with it before its fidelity falls below some threshold. This is found to scale as the square of the size of the reference frame under for a range of physically interesting cases. To prove that result a new general form for any rotationally invariant map. This could have many applications is comparing and classifying rotationally invariant behaviour of quantum systems. Phase references are also considered for the case of performing quantum computations under an energy conservation law. The restriction that the expected energy be conserved for large quantum computations is shown to be manageable in many different potential architectures. In the case of completing computations is an energy conserving subspace, the requirements for ancillas are sublinear in the number of qubits, and even in a circuit model implementation, the errors due to phase reference imperfections are shown to not limit the apparent algorithmic improvements of quantum computing over classical computing. A quantum walk for the novel concept of two entangled walkers is proposed and analyzed. A modest improvement is found in the scaling of the expected separation of the walkers over the separable case. It illustrates the potential for making use of particle statistic behaviour in algorithms. Lastly, the relation between discrete and continuous time models of quantum computing is explored through the analysis of a new algorithm for simulating the Hamiltonian behaviour of a black box unitary operation. The scaling of the number of calls to the unitary required to obtain a simulation correct to within a parameter ϵ is found, as is a case where the efficiency of the algorithm is superior to directly applying the unitary repeatedly. Applications of the algorithm are considered.

Thesis (Honors)--College of William and Mary, 2009. / Includes bibliographical references (leaves 28-29). Also available via the World Wide Web.