Abstract This note surveys results for computing the inequality probability P (X> Y) in closed fo... more Abstract This note surveys results for computing the inequality probability P (X> Y) in closed form where X and Y are independent continuous random variables. Distribution families discussed include normal, Cauchy, gamma, inverse gamma, evy, folded normal, and beta. Mixture distributions are also discussed.
Abstract We examine the effect of a parameter λ used to calibrate how responsive randomization pr... more Abstract We examine the effect of a parameter λ used to calibrate how responsive randomization probabilities are to observed data in an adaptively randomized clinical trial. We define and motivate the parameter λ and demonstrate how varying this parameter effects the operating characteristics of example clinical trial designs.
Abstract: Many if not most runways and taxiways on military airfields are constructed of jointed ... more Abstract: Many if not most runways and taxiways on military airfields are constructed of jointed unreinforced concrete pavements or composite pavements with a cement-bound layer and asphalt surfacing. Asphalt overlays can effectively strengthen both types of pavement, and overcome surface defects such as cracking, spalling, or loss of skid resistance. However, reflection cracking is a major problem of asphalt overlays.
Abstract The simplest Bayesian adaptive randomization scheme is to randomize patients to a treatm... more Abstract The simplest Bayesian adaptive randomization scheme is to randomize patients to a treatment with probability equal to the probability p that the treatment is better. We examine three variations on adaptive randomization which are used to compromise between this scheme and equal randomization. The first variation is to apply a power transformation to p to obtain randomization probabilities. The second is to clip p to live within specified lower and upper bounds.
Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It... more Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context.
This paper considers a system of equations consisting of a nonlinear evolution equation on an ope... more This paper considers a system of equations consisting of a nonlinear evolution equation on an open set Ωin coupled to another nonlinear evolution equation on the boundary GΩ. Rather general assumptions are made concerning the operators involved and the coupling between the two problems. Existence and uniqueness are demonstrated via a semigroup of nonlinear operators on L1 (Ω) XL1 (GΩ).
Abstract: Special requirements for airfields are driven by the need to design, construct and main... more Abstract: Special requirements for airfields are driven by the need to design, construct and maintain airfield pavements, which will satisfy the concerns of the international aviation community over potential safety issues.
Abstract: In the United Kingdom the Ministry of Defense and TRL have been working together since ... more Abstract: In the United Kingdom the Ministry of Defense and TRL have been working together since the late 1980s in order to reduce the impact of reflection cracking on military airfields. Reflection cracking affects pavements to a greater or lesser extent at over 85% of MOD airfields.
Many Bayesian clinical trial methods are based on random inequalities. For some distribution fami... more Many Bayesian clinical trial methods are based on random inequalities. For some distribution families, these inequalities can be computed in closed form. For example, [1] gives closed-form solutions to computing P(X > Y) when X and Y are either independent normal or independent gamma random variables. However the case of beta random variables is very important and no closed form solution for this case is known. Such inequalities must be evaluated numerically.
Abstract This report examines in detail a family of efficacy-toxicity trade-off functions simpler... more Abstract This report examines in detail a family of efficacy-toxicity trade-off functions simpler and more general than those originally proposed in [1]. The new trade-off functions are based on distance in Lp norm to the ideal point and were first presented in [2]. We define and illustrate these functions and demonstrate how to compute their parameters based on elicited values.
Abstract: This paper describes how airfield pavements must facilitate safe aircraft ground operat... more Abstract: This paper describes how airfield pavements must facilitate safe aircraft ground operations. This in turn necessitates special design considerations with respect to several key functional requirements. The structural design and evaluation of airfield pavements can involve wheel loads up to 28 tons and arranged in various multiple configurations. Surface serviceability requirements can necessitate special considerations in respect of material specifications, construction and maintenance of airfield pavements.
Abstract Adaptively randomized trials aim to treat patients in clinical trials more effectively b... more Abstract Adaptively randomized trials aim to treat patients in clinical trials more effectively by increasing the probability of assigning treatments that appear to have a higher probability of response. Studies of adaptive randomization to date have assumed constant probabilities of response on each treatment. This paper examines the effect of response probabilities that change over time due to population drift.
Totally fissured media in which the cells are isolated by the fissure system are effectively desc... more Totally fissured media in which the cells are isolated by the fissure system are effectively described by double porosity models with microstructure. These models contain the geometry of the individual cells or pores in the medium and the flux across their interface with the fissures which surrounds them. We extend these models to include the case of partially fissured media in which a secondary flux effect arises from cell-to-cell diffusion paths.
Abstract This note surveys results for computing the inequality probability P (X> Y) in closed fo... more Abstract This note surveys results for computing the inequality probability P (X> Y) in closed form where X and Y are independent continuous random variables. Distribution families discussed include normal, Cauchy, gamma, inverse gamma, evy, folded normal, and beta. Mixture distributions are also discussed.
Abstract We examine the effect of a parameter λ used to calibrate how responsive randomization pr... more Abstract We examine the effect of a parameter λ used to calibrate how responsive randomization probabilities are to observed data in an adaptively randomized clinical trial. We define and motivate the parameter λ and demonstrate how varying this parameter effects the operating characteristics of example clinical trial designs.
Abstract: Many if not most runways and taxiways on military airfields are constructed of jointed ... more Abstract: Many if not most runways and taxiways on military airfields are constructed of jointed unreinforced concrete pavements or composite pavements with a cement-bound layer and asphalt surfacing. Asphalt overlays can effectively strengthen both types of pavement, and overcome surface defects such as cracking, spalling, or loss of skid resistance. However, reflection cracking is a major problem of asphalt overlays.
Abstract The simplest Bayesian adaptive randomization scheme is to randomize patients to a treatm... more Abstract The simplest Bayesian adaptive randomization scheme is to randomize patients to a treatment with probability equal to the probability p that the treatment is better. We examine three variations on adaptive randomization which are used to compromise between this scheme and equal randomization. The first variation is to apply a power transformation to p to obtain randomization probabilities. The second is to clip p to live within specified lower and upper bounds.
Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It... more Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context.
This paper considers a system of equations consisting of a nonlinear evolution equation on an ope... more This paper considers a system of equations consisting of a nonlinear evolution equation on an open set Ωin coupled to another nonlinear evolution equation on the boundary GΩ. Rather general assumptions are made concerning the operators involved and the coupling between the two problems. Existence and uniqueness are demonstrated via a semigroup of nonlinear operators on L1 (Ω) XL1 (GΩ).
Abstract: Special requirements for airfields are driven by the need to design, construct and main... more Abstract: Special requirements for airfields are driven by the need to design, construct and maintain airfield pavements, which will satisfy the concerns of the international aviation community over potential safety issues.
Abstract: In the United Kingdom the Ministry of Defense and TRL have been working together since ... more Abstract: In the United Kingdom the Ministry of Defense and TRL have been working together since the late 1980s in order to reduce the impact of reflection cracking on military airfields. Reflection cracking affects pavements to a greater or lesser extent at over 85% of MOD airfields.
Many Bayesian clinical trial methods are based on random inequalities. For some distribution fami... more Many Bayesian clinical trial methods are based on random inequalities. For some distribution families, these inequalities can be computed in closed form. For example, [1] gives closed-form solutions to computing P(X > Y) when X and Y are either independent normal or independent gamma random variables. However the case of beta random variables is very important and no closed form solution for this case is known. Such inequalities must be evaluated numerically.
Abstract This report examines in detail a family of efficacy-toxicity trade-off functions simpler... more Abstract This report examines in detail a family of efficacy-toxicity trade-off functions simpler and more general than those originally proposed in [1]. The new trade-off functions are based on distance in Lp norm to the ideal point and were first presented in [2]. We define and illustrate these functions and demonstrate how to compute their parameters based on elicited values.
Abstract: This paper describes how airfield pavements must facilitate safe aircraft ground operat... more Abstract: This paper describes how airfield pavements must facilitate safe aircraft ground operations. This in turn necessitates special design considerations with respect to several key functional requirements. The structural design and evaluation of airfield pavements can involve wheel loads up to 28 tons and arranged in various multiple configurations. Surface serviceability requirements can necessitate special considerations in respect of material specifications, construction and maintenance of airfield pavements.
Abstract Adaptively randomized trials aim to treat patients in clinical trials more effectively b... more Abstract Adaptively randomized trials aim to treat patients in clinical trials more effectively by increasing the probability of assigning treatments that appear to have a higher probability of response. Studies of adaptive randomization to date have assumed constant probabilities of response on each treatment. This paper examines the effect of response probabilities that change over time due to population drift.
Totally fissured media in which the cells are isolated by the fissure system are effectively desc... more Totally fissured media in which the cells are isolated by the fissure system are effectively described by double porosity models with microstructure. These models contain the geometry of the individual cells or pores in the medium and the flux across their interface with the fissures which surrounds them. We extend these models to include the case of partially fissured media in which a secondary flux effect arises from cell-to-cell diffusion paths.
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