A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

Nonstationary brand variables in category management: A cointegration perspective

Category-management models serve to assist in the development of plans for pricing and promotions of individual brands. Techniques to solve the models can have problems of accuracy and interpretability because they are susceptible to spurious regression problems due to nonstationary time-series data. Improperly stated nonstationary systems can reduce the accuracy of the forecasts and undermine the interpretation of the results. This is problematic because recent studies indicate that sales are often a nonstationary time-series. Newly developed correction techniques can account for nonstationarity by incorporating error-correction terms into the model when using a Bayesian Vector Error-Correction Model. The benefit of using such a technique is that shocks to control variates can be separated into permanent and temporary effects and allow cointegration of series for analysis purposes. Analysis of a brand data set indicates that this is important even at the brand level. Thus, additional information is generated that allows a decision maker to examine controllable variables in terms of whether they influence sales over a short or long duration. Only products that are nonstationary in sales volume can be manipulated for long-term profit gain, and promotions must be cointegrated with brand sales volume. The brand data set is used to explore the capabilities and interpretation of cointegration.

Earthquake statistics in a Block Slider Model and a fully dynamic Fault Model

We examine the event statistics obtained from two differing simplified models for earthquake faults. The first model is a reproduction of the Block-Slider model of Carlson et al. (1991), a model often employed in seismicity studies. The second model is an elastodynamic fault model based upon the Lattice Solid Model (LSM) of Mora and Place (1994). We performed simulations in which the fault length was varied in each model and generated synthetic catalogs of event sizes and times. From these catalogs, we constructed interval event size distributions and inter-event time distributions. The larger, localised events in the Block-Slider model displayed the same scaling behaviour as events in the LSM however the distribution of inter-event times was markedly different. The analysis of both event size and inter-event time statistics is an effective method for comparative studies of differing simplified models for earthquake faults.

Increased potency of a novel complement factor 5a receptor antagonist in a rat model of inflammatory bowel disease

We have previously shown that complement factor 5a(C5a) plays a role in the pathogenesis of 2,4,6-trinitrobenzene sulfonic acid (TNBS)-induced colitis in rats by using the selective, orally active C5a antagonist AcF-[OP(D-Cha) WR]. This study tested the efficacy and potency of a new C5a antagonist, hydrocinnamate (HC)-[OP(D-Cha) WR], which has limited intestinal lumenal metabolism, in this model of colitis. Analogs of AcF-[OP(D-Cha) WR] were examined for their susceptibility to alimentary metabolism in the rat using intestinal mucosal washings. One metabolically stable analog, HC-[OP(D-Cha)WR], was then evaluated pharmacokinetically and investigated at a range of doses (0.03 - 10 mg/kg/ day p.o.) in the 8-day rat TNBS- colitis model, against the comparator drug AcF-[OP(D-Cha) WR]. Using various amino acid substitutions, it was determined that the AcF moiety of AcF-[OP(D-Cha) WR] was responsible for the metabolic instability of the compound in intestinal mucosal washings. The analog HC-[OP( D-Cha) WR], equiactive in vitro to AcF-[OP(D-Cha) WR], was resistant to intestinal metabolism, but it displayed similar oral bioavailability to AcF-[OP(D-Cha) WR]. However, in the rat TNBS- colitis model, HC-[OP(D-Cha) WR] was effective at reducing mortality, colon edema, colon macroscopic scores, and increasing food consumption and body weights, at 10- to 30- fold lower oral doses than AcF-[OP( D-Cha) WR]. These studies suggest that resistance to intestinal metabolism by HC-[OP(D-Cha) WR] may result in increased local concentrations of the drug in the colon, thus affording efficacy with markedly lower oral doses than AcF-[OP(D-Cha) WR] against TNBS-colitis. This large increase in potency and high efficacy of this compound makes it a potential candidate for clinical development against intestinal diseases such as inflammatory bowel disease.

An inverse method for designing loaded RF coils in MRI

Radio-frequency ( RF) coils are designed such that they induce homogeneous magnetic fields within some region of interest within a magnetic resonance imaging ( MRI) scanner. Loading the scanner with a patient disrupts the homogeneity of these fields and can lead to a considerable degradation of the quality of the acquired image. In this paper, an inverse method is presented for designing RF coils, in which the presence of a load ( patient) within the MRI scanner is accounted for in the model. To approximate the finite length of the coil, a Fourier series expansion is considered for the coil current density and for the induced fields. Regularization is used to solve this ill-conditioned inverse problem for the unknown Fourier coefficients. That is, the error between the induced and homogeneous target fields is minimized along with an additional constraint, chosen in this paper to represent the curvature of the coil windings. Smooth winding patterns are obtained for both unloaded and loaded coils. RF fields with a high level of homogeneity are obtained in the unloaded case and a limit to the level of homogeneity attainable is observed in the loaded case.

Network topology and the evolution of dynamics in an artificial genetic regulatory network model created by whole genome duplication and divergence

Topological measures of large-scale complex networks are applied to a specific artificial regulatory network model created through a whole genome duplication and divergence mechanism. This class of networks share topological features with natural transcriptional regulatory networks. Specifically, these networks display scale-free and small-world topology and possess subgraph distributions similar to those of natural networks. Thus, the topologies inherent in natural networks may be in part due to their method of creation rather than being exclusively shaped by subsequent evolution under selection. The evolvability of the dynamics of these networks is also examined by evolving networks in simulation to obtain three simple types of output dynamics. The networks obtained from this process show a wide variety of topologies and numbers of genes indicating that it is relatively easy to evolve these classes of dynamics in this model. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

Epidermal iontophoresis: I. Development of the ionic mobility-pore model

Purpose, An integrated ionic mobility-pore model for epidermal iontophoresis is developed from theoretical considerations using both the free volume and pore restriction forms of the model for a range of solute radii (r(j)) approaching the pore radii (r(p)) as well as approximation of the pore restriction form for r(j)/r(p) < 0.4. In this model, we defined the determinants for iontophoresis as solute size (defined by MV, MW or radius), solute mobility, solute shape, solute charge, the Debye layer thickness, total current applied, solute concentration, fraction ionized, presence of extraneous ions (defined by solvent conductivity), epidermal permselectivity, partitioning rates to account for interaction of unionized and ionized lipophilic solutes with the wall of the pore and electroosmosis. Methods, The ionic mobility-pore model was developed from theoretical considerations to include each of the determinants of iontophoretic transport. The model was then used to reexamine iontophoretic flux conductivity and iontophoretic flux-fraction ionized literature data on the determinants of iontophoretic flux. Results. The ionic mobility-pore model was found to be consistent with existing experimental data and determinants defining iontophoretic transport. However, the predicted effects of solute size on iontophoresis are more consistent with the pore-restriction than free volume form of the model. A reanalysis of iontophoretic flux-conductivity data confirmed the model's prediction that, in the absence of significant electroosmosis, the reciprocal of flux is linearly related to either donor or receptor solution conductivity. Significant interaction with the pore walls, as described by the model, accounted for the reported pH dependence of the iontophoretic transport for a range of ionizable solutes. Conclusions. The ionic mobility-pore iontophoretic model developed enables a range of determinants of iontophoresis to be described in a single unifying equation which recognises a range of determinants of iontophoretic flux.

A comparison of lipopolysaccharide-induced hepatitis in ethanol-fed Wistar and Lewis rats

Elevated concentrations of plasma proinflammatory cytokines have been detected in patients with alcoholic hepatitis (AH) and in a model of lipopolysaccharide-induced hepatitis in ethanol-fed Wistar rats. These cytokines have been implicated in the pathogenesis of the liver damage. Considering the likely involvement of the immune system in AH, and the frequent use of Lewis rats in autoimmune disease models, Lewis rats were examined in the model to determine whether they would more closely mimic the immune status of a chronic alcoholic and be a preferable strain for use in future experiments. Lipopolysaccharide-induced hepatic tumor necrosis factor-cu, interleukin-1 alpha, interleukin-1 beta, and interleukin-6 mRNA expression was examined in both rat strains. The overall pattern of histological (panlobular piecemeal necrosis) and biochemical liver damage (plasma ALT levels), and cytokine expression was similar in both strains. Thus, it would appear that, despite the known susceptibility of Lewis rats to autoimmune phenomena, they do not respond to the experimental regime significantly better than Wistar rats. This study confirms that unknown mediators are contributing to the liver damage seen in this model and possibly in AH.

Chemokine and cell adhesion molecule mRNA expression and neutrophil infiltration in lipopolysaccharide-induced hepatitis in ethanol-fed rats

Neutrophil infiltration is a feature of alcoholic hepatitis (AH), and although the mechanism by which this occurs is unclear, it may involve a chemotactic gradient. We used lipopolysaccharide (LPS) to induce, in ethanol-fed rats, liver damage similar to that seen in AH. To our knowledge, this study is the first to examine the effect of ethanol on LPS-stimulated chemokine mRNA expression in this model. Hepatic cytokine-induced neutrophil chemoattractant (CINC)-1, CINC-2, monocyte chemoattractant protein-1 (MCP-1), macrophage inflammatory protein (MIP)-1 beta, MIP-2, and eotaxin mRNA levels were elevated 1 to 3 hr post-LPS in both groups. Maximal expression of MIP-2 and MCP-1 mRNA was higher in ethanol-fed rats 1 hr post-LPS, whereas CINC-2 mRNA expression was elevated above controls at 12 to 24 hr. Hepatic intercellular adhesion molecule-1 and vascular cell adhesion molecule-1 mRNA levels were elevated in both groups at 1 hr, whereas L-selectin expression in ethanol-fed rats was elevated above controls at 12 to 24 hr. Hepatic neutrophil infiltration was highest during maximal hepatocyte necrosis. These data suggest that cell adhesion molecules, in conjunction with elevated cytokines and the subsequently induced chemokines, may assist in the formation of a chemotactic gradient within the liver, causing the neutrophil infiltration seen both in this model and possibly in AH.

Evolution of three-dimensional folds for a non-Newtonian plate in a viscous medium

We derive analytical solutions for the three-dimensional time-dependent buckling of a non-Newtonian viscous plate in a less viscous medium. For the plate we assume a power-law rheology. The principal, axes of the stretching D-ij in the homogeneously deformed ground state are parallel and orthogonal to the bounding surfaces of the plate in the flat state. In the model formulation the action of the less viscous medium is replaced by equivalent reaction forces. The reaction forces are assumed to be parallel to the normal vector of the deformed plate surfaces. As a consequence, the buckling process is driven by the differences between the in-plane stresses and out of plane stress, and not by the in-plane stresses alone as assumed in previous models. The governing differential equation is essentially an orthotropic plate equation for rate dependent material, under biaxial pre-stress, supported by a viscous medium. The differential problem is solved by means of Fourier transformation and largest growth coefficients and corresponding wavenumbers are evaluated. We discuss in detail fold evolutions for isotropic in-plane stretching (D-11 = D-22), uniaxial plane straining (D-22 = 0) and in-plane flattening (D-11 = -2D(22)). Three-dimensional plots illustrate the stages of fold evolution for random initial perturbations or initial embryonic folds with axes non-parallel to the maximum compression axis. For all situations, one dominant set of folds develops normal to D-11, although the dominant wavelength differs from the Biot dominant wavelength except when the plate has a purely Newtonian viscosity. However, in the direction parallel to D-22, there exist infinitely many modes in the vicinity of the dominant wavelength which grow only marginally slower than the one corresponding to the dominant wavelength. This means that, except for very special initial conditions, the appearance of a three-dimensional fold will always be governed by at least two wavelengths. The wavelength in the direction parallel to D-11 is the dominant wavelength, and the wavelength(s) in the direction parallel to D-22 is determined essentially by the statistics of the initial state. A comparable sensitivity to the initial geometry does not exist in the classic two-dimensional folding models. In conformity with tradition we have applied Kirchhoff's hypothesis to constrain the cross-sectional rotations of the plate. We investigate the validity of this hypothesis within the framework of Reissner's plate theory. We also include a discussion of the effects of adding elasticity into the constitutive relations and show that there exist critical ratios of the relaxation times of the plate and the embedding medium for which two dominant wavelengths develop, one at ca. 2.5 of the classical Biot dominant wavelength and the other at ca. 0.45 of this wavelength. We propose that herein lies the origin of parasitic folds well known in natural examples.

Kinetics of propranolol uptake in muscle, skin, and fat of the isolated perfused rat hindlimb

The tissue distribution kinetics of a highly bound solute, propranolol, was investigated in a heterogeneous organ, the isolated perfused limb, using the impulse-response technique and destructive sampling. The propranolol concentration in muscle, skin, and fat as well as in outflow perfusate was measured up to 30 min after injection. The resulting data were analysed assuming (1) vascular, muscle, skin and fat compartments as well mixed (compartmental model) and (2) using a distributed-in-space model which accounts for the noninstantaneous intravascular mixing and tissue distribution processes but consists only of a vascular and extravascular phase (two-phase model). The compartmental model adequately described propranolol concentration-time data in the three tissue compartments and the outflow concentration-time curve (except of the early mixing phase). In contrast, the two-phase model better described the outflow concentration-time curve but is limited in accounting only for the distribution kinetics in the dominant tissue, the muscle. The two-phase model well described the time course of propranolol concentration in muscle tissue, with parameter estimates similar to those obtained with the compartmental model. The results suggest, first that the uptake kinetics of propranolol into skin and fat cannot be analysed on the basis of outflow data alone and, second that the assumption of well-mixed compartments is a valid approximation from a practical point of view las, e.g., in physiological based pharmacokinetic modelling). The steady-state distribution volumes of skin and fat were only 16 and 4%, respectively, of that of muscle tissue (16.7 ml), with higher partition coefficient in fat (6.36) than in skin (2.64) and muscle (2.79. (C) 2000 Elsevier Science B.V. All rights reserved.

Prediction of rock alteration patterns: a potential tool in mineral exploration

Hydrothermal alteration of a quartz-K-feldspar rock is simulated numerically by coupling fluid flow and chemical reactions. Introduction of CO2 gas generates an acidic fluid and produces secondary quartz, muscovite and/or pyrophyllite at constant temperature and pressure of 300 degrees C and 200 MPa. The precipitation and/or dissolution of the secondary minerals is controlled by either mass-action relations or rate laws. In our simulations the mass of the primary elements are conserved and the mass-balance equations are solved sequentially using an implicit scheme in a finite-element code. The pore-fluid velocity is assumed to be constant. The change of rock volume due to the dissolution or precipitation of the minerals, which is directly related to their molar volume, is taken into account. Feedback into the rock porosity and the reaction rates is included in the model. The model produces zones of pyrophyllite quartz and muscovite due to the dissolution of K-feldspar. Our model simulates, in a simplified way, the acid-induced alteration assemblages observed in various guises in many significant mineral deposits. The particular aluminosilicate minerals produced in these experiments are associated with the gold deposits of the Witwatersrand Basin.

Evolution of stress deficit and changing rates of seismicity in cellular automaton models of earthquake faults

We investigate the internal dynamics of two cellular automaton models with heterogeneous strength fields and differing nearest neighbour laws. One model is a crack-like automaton, transferring ail stress from a rupture zone to the surroundings. The other automaton is a partial stress drop automaton, transferring only a fraction of the stress within a rupture zone to the surroundings. To study evolution of stress, the mean spectral density. f(k(r)) of a stress deficit held is: examined prior to, and immediately following ruptures in both models. Both models display a power-law relationship between f(k(r)) and spatial wavenumber (k(r)) of the form f(k(r)) similar tok(r)(-beta). In the crack model, the evolution of stress deficit is consistent with cyclic approach to, and retreat from a critical state in which large events occur. The approach to criticality is driven by tectonic loading. Short-range stress transfer in the model does not affect the approach to criticality of broad regions in the model. The evolution of stress deficit in the partial stress drop model is consistent with small fluctuations about a mean state of high stress, behaviour indicative of a self-organised critical system. Despite statistics similar to natural earthquakes these simplified models lack a physical basis. physically motivated models of earthquakes also display dynamical complexity similar to that of a critical point system. Studies of dynamical complexity in physical models of earthquakes may lead to advancement towards a physical theory for earthquakes.

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying U-q(sl (2/1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.

Three-dimensional model for multi-component reactive transport with variable density groundwater flow

PHWAT is a new model that couples a geochemical reaction model (PHREEQC-2) with a density-dependent groundwater flow and solute transport model (SEAWAT) using the split-operator approach. PHWAT was developed to simulate multi-component reactive transport in variable density groundwater flow. Fluid density in PHWAT depends not on only the concentration of a single species as in SEAWAT, but also the concentrations of other dissolved chemicals that can be subject to reactive processes. Simulation results of PHWAT and PHREEQC-2 were compared in their predictions of effluent concentration from a column experiment. Both models produced identical results, showing that PHWAT has correctly coupled the sub-packages. PHWAT was then applied to the simulation of a tank experiment in which seawater intrusion was accompanied by cation exchange. The density dependence of the intrusion and the snow-plough effect in the breakthrough curves were reflected in the model simulations, which were in good agreement with the measured breakthrough data. Comparison simulations that, in turn, excluded density effects and reactions allowed us to quantify the marked effect of ignoring these processes. Next, we explored numerical issues involved in the practical application of PHWAT using the example of a dense plume flowing into a tank containing fresh water. It was shown that PHWAT could model physically unstable flow and that numerical instabilities were suppressed. Physical instability developed in the model in accordance with the increase of the modified Rayleigh number for density-dependent flow, in agreement with previous research. (c) 2004 Elsevier Ltd. All rights reserved.