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PubMed1997

Modeling volatility using state space models.

In time series problems, noise can be divided into two categories: dynamic noise which drives the process, and observational noise which is added in the measurement process, but does not influence future values of the system. In this framework, we show that empirical volatilities (the squared relative returns of prices) exhibit a significant amount of observational noise. To model and predict their time evolution adequately, we estimate state space models that explicitly include observational noise. We obtain relaxation times for shocks in the logarithm of volatility ranging from three weeks (for foreign exchange) to three to five months (for stock indices). In most cases, a two-dimensional hidden state is required to yield residuals that are consistent with white noise. We compare these results with ordinary autoregressive models (without a hidden state) and find that autoregressive models underestimate the relaxation times by about two orders of magnitude since they do not distinguish between observational and dynamic noise. This new interpretation of the dynamics of volatility in terms of relaxators in a state space model carries over to stochastic volatility models and to GARCH models, and is useful for several problems in finance, including risk management and the pricing of derivative securities. Data sets used: Olsen & Associates high frequency DEM/USD foreign exchange rates (8 years). Nikkei 225 index (40 years). Dow Jones Industrial Average (25 years).

Artificial Intelligence↗

PubMed2006

Model selection for geostatistical models.

We consider the problem of model selection for geospatial data. Spatial correlation is often ignored in the selection of explanatory variables, and this can influence model selection results. For example, the importance of particular explanatory variables may not be apparent when spatial correlation is ignored. To address this problem, we consider the Akaike Information Criterion (AIC) as applied to a geostatistical model. We offer a heuristic derivation of the AIC in this context and provide simulation results that show that using AIC for a geostatistical model is superior to the often-used traditional approach of ignoring spatial correlation in the selection of explanatory variables. These ideas are further demonstrated via a model for lizard abundance. We also apply the principle of minimum description length (MDL) to variable selection for the geostatistical model. The effect of sampling design on the selection of explanatory covariates is also explored. R software to implement the geostatistical model selection methods described in this paper is available in the Supplement.

Animals↗

PubMed1999

Biomass accumulation and clogging in biotrickling filters for waste gas treatment. Evaluation of a dynamic model using dichloromethane as a model pollutant.

A dynamic model is developed that describes the degradation of volatile acidifying pollutants in biotrickling filters (BTFs) for waste gas purification. Dynamic modelling enables the engineer to predict the clogging rate of a filter bed and the time it takes the BTF to adapt to changes in its inlet concentration. The most important mechanisms that govern the behaviour of the BTF are incorporated in the model. The time scale of the accumulation of biomass in a filter is investigated, and an approach is presented that can be used to estimate how long a BTF can be operated before its packing has to be cleaned. A three-month experiment was carried out to validate the model, using dichloromethane (DCM) as a model acidifying pollutant. Valuable experimental data about biomass accumulation and liquid hold-up in the reactor were obtained with an experimental set-up that allows the continuous registration of the weight of the BTF. The results show that in BTFs eliminating DCM from a waste gas, clogging is not to be expected up to concentrations of several g/m3. Model calculations based on the measurements also suggest that the maximum carbon load that can safely be applied per unit void packing volume should not exceed 0.5-1.6 C mol/(m3. h), depending on the density of the biofilm formed. The model is a good predictor of the elimination of the pollutant in the system, the axial gas and liquid concentration profiles, the axial biomass distribution, and the response of the system upon a stepwise increase in the DCM inlet concentration. The influence of the buffer concentrations in the liquid phase upon the performance of the BTF is investigated.

Air Pollutants↗

PubMedDate not supplied

Posterior predictive model checks for disease mapping models.

Disease incidence or disease mortality rates for small areas are often displayed on maps. Maps of raw rates, disease counts divided by the total population at risk, have been criticized as unreliable due to non-constant variance associated with heterogeneity in base population size. This has led to the use of model-based Bayes or empirical Bayes point estimates for map creation. Because the maps have important epidemiological and political consequences, for example, they are often used to identify small areas with unusually high or low unexplained risk, it is important that the assumptions of the underlying models be scrutinized. We review the use of posterior predictive model checks, which compare features of the observed data to the same features of replicate data generated under the model, for assessing model fitness. One crucial issue is whether extrema are potentially important epidemiological findings or merely evidence of poor model fit. We propose the use of the cross-validation posterior predictive distribution, obtained by reanalyzing the data without a suspect small area, as a method for assessing whether the observed count in the area is consistent with the model. Because it may not be feasible to actually reanalyze the data for each suspect small area in large data sets, two methods for approximating the cross-validation posterior predictive distribution are described.

Algorithms↗

PubMed2005

Application of model discriminating experimental design for modeling and development of a fermentative fed-batch L-valine production process.

A model discriminating experimental design approach for fed-batch processes has been developed and applied to the fermentative production of L-valine by a genetically modified Corynebacterium glutamicum strain possessing multiple auxotrophies as an example. Being faced with the typical situation of uncertain model information based on preliminary experiments, model discriminating design was successfully applied to improve discrimination between five competing models. Within the same modeling and experimental design framework, also the planning of an optimized production process with respect to the total volumetric productivity is shown. Simulation results were experimentally affirmed, yielding an increased total volumetric productivity of 6.2 mM L-valine per hour. However, also so far unknown metabolic mechanisms were observed in the optimized process, underlining the importance of process optimization during modeling to avoid problems of extreme extrapolation of model predictions during the final process optimization.

Biotechnology↗

PubMed1989

Modelling sibship environment in the regressive logistic model for familial disease.

Recently analytical models for pedigree disease data have been developed that combine genetic and epidemiological modelling techniques. The regressive logistic model [Bonney, Biometrics 42: 611-625; 1986] relies on decomposing the likelihood of a pedigree into the product of conditional probabilities, one for each individual, by imposing a (natural) order on pedigree members. In addition to modelling measured epidemiological variables, vertical transmission, transmission of unmeasured ousiotypes (a special case being genotypes), and some modelling of sibship dependencies have been proposed. In this paper the model is extended to include an unmeasured sibship environment factor using a log-linear model for binary pedigree traits [Hopper et al., Genet Epidemiol 1: 183-188; 1984], which breaks the pedigree into conditionally independent groups. Statistical issues, such as designs for which these factors will be discernible and tests of fit, are discussed.

Environment↗

PubMed1994

Genetic analysis combining path analysis with regressive models: the BETA path model of polygenic and familial environmental transmission.

We have extended the class D regressive model for the purpose of combined path and segregation analyses by incorporating the BETA path model. We have done this by expressing correlations among residuals from major genotype (RMGs) of family members under the class D regressive model as functions of path coefficients under the BETA path model. The likelihood function under the combined model was factorized into a product of conditional densities, which is dominated by bivariate normal densities. Statistical inferences under the combined model are analogous to those under the class D regressive model.

Binomial Distribution↗

PubMed2004

Solvation model induced structural changes in peptides. A quantum chemical study on Ramachandran surfaces and conformers of alanine diamide using the polarizable continuum model.

Potential energy surfaces of the model peptide HCO-L-Ala-NH2 were calculated using polarizable continuum model (PCM) for the description of aqueous solution at RHF/3-21G, RHF/6-31+G(d), and B3LYP/6-31+G(d) levels of theory. Energy minima were optimized at all three levels as well as at B3LYP/PCM/6-311++G(d,p) level of theory. Results were correlated to experimental data of protein structures retrieved from PDB SELECT. It is concluded that alanine residues of proteins are modeled better by PCM results than by gas-phase calculations on the alanine diamide model (frequently called alanine dipeptide model). The currently available version of the PCM model implemented in Gaussian 03 provides a reasonable alternative to anticipate solvation effects without the computational costs of introducing explicit solvent molecules into the model system. Frequencies calculated at RHF/PCM/6-31+G(d) and B3LYP/PCM/6-31+G(d) levels of theory show high correlation; thus, RHF results have their own merit.

Alanine↗

PubMed2004

Adjusting for differential proportions of second-line treatment in cancer clinical trials. Part I: structural nested models and marginal structural models to test and estimate treatment arm effects.

In randomized trials, post-randomization variables such as compliance, prescription of alternative treatments and so on are usually ignored to compare treatment arms. Intent-to-treat (ITT) analysis is a standard approach but it does not adjust for those variables. However, we may need to evaluate treatment arm effects that have the desired causal interpretation. Previously proposed methods such as time-dependent Cox model may not properly adjust for post-randomization variables and may produce biased results. Alternatively, we propose to use two causal models, structural nested models and marginal structural models. The two models appropriately adjust for such variables. We apply these models to adjust for differential proportions of post-randomization second-line treatment in cancer clinical trials. With sufficient care to several assumptions, these methods, especially structural nested failure time models with randomized analyses, are useful to take the influence of second-line treatment into account and to test and estimate the direct treatment arm effect.

Humans↗

PubMedDate not supplied

Modelling survival data with a cured fraction using frailty models.

Cure models have historically been utilized to analyse time-to-event data with a cured fraction. We consider the use of frailty models as an alternative approach to modelling such data. An attractive feature of the models is the allowance for heterogeneity in risk among those individuals experiencing the event of interest in addition to the incorporation of a cured component. Utilizing maximum likelihood techniques, we fit models to data concerning the recurrence of leukaemia among patients receiving autologous transplantation treatment. The analysis suggests that the gamma frailty mixture model and the compound Poisson improve on the fit of the leukaemia data as compared to the standard cure model.

Humans↗

PubMed1994

Numerical analysis of a model of ligand-induced B-cell antigen-receptor clustering. Implications for simple models of B-cell activation in an immune network.

B-cell activation driven by ligand-induced crosslinking of membrane immunoglobulin (mIg) is one of the most important processes in experimental and theoretical immunology. Although the activation of B cells through mIgs involves a complex series of intracellular processes, in immune network models it is usually assumed that there is a correlation between the degree of mIg crosslinking and the probability of B-cell activation. We explore the implications of this hypothesis by studying a model of ligand-induced B-cell receptor clustering proposed by Bell and further elaborated by Delisi and Perelson (BDP model). In this model, a critical time (tc) is defined at which the probability of infinite size complex formation (i.e., percolation) becomes non-zero. We use this variable, tc, as a means to characterize the degree of mIg crosslinking. To study the dependence of tc with respect to ligand valence, kinetic constants and ligand-receptor affinity x ligand concentration (K x C), we perform a systematic numerical study of the BDP model for parameter ranges including current empirical estimates for the kinetic constants. Concerning tc, we find that, for ranges of immunological interest (namely, those including current estimates of dissociation and receptor crosslinking rate constants), the curves obtained by plotting 1/tc vs. log(K x C) shift sensibly towards higher values of log(K x C), broadening and increasing its maximum amplitude, as the dissociation rate constant increases. As this finding suggests important consequences for immune network models, we further study the BDP model in an extended version for the case of two different ligands interacting simultaneously with a given B cell.3+

Animals↗

PubMed2002

Modelling mammary metabolism in the dairy cow to predict milk constituent yield, with emphasis on amino acid metabolism and milk protein production: model evaluation.

A model of mammary metabolism has been constructed and parameterized, with milk protein synthesis represented as a function of five essential amino acids (EAA) (Hanigan et al., 2001). Herein the model is evaluated using both the data used to construct the model (reference data) and an independent data set (literature data), and sensitivity to inputs and parameter estimates is assessed. The model predicted metabolite removal well for the reference data with exceptions for glutamate, glucose, and acetate. However, predictions of milk protein synthesis exhibited significant mean positive bias, which apparently was associated with the representation of milk protein synthesis. Adjustment of model parameters removed the mean bias, however, prediction accuracy was still inadequate. Simulation of the single reference experiment containing all critical inputs resulted in predictions of milk protein output that explained 53% of the observed variation, suggesting that the limited accuracy of the model when applied to the entire reference data set was due to assumptions regarding missing inputs. Mammary removal of glutamate, isoleucine, lysine, phenylalanine, tyrosine, valine, glycerol, beta -hydroxybutyrate (BHBA), and acetate were predicted less accurately when simulations of the independent data set were conducted. Twenty-five percent of the observed variation in milk protein yields for the independent data set was explained by the model. Refitting parameters for removal of isoleucine, lysine, phenylalanine, tyrosine, valine, glycerol, BHBA, and acetate raised the variation explained to 43%. Sensitivity analysis indicated that milk protein synthesis was responsive to only the five EAA used in its determination, with sensitivity to any single EAA falling to zero as supply of the EAA exceeded protein synthetic needs. Similarly, milk protein synthesis was readily affected by parameters associated with removal and metabolism of the five EAA. Milk lactose was found to be sensitive to glucose input as well as to similar parameters and inputs as milk protein. It is concluded that representation of the milk protein synthesis process as a function of a single limiting EAA may not be adequate and might be better represented by simultaneous consideration of multiple EAA. Additional work on the description of energy metabolism is also suggested.

Amino Acids↗

PubMed1997

Tumor specific contrast enhancement study of Mn-metalloporphyrin (ATN-10)--comparison of rat brain tumor model, cytotoxic and vasogenic edema models.

ATN-10, Mn-metalloporphyrin, has been developed as a tumor selective contrast agent for magnetic resonance (MR) imaging. To investigate the tumor specificity of ATN-10, we produced three experimental in vivo models; rat bran tumor (9L glioma) model, vasogenic (cold injury) and cytotoxic brain edema (24-hour MCA occlusion) models. The time course of contrast enhancement was compared after intravenous injection of ATN-10 or Gd-DTPA, measuring the signal intensity of the region of interest. After ATN-10 administration, the 9L glioma model showed early (5 min) and delayed (24 hr-) peak enhancement whereas the cold injury model showed only early enhancement and the 24-hour MCA occlusion model did not show significant enhancement. After Gd-DTPA administration, all three models showed similar pattern of only early enhancement. As a contrast agent for MR imaging, ATN-10 showed different behavior than Gd-DTPA in demonstrating the blood-brain barrier disruption and moreover ATN-10 showed selective enhancement in experimental brain tumors.

Animals↗

PubMed1981

An advanced version of the dynamic receptor pattern generation model: the flux model.

In the recently described simple model of dynamic receptor pattern generation we used a two dimensional hexagonal area of a regular triangular network, formed by a statistically constant distribution of unit electostatic changes in a dynamic equilibrium. A set of 16 trnasition rules was applied to all units simultaneously; the next state of each unit depended only on the previous state of its six nearest neighbours, and the transition of the total pattern into the new one occurred in a single jump. Hence we designated the initial simple model as "jump model". In this paper we described an advanced version of the model, in which simplified rules are applied to one unit after the other in a sequential order, from left to right, starting with the top row of units. In the advanced version the state of a unit depends not only on that of its six nearest neighbours, but also on the state of all units preceding in sequence the one actually considered. This results in flux-like transitions. We therefore designated the advanced version as the "flux model". It is shown that the flux model represents a closer approximation of physical and biological realities than the original jump model.

Animals↗

PubMed1992

Building population pharmacokinetic--pharmacodynamic models. I. Models for covariate effects.

One major task in clinical pharmacology is to determine the pharmacokinetic-pharmacodynamic (PK-PD) parameters of a drug in a patient population. NONMEM is a program commonly used to build population PK-PD models, that is, models that characterize the relationship between a patient's PK-PD parameters and other patient specific covariates such as the patient's (patho) physiological condition, concomitant drug therapy, etc. This paper extends a previously described approach to efficiently find the relationships between the PK-PD parameters and covariates. In a first step, individual estimates of the PK-PD parameters are obtained as empirical Bayes estimates, based on a prior NONMEN fit using no covariates. In a second step, the individual PK-PD parameter estimates are regressed on the covariates using a generalized additive model. In a third and final step, NONMEM is used to optimize and finalize the population model. Four real-data examples are used to demonstrate the effectiveness of the approach. The examples show that the generalized additive model for the individual parameter estimates is a good initial guess for the NONMEM population model. In all four examples, the approach successfully selects the most important covariates and their functional representation. The great advantage of this approach is speed. The time required to derive a population model is markedly reduced because the number of necessary NONMEM runs is reduced. Furthermore, the approach provides a nice graphical representation of the relationships between the PK-PD parameters and covariates.

Adult↗

PubMed1994

Mathematical model of cardiovascular mechanics for diagnostic analysis and treatment of heart failure: Part 1. Model description and theoretical analysis.

The planning of drug therapy for heart failure should involve both the diagnostic analysis of the patient's defective state and a prediction of the drug effects on the identified state. We have devised a mathematical model of cardiovascular system mechanics, on which both quantitative diagnosis and evaluation of drug effects can be made. The model was composed of systemic and pulmonary circulatory networks including the dynamics of the left and right ventricles. The model of the ventricles can represent both systolic and diastolic problems in heart failure through the parameters of ventricular contractility and diastolic stiffness. Each vascular network was composed of arterial and venous resistances and total vascular capacitance. Patient's ventricular and vascular parameters were estimated simultaneously from the clinically measurable haemodynamic variables based on the model. Despite the simplicity of the model, the results showed good agreement with clinical and experimental data. The clinically significant haemodynamic classification of heart failure by Forrester et al. (Forrester et al., 1977) was simulated well by the model. This model provides a useful basis for analysing pathophysiological states in heart failure and evaluating drug effects on the disease.

Heart↗

PubMed1996

Modeling facilitative sugar transporters: transitions between single and double ligand occupancy of multiconformational channel models explain anomalous kinetics.

The four-state simple carrier model (SCM) is employed to describe ligand translocation by diverse passive membrane transporters. However, its application to systems like facilitative sugar transporters (GLUTs) is controversial: unidirectional fluxes under zero-trans and equilibrium-exchange experimental conditions fit a SCM, but flux data from infinite-cis and infinite-trans experiments appear not to fit the same SCM. More complex kinetic models have been proposed to explain this "anomalous" behavior of GLUTs, but none of them accounts for all the experimental findings. We propose an alternative model in which GLUTs are channels subject to conformational transitions, and further assume that the results from zero-trans and equilibrium-exchange experiments as well as trans-effects corresponds to a single-occupancy channel regime, whereas the results from the infinite-cis and infinite-trans experiments correspond to a regime including higher channel occupancies. We test the plausibility of this hypothesis by studying a kinetic model of a two-site channel with two conformational states. In each state, the channel can bind the ligand from only one of the compartments. Under single-occupancy, for conditions corresponding to zero-trans and equilibrium-exchange experiments, the model behaves as a SCM capable of exhibiting trans-stimulations. For a regime including higher degrees of occupancy and infinite-cis and infinite-trans conditions, the same channel model can exhibit a behavior qualitatively similar to a SCM, albeit with kinetic parameters different from those for the single-occupancy regime. Numerical results obtained with our model are consistent with available experimental data on facilitative glucose transport across erythrocyte membranes. Hence, if GLUTs are multiconformational channels, their particular kinetic properties can result from transitions between single and double channel occupancies.

Carbohydrate Metabolism↗

PubMed2002

Modeling the spatial dynamics of regional land use: the CLUE-S model.

Land-use change models are important tools for integrated environmental management. Through scenario analysis they can help to identify near-future critical locations in the face of environmental change. A dynamic, spatially explicit, land-use change model is presented for the regional scale: CLUE-S. The model is specifically developed for the analysis of land use in small regions (e.g., a watershed or province) at a fine spatial resolution. The model structure is based on systems theory to allow the integrated analysis of land-use change in relation to socio-economic and biophysical driving factors. The model explicitly addresses the hierarchical organization of land use systems, spatial connectivity between locations and stability. Stability is incorporated by a set of variables that define the relative elasticity of the actual land-use type to conversion. The user can specify these settings based on expert knowledge or survey data. Two applications of the model in the Philippines and Malaysia are used to illustrate the functioning of the model and its validation.

Agriculture↗