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PubMed2001

Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling.

We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics, which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge of the distribution of couplings between the random variables is required, our method adapts to the concrete set of couplings. We show the significance of the approach in two ways: Our approach reproduces replica symmetric results for a wide class of toy models (assuming a nonglassy phase) with given disorder distributions in the thermodynamic limit. On the other hand, simulations on a real data model demonstrate that the method achieves more accurate predictions as compared to conventional TAP approaches.

Journal Article↗
PubMed1998

A Probabilistic Model of Criticality in a Sequential Public Good Dilemma.

A public good (PG) is a commodity or service made available to all members of a group: its provision depends on the voluntary contribution of its members. Once provided, all members can enjoy the benefits of the PG, regardless of whether they contributed or not; hence, there is a temptation to "free-ride" in the hope that others will contribute. Rapoport (1987) showed that an important factor that affects cooperation (contribution) in a PG dilemma is the extent to which a group member is critical in providing it. Erev and Rapoport (1990) tested a game-theoretic model that yields deterministic predictions about the effects of criticality on cooperation in public good dilemmas. Based on research by Chen, Au, and Komorita (1996), we propose a probabilistic model of criticality. The model is tested and found to fit empirical data. Extensions of the model to situations with uncertain group size or provision point are discussed. Copyright 1998 Academic Press.

Journal Article↗
PubMed1986

A probabilistic model for fitting MWC polynomials in protein-ligand binding.

Given a binding polynomial in Adair form, A(x) = 1 + beta 1 x + ... + beta n x n, beta i greater than or equal to 0, a basic problem is to determine a method of fitting a model polynomial to A(x) and a quantitative measure of the goodness of fit. This paper presents such a method for fitting Monod-Wyman-Changeux (MWC) model polynomials when A(x) is of degree three or four. The method of fitting is based on the property that the zeros of an MWC polynomial of any degree lie on a circle in the complex plane. The parameters in the MWC model are determined so that if possible this circle coincides with the circle on which lie the zeros of A(x). The measure of goodness of fit is provided by a probabilistic model which gives the probability that a binding polynomial has its zeros on a circle on which lie the zeros of an MWC polynomial and if so, the probability that the juxtaposition of the two sets of zeros can occur by chance alone.

Kinetics↗
PubMed1975

Mutation and childhood cancer: a probabilistic model for the incidence of retinoblastoma.

The incidences of some childhood cancers have been shown to fit a two-mutation hypothesis for cancer initiation. According to this hypothesis, the first mutation can be either germinal or somatic while the second is always somatic. A probabilistic model involving the mean number of tumors per genetically susceptible individual is developed as a function of age and is compared with age incidence data for retinoblastoma. The change in the mean number of tumors with time is interpreted in terms of the growth of retinal cells. In patients who are not genetically susceptible, the times of occurrence of the first and second somatic mutations can be inferred from a comparison of familial and non-familial unilateral case incidences. The total incidences of hereditary and nonhereditary forms of retinoblastoma are related to germinal and somatic mutation rates. The even distribution of certain childhood cancers throughout the world suggests that their incidences are determined by spontaneous mutation rates rather than by local environmental mutagenic carcinogens.

Child↗
PubMed2000

Evaluation of a probabilistic model for staging of oesophageal carcinoma.

With the help of two experts in gastrointestinal oncology from the Netherlands Cancer Institute, Antoni van Leeuwenhoekhuis, a decision-support system is being developed for patient-specific therapy selection for oesophageal carcinoma. The kernel of the system is a probabilistic model describing the characteristics of oesophageal carcinoma and the pathophysiological processes of invasion and metastasis. Using data from 185 patients, an evaluation study of the model was conducted. We found that for 86% of the patients, the model established the stage of the patient's carcinoma correctly.

Artificial Intelligence↗
PubMed2001

Rich probabilistic models for gene expression.

Clustering is commonly used for analyzing gene expression data. Despite their successes, clustering methods suffer from a number of limitations. First, these methods reveal similarities that exist over all of the measurements, while obscuring relationships that exist over only a subset of the data. Second, clustering methods cannot readily incorporate additional types of information, such as clinical data or known attributes of genes. To circumvent these shortcomings, we propose the use of a single coherent probabilistic model, that encompasses much of the rich structure in the genomic expression data, while incorporating additional information such as experiment type, putative binding sites, or functional information. We show how this model can be learned from the data, allowing us to discover patterns in the data and dependencies between the gene expression patterns and additional attributes. The learned model reveals context-specific relationships, that exist only over a subset of the experiments in the dataset. We demonstrate the power of our approach on synthetic data and on two real-world gene expression data sets for yeast. For example, we demonstrate a novel functionality that falls naturally out of our framework: predicting the "cluster" of the array resulting from a gene mutation based only on the gene's expression pattern in the context of other mutations.

Algorithms↗
PubMed2003

Probabilistic modelling for estimating gas kinetics and decompression sickness risk in pigs during H2 biochemical decompression.

We modelled the kinetics of H2 flux during gas uptake and elimination in conscious pigs exposed to hyperbaric H2. The model used a physiological description of gas flux fitted to the observed decompression sickness (DCS) incidence in two groups of pigs: untreated controls, and animals that had received intestinal injections of H2-metabolizing microbes that biochemically eliminated some of the H2 stored in the pigs' tissues. To analyse H2 flux during gas uptake, animals were compressed in a dry chamber to 24 atm (ca 88% H2, 9% He, 2% O2, 1% N2) for 30-1440 min and decompressed at 0.9 atm min(-1) (n = 70). To analyse H2 flux during gas elimination, animals were compressed to 24 atm for 3 h and decompressed at 0.45-1.8 atm min(-1) (n = 58). Animals were closely monitored for 1 h post-decompression for signs of DCS. Probabilistic modelling was used to estimate that the exponential time constant during H2 uptake (tau(in)) and H2 elimination (tau(out)) were 79 +/- 25 min and 0.76 +/- 0.14 min, respectively. Thus, the gas kinetics affecting DCS risk appeared to be substantially faster for elimination than uptake, which is contrary to customary assumptions of gas uptake and elimination kinetic symmetry. We discuss the possible reasons for this asymmetry, and why absolute values of H2 kinetics cannot be obtained with this approach.

Animals↗
PubMed2001

Population pharmacokinetic-pharmacodynamic model of craving in an enforced smoking cessation population: indirect response and probabilistic modeling.

PURPOSE: A population pharmacokinetic-pharmacodynamic model accounting for placebo effect was used to relate nicotine concentration and enforced smoking cessation craving score measured by the Tiffany rating scale short form. METHODS: Twenty-four smokers were enrolled in a placebo-controlled, randomized, double-blind, three periods, crossover trial. The study objective was to describe the nicotine-induced changes on craving scores. Two modeling strategies based on a mechanistic (indirect response models with drug-related inhibition on the k(in) synthesis rate and with a drug-related stimulation of the k(out) removal rate were evaluated) and a probabilistic (logistic regression) approach were used. RESULTS: Placebo response model properly fitted the circadian changes on craving scores. The analysis revealed that the indirect response model with inhibition on k(in) was the preferred model for the smoking data whereas the preferred model for the Nicotine Replacement Therapy data was the one with stimulation on k(out). The logistic analysis showed that the nicotine concentration was a significant predictor of reduction in craving during the free-smoking period. CONCLUSIONS: Nicotine dosage regimen can influence the nicotine mechanism of action: an instantaneous delivery at an individually selected time seems to inhibit the onset of craving while constant delivery at a pre-defined time seems to attenuate the craving.

Adult↗
PubMed2000

Probabilistic modeling of Saccharomyces cerevisiae inhibition under the effects of water activity, pH, and potassium sorbate concentration.

Probabilistic microbial modeling using logistic regression was used to predict the boundary between growth and no growth of Saccharomyces cerevisiae at selected incubation periods (50 and 350 h) in the presence of growth-controlling factors such as water activity (a(w); 0.97, 0.95, and 0.93), pH (6.0, 5.0, 4.0, and 3.0), and potassium sorbate (0, 50, 100, 200, 500, and 1,000 ppm). The proposed model predicts the probability of growth under a set of conditions and calculates critical values of a(w), pH, and potassium sorbate concentration needed to inhibit yeast growth for different probabilities. The reduction of pH increased the number of combinations of a(w) and potassium sorbate concentration with probabilities to inhibit yeast growth higher than 0.95. With a probability of growth of 0.05 and using the logistic models, the critical pH values were higher for 50 h of incubation than those required for 350 h. With lower a(w) values and increasing potassium sorbate concentration the critical pH values increased. Logistic regression is a useful tool to evaluate the effects of the combined factors on microbial growth.

Food Microbiology↗
PubMed2000

Probabilistic modeling of single-trial fMRI data.

This paper describes a probabilistic framework for modeling single-trial functional magnetic resonance (fMR) images based on a parametric model for the hemodynamic response and Markov random field (MRF) image models. The model is fitted to image data by maximizing a lower bound on the log likelihood. The result is an approximate maximum a posteriori estimate of the joint distribution over the model parameters and pixel labels. Examples show how this technique can used to segment two-dimensional (2-D) fMR images, or parts thereof, into regions with different characteristics of their hemodynamic response.

Brain↗
PubMed2001

Tractable approximations for probabilistic models: the adaptive Thouless-Anderson-Palmer mean field approach.

We develop an advanced mean field method for approximating averages in probabilistic data models that is based on the Thouless-Anderson-Palmer (TAP) approach of disorder physics. In contrast to conventional TAP, where the knowledge of the distribution of couplings between the random variables is required, our method adapts to the concrete couplings. We demonstrate the validity of our approach, which is so far restricted to models with nonglassy behavior, by replica calculations for a wide class of models as well as by simulations for a real data set.

Journal Article↗
PubMed2002

The use of food consumption data in assessments of exposure to food chemicals including the application of probabilistic modelling.

Emphasis on public health and consumer protection, in combination with globalisation of the food market, has created a strong demand for exposure assessments of food chemicals. The food chemicals for which exposure assessments are required include food additives, pesticide residues, environmental contaminants, mycotoxins, novel food ingredients, packaging-material migrants, flavouring substances and nutrients. A wide range of methodologies exists for estimating exposure to food chemicals, and the method chosen for a particular exposure assessment is influenced by the nature of the chemical, the purpose of the assessment and the resources available. Sources of food consumption data currently used in exposure assessments range from food balance sheets to detailed food consumption surveys of individuals and duplicate-diet studies. The fitness-for-purpose of the data must be evaluated in the context of data quality and relevance to the assessment objective. Methods to combine the food consumption data with chemical concentration data may be deterministic or probabilistic. Deterministic methods estimate intakes of food chemicals that may occur in a population, but probabilistic methods provide the advantage of estimating the probability with which different levels of intake will occur. Probabilistic analysis permits the exposure assessor to model the variability (true heterogeneity) and uncertainty (lack of knowledge) that may exist in the exposure variables, including food consumption data, and thus to examine the full distribution of possible resulting exposures. Challenges for probabilistic modelling include the selection of appropriate modes of inputting food consumption data into the models.

Consumer Product Safety↗
PubMed1997

Constructing probabilistic models.

Bayesian networks have become one of the most popular probabilistic techniques in AI, largely due to the development of several efficient inference algorithms. In this paper we describe a heuristic method for constructing Bayesian networks. Our construction method relies on the relationship between Bayesian networks and decomposable models, a special kind of graphical model. We explain this relationship and then show how it can be used to facilitate model construction. Finally, we describe an implemented computer program that illustrates these ideas.

Algorithms↗
PubMed1999

Probabilistic model for fluences and peak fluxes of solar energetic particles.

The model is intended for calculating the probability for solar energetic particles (SEP), i.e., protons and Z=2-28 ions, to have an effect on hardware and on biological and other objects in the space. The model describes the probability for the > or = 10 MeV/nucleon SEP fluences and peak fluxes to occur in the near-Earth space beyond the Earth magnetosphere under varying solar activity. The physical prerequisites of the model are as follows. 1. The occurrence of SEP is a probabilistic process. 2. The mean SEP occurrence frequency is a power-law function of solar activity (sunspot number). 3. The SEP size (taken to be the > or = 30 MeV proton fluence size) distribution is a power-law function within a 10(5)-10(11) proton/cm2 range. 4. The SEP event particle energy spectra are described by a common function whose parameters are distributed log-normally. 5. The SEP mean composition is energy-dependent and suffers fluctuations described by log-normal functions in separate events.

Cosmic Radiation↗
PubMed1997

Diagnostic boundaries, reasoning and depressive disorder, II. Application of a probabilistic model to the OPCS general population survey of psychiatric morbidity in Great Britain.

BACKGROUND: Reliable prevalence and risk estimation of psychiatric disorder is a cornerstone to achieving objectives in public health psychiatry. Research strategies have increasingly depended, therefore, upon the progressive evolution and refinement of diagnostic approaches designed to reflect better current knowledge concerning prognosis, course and outcome but essentially the need to improve agreement between users of the various schemes. METHODS: This paper contrasts a conventional with a probabilistic approach to the diagnosis of depression based upon the OPCS United Kingdom National survey of psychiatric morbidity. The probabilistic approach, while designed to mimic current diagnostic practice in relation to the depressive disorders, naturally includes provision for the allocation of respondents on a scale of diagnostic uncertainty according to the severity of their presenting condition. RESULTS: Findings are reported arising from the application of the probabilistic method to three areas of research interest in public health psychiatry, namely; an evaluation of additivity of event exposure and depressive morbidity, secondly use of the approach for investigating psychosocial models of depressive disorder and thirdly for assessing the agreement between depressive disorder when classified according to competing diagnostic schemes. CONCLUSIONS: The results show application of the probabilistic approach to provide a firm basis for achieving gains in both the stability and precision of risk profile estimation for depressive conditions.

Adolescent↗
PubMed1987

A probabilistic model of mosaicism based on the histological analysis of chimaeric rat liver.

The analysis of pattern development in mosaic and chimaeric animals has provided insight into a number of developmental problems. In order to aid the understanding of the dynamics of the development of mosaic tissues, a computer simulation of the generation of a mosaic tissue was created using simple probabilistic decisions. Results of quantitative analysis of the simulated mosaicism were compared with chimaeric liver. Chimaeric animals were produced by morula aggregation between histologically distinguishable strains of congenic rats. The livers of these animals revealed a pattern of patchy mosaicism unrelated to either acinar or lobular architecture of the organ. Independent quantifiable parameters were correlated and compared between the simulation and chimaeric liver tissue. This analysis showed that extensive cell migration is not required to develop finely variegated mosaic tissue and that the patterns of mosaicism observed could have resulted from tissue development in which as few as three reiterated decisions were required. First, the simulation established anlagen of two cell types of various specified proportions with randomly chosen placement. Second, in each generation of the simulation the order in which the cells divided was established randomly. Third, there was a random choice of the direction of placement of the daughter cell. The quantitative relationships between the proportion of cell types, the area of patches and the number of patches per unit area was consistent between the simulation and the chimaeric tissue.

Animals↗
PubMed2000

A practical application of probabilistic modelling in assessment of dietary exposure of fruit consumers to pesticide residues.

In 1996, studies on a range of organophosphate and carbamate pesticide residues in fruit that may be eaten as single items reported variability. The usual point estimate exposure model did not take account of the variation in residue levels between items or variation in consumption patterns of individual consumers. Using only the highest residue levels and consumption values for each of the multiple sources (different fruit) could lead to overestimates of residue intakes which would indicate higher than actual levels of risk. Probabilistic simulation was identified as a tool that could utilize all the available information from the variability studies and fruit consumption data collected from dietary surveys. The estimation of exposure of toddlers to carbaryl is shown as an example. The number of samples representing some combinations of fruit in the toddler dietary survey was particularly low and the validity of extrapolating from these was unknown. Therefore, consumption values were simulated using the data for frequency and amount eaten from the whole database. The data indicated that there were some weak positive associations between consumption levels of the different fruit. However, inclusion of correlated sampling in the model simulation was considered too conservative. The profiles of carbaryl residues in different retail batches differed. Therefore a model was constructed that differentiated between different residue profiles and sampled separate residue levels for each item assumed to be eaten. Two simpler models, both ignoring the effect of re-sampling from the same batch, were also used to estimate exposure. All three models were considered to give realistic views of the likely short-term intakes and the outputs were useful as an aid to decision-making in terms of necessary regulatory action.

Carbaryl↗
PubMed1991

A probabilistic model for genetic recombination of nonreplicating lambda-phage DNA, stimulated by "mismatch repair" of UV photoproducts.

Genetic recombination of nonreplicating phage lambda-DNA, during infection of homoimmune lysogenic bacteria, was previously observed to be dramatically stimulated by prior uv irradiation of the phages, even when the Escherichia coli hosts lacked the major uv-photo-product excision-repair system (UvrABC). UvrABC-independent recombination of circular phage molecules depends on host MutHLS functions and on undermethylation of adenines at GATC sites in the phage DNA, and thus appears to be the result of "mismatch repair" of uv photoproducts. Recombinant frequencies pass through a relatively sharp maximum at 20 J/m2 and decrease at higher doses, whereas most plausible models for the process predict monotonic increases with dose, or a plateau at high uv doses. A uv-dose-dependent loss of biological activity (restriction) of all intracellular phage DNA was also observed previously. In order to provide a framework for testing possible explanations for the unusual recombinant-frequency vs uv-dose curve, a statistical model was constructed. This model includes probability terms for all possible one-exchange and two-exchange recombination processes, and incorporates the assumption that dimer recombinants are more susceptible to restriction than monomer parents (or recombinants), because of their larger target size. By adjustment of model parameters, particularly epsilon, the efficiency per photoproduct of initiation of a recombinational exchange, a theoretical dose-response curve that agreed well with experiment was obtained. The best fit corresponded to epsilon = 0.035, close to the previously observed restriction efficiency of 0.053. In the calculations, the value for h0, the average length of heteroduplex DNA, was taken to be 0.5 lambda units, i.e., about 25 kilobase pairs. This estimate for h0 was obtained here by analysis of the density distributions of the progeny of crosses between nonreplicating density-labeled lambda-phage chromosomes, published by others [M. S. Fox, C. S. Dudney and E. J. Sodergren (1979) Cold Spring Harbor Symposium on Quantitative Biology, Vo. 43, pp. 999-1007].

Bacteriophage lambda↗