PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “Probability Theory”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 recordsLinked to original sources
PubMed1983

[Application of terms of probability theory in embryology and teratology].

The aim of the paper was to show that accurate morphological statements can be made with the help of simple concepts of the theory of probability. Binomial distribution was used to find out whether the number of male and female births in large families was random or whether a particular disposition to boys/girls was to be assumed. It was found that the relation was random as a rule. A second question was that of the connection between a number of simultaneous variations and deformities. After the injection of trypan blue, combined deformities were studies in rats and found to be independent of each other, i.e. all had been directly caused by trypan blue.

Abnormalities, Severe Teratoid↗
PubMed1992

Clusters galore: insights about environmental clusters from probability theory.

The posterior probability of a causal explanation given that an environmental cancer cluster is statistically significant depends on the prior probability of an environmentally caused cluster, the sensitivity of the statistical test and its specificity. The prior probability is low, because it is rare to have enough carcinogen in the general environment to cause a relative risk of cancer high enough to achieve statistical significance in a small geographic area. The sensitivity and specificity are not great. The likelihood that a census tract escapes statistically significant elevations in all 80 types of cancer can be calculated. Many of the thousands of census tracts will, by chance alone, have at least one type of cancer whose elevation is statistically significant. Actual observation from a large cancer registry confirms this probabilistic prediction. Applying the principles of Bayes' Theorem would suggest that most statistically significant environmental cancer clusters are not due to environmental carcinogens. One would have to investigate hundreds of environmental cancer clusters to find one with a true environmental cause.

Bayes Theorem↗
PubMed1993

On the use of Bayesian probability theory for analysis of exponential decay data: an example taken from intravoxel incoherent motion experiments.

Traditionally, the method of nonlinear least squares (NLLS) analysis has been used to estimate the parameters obtained from exponential decay data. In this study, we evaluated the use of Bayesian probability theory to analyze such data; specifically, that resulting from intravoxel incoherent motion NMR experiments. Analysis was done both on simulated data to which different amounts of Gaussian noise had been added and on actual data derived from rat brain. On simulated data, Bayesian analysis performed substantially better than NLLS under conditions of relatively low signal-to-noise ratio. Bayesian probability theory also offers the advantages of: a) not requiring initial parameter estimates and hence not being susceptible to errors due to incorrect starting values and b) providing a much better representation of the uncertainty in the parameter estimates in the form of the probability density function. Bayesian analysis of rat brain data was used to demonstrate the shape of the probability density function from data sets of different quality.

Animals↗
PubMed1996

TMD diagnostic decision-making and probability theory. Part I.

This article is an educational analysis and discussion of some recently proposed diagnostic criteria, diagnostic methods, and diagnostic decision processes, pertaining specifically to temporomandibular disorders (TMD). On the basis of a discussion of classic probability theory, classic measurement theory, and examples using nonparametric inferential statistical tests, it is suggested that certain TMD diagnostic criteria and methods, and their associated decision matrix, favor subjective clinical opinions (largely pseudoscientific observations) and arbitrary clinical indices rather than objective scientific facts.

Binomial Distribution↗
PubMed1996

TMD diagnostic decision-making and probability theory. Part II.

As it specifically pertains to temporomandibular disorders (TMD), this article is an educational analysis and discussion of some recently proposed diagnostic criteria, diagnostic methods, and diagnostic decision processes. On the basis of a discussion of classic probability theory, classic measurement theory, and examples using nonparametric inferential statistical tests, it is suggested that certain TMD diagnostic criteria and methods, and their associated decision matrix, favor subjective clinical opinions (largely pseudoscientific observations) and arbitrary clinical indices rather than objective scientific facts.

Data Interpretation, Statistical↗
PubMed1995

Modeling the average molecular weights of antigen-antibody complexes by probability theory.

A method is presented to calculate average molecular weights for linear antigen-antibody complexes. Instead of determining the whole distributions and then using the distributions to calculate average properties, this method allows one to calculate the number-average, the weight-average, and the z-average molecular weights of the linear antigen-antibody complexes directly based on elementary probability theory and the recursive nature of antigen-antibody complexes.

Antigen-Antibody Complex↗
PubMed2002

Decomposition of multicomponent mass spectra using Bayesian probability theory.

We present a method for the decomposition of the mass spectra of mixed gases using Bayesian probability theory. The method works without any calibration measurement and therefore applies also to the analysis of spectra containing unstable species. For the example of mixtures of three different hydrocarbon gases the algorithm provides concentrations and cracking coefficients of each mixture component and also their confidence intervals. The amount of information needed to obtain reliable results and its relation to the accuracy of our analysis are discussed.

Journal Article↗
PubMed2001

Analysis of multicomponent mass spectra applying Bayesian probability theory.

In this paper we develop a method for the decomposition of mass spectra of gas mixtures, together with the relevant calibration measurements. The method is based on Bayesian probability theory. Given a set of spectra, the algorithm returns the relative concentrations and the associated margin of confidence for each component of the mixture. In addition to the concentrations, such a data set enables the derivation of improved values of the cracking coefficients of all contributing species, even for those components for which the set does not contain a calibration measurement. This latter feature also allows one to analyze mixtures that contain radicals in addition to stable molecules. As an example, we analyze and discuss the mass spectra obtained from the pyrolysis of azomethane, which contain the radical CH3 apart from nitrogen and C1- and C2-hydrocarbons.

Azo Compounds↗
PubMed1999

Quality control in nucleic acid amplification methods: use of elementary probability theory.

Since it is not possible to state with certainty that contamination has occurred during a nucleic acid amplification assay in the absence of a positive result for a negative control, methods of elementary probability theory are used to illustrate how to identify those runs in which the possibility of contamination should be considered. The use of binomial and Poisson distributions and an analysis of clusters are presented with illustrative examples to demonstrate their use.

Artifacts↗
PubMed1985

Use of the average antibody-antigen bond concept and probability theory to simplify modeling of linear and circular antibody-antigen complex formation.

We illustrate use of a simple approach to describe the equilibrium interactions of mixtures of monoclonal antibodies and antigens. This procedure is based on elementary concepts in probability theory and is readily suited to describing interactions of antibodies and antigens which form circular as well as linear complexes. The method is also suited to describing the inhibitory effects of antibodies which compete for overlapping epitopes and an example is provided to show how the procedure can be used to describe the interactions of antibodies which inhibit circular complex formation. We also outline simple strategies for preparing computer programs to simulate binding of antigens to defined antibody mixtures. The methods described should facilitate design of immunoassay procedures based on the use of defined mixtures of monoclonal antibodies.

Antibodies, Monoclonal↗
PubMed1990

An application of probability theory to a group of breath-alcohol and blood-alcohol data.

Many jurisdictions have "per se" driving-while-intoxicated (DWI) status expressed in terms of a blood-alcohol concentration (BAC) standard (in grams per 100 mL or the equivalent). Since breath-alcohol (BrAC) analysis is typically employed to determine BAC, there is often challenge to the use of an assumed 2100:1 conversion ratio. This concern may be relevant in light of considerable data that show a low percentage of cases in which BrAC greater than BAC, and this concern increases when the BrAC is used to predict BAC in the context of "per se" legislation. Probability theory provides a basis for estimating the likelihood of an individual having a BrAC greater than or equal to g/210 L with a corresponding BAC less than 0.10 g/100 mL. Actual field data from the state of Wisconsin (n = 404) were evaluated to determine the probability of this occurrence. The probability for this occurrence involves the multiplication law for independent events. The computed probability from the data was 0.018. The actual number of occurrences where BrAC greater than or equal to 0.10 g/210 L and BAC less than 0.10 g/100 mL was 5, resulting in a probability of 0.012. The concern of having BrAC greater than BAC at the critical "per se" level has a very low probability of occurrence, which thus supports the reasonableness of "per se" DWI legislation based upon a blood-alcohol standard determined by breath-alcohol analysis.

Alcoholic Intoxication↗
PubMed2005

Probability theory for number of mixture components resolved by n independent columns.

A general theory is proposed for the probability of different outcomes of success and failure of component resolution, when complex mixtures are partially separated by n independent columns. Such a separation is called an n-column separation. An outcome of particular interest is component resolution by at least one column. Its probability is identified with the probability of component resolution by a single column, thereby defining the effective saturation of the n-column separation. Several trends are deduced from limiting expressions of the effective saturation. In particular, at low saturation the probability that components cluster together as unresolved peaks decreases exponentially with the number of columns, and the probability that components cluster together on addition of another column decreases by a factor equal to twice the column saturation. The probabilities of component resolution by n-column and two-dimensional separations also are compared. The theory is applied by interpreting three sets of previously reported retention indices of the 209 polychlorinated biphenyls (PCBs), as determined by GC. The origin of column independence is investigated from two perspectives. First, it is suggested that independence exists when the difference between indices of the same compound on two columns is much larger than the interval between indices required for separation. Second, it is suggested that independence exists when the smaller of the two intervals between a compound and its adjacent neighbors is not correlated with its counterpart on another column.

Chromatography↗