Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Probability Theory”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

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

At least 991 records · Page 55Linked to original sources
PubMed1986

Determination of discriminatory power of prognostic factors for recurrence of breast cancer.

Vascular and lymphatic invasion of cancer cells, type of histology, histopathological TNM classification, level of tumor invasion, menopausal status, and age were reported as prognostic factors for breast cancer. We determined the discriminatory power of these prognostic factors for predicting breast cancer recurrence in 98 patients with the method of quantification theory type II, using a computer, model Hi-TAC M-150. The discriminatory rate of these combined seven factors for recurrence was 82.609%. We calculated the probability of breast cancer recurrence using the method of quantification theory type II. The probability of breast cancer recurrence (P) was given as follows. P = 1/1 + 7.333e5.468X. The score X is given by the sum of category weight of seven prognostic factors. Averages of P values of patients with recurrence and without recurrence were statistically different (p less than 0.01). The rate of having more than 30% of P values was 78% in 23 patients with breast cancer recurrence, and it was only 3% in 75 patients without breast cancer recurrence. The difference was statistically significant (X2 = 61.83, p less than 0.001). These results suggest that we can discriminate a high-risk patient with breast cancer recurrence using this method.

Age Factors↗
PubMed1984

[Determination of discriminatory power of prognostic factors for recurrence of breast cancer].

Vascular and lymphatic invasion of cancer cells, type of histology, histopathological TNM classification, level of tumor invasion, menopausal status and age, were reported as prognostic factors of breast cancer. We determined the discriminatory power of above prognostic factors for predicting breast cancer recurrence in 98 patients, with the method of quantification theory type II using a computer, model Hi-TAC M-150. The discriminatory rate of these combined seven factors for recurrence was 82.609%. We calculated the probability of breast cancer recurrence using the method of quantification theory type II. The probability of breast cancer recurrence (P) was given as follows. P = 1/1 + 7.333 e5.468x The score x is given by sum of category weight of seven prognostic factors. Averages of P values of patients with recurrence and without recurrence were statistically different (p less than 0.01). The rate of having more than 30% of P values was 78% in 23 patients with breast cancer recurrence, and its was only 3% in 75 patients without breast cancer recurrence. The difference was statistically significant. (x2 = 61.83, p less than 0.001). These results suggest that we can discriminate a high risk patient with breast cancer recurrence using this method.

Adult↗
PubMed2006

Beyond statistical inference: a decision theory for science.

Traditional null hypothesis significance testing does not yield the probability of the null or its alternative and, therefore, cannot logically ground scientific decisions. The decision theory proposed here calculates the expected utility of an effect on the basis of (1) the probability of replicating it and (2) a utility function on its size. It takes significance tests--which place all value on the replicability of an effect and none on its magnitude--as a special case, one in which the cost of a false positive is revealed to be an order of magnitude greater than the value of a true positive. More realistic utility functions credit both replicability and effect size, integrating them for a single index of merit. The analysis incorporates opportunity cost and is consistent with alternate measures of effect size, such as r2 and information transmission, and with Bayesian model selection criteria. An alternate formulation is functionally equivalent to the formal theory, transparent, and easy to compute.

Data Interpretation, Statistical↗
PubMed1992

Theory and practice and the preparation of teachers of nursing.

Questions of the relationship between theory and practice frequently occur both within educational and nursing literature and they are the questions that are going to be explored in this paper. Like the double helix, this paper is going to intertwine and interlink nursing and education, since they possess so many similarities and the overall thesis of the paper is that the relationship between theory and practice presents problems because the nature of the problem has been inadequately formulated. The paper falls into four main parts: 1. Four types of relationship between theory and practice. 2. Nursing and education as fields of practice and the nature of fields of practice--implications of this for knowledge, skills, attitudes and values--skills/practical knowledge/knowledge how. 3. Nature of the fields of study and the implications of this for knowledge. 4. Theory and practice--eight possible relationships. The conclusion offers a tentative reformulation of theory and practice in terms of probability and relates this to the preparation of nurses and teachers.

Education, Nursing↗
PubMed2004

Evaluation of canonical and microcanonical nonadiabatic reaction rate constants by using the Zhu-Nakamura formulas.

We consider a problem of calculating both thermal and microcanonical rate constants for nonadiabatic chemical reactions. Instead of using the conventional transition state theory, we use a generalized seam surface and introduce a concept of a coordinate dependent effective nonadiabatic transition probability based on the Zhu-Nakamura theory which can treat the nonadiabatic tunneling properly. The present approach can be combined with Monte Carlo method so as to be applicable to chemical reactions in complicated systems. The method is demonstrated to work well in wide energy and temperature range. Numerical tests also show that it is very essential for accurate evaluation of the thermal rate constant to use the generalized seam surface and take into account the nonadiabatic tunneling effect.

Journal Article↗
PubMedDate not supplied

Affinity in paired event probability.

It is shown that a general parametric functional generates the conditional and joint probabilities of event pairs when the order within paired events is irrelevant. The parameters represent affinities or associations between single events. If the marginal probabilities of the single events are known, then these parameters specify a hypersurface on which all the joint probabilities of event pairs must lie. Examples are presented, and applications in probability, ecology, epidemiology, genetics, and distribution theory are offered.

Ecology↗
PubMedDate not supplied

Brain mechanisms of emotions.

At the 23rd International Congress of Physiology Sciences (Tokyo, 1965) the results of experiment led us to the conclusion that emotions were determined by the actual need and estimation of probability (possibility) of its satisfaction. Low probability of need satisfaction leads to negative emotions actively minimized by the subject. Increased probability of satisfaction, as compared to the earlier forecast, generates positive emotions which the subject tries to maximize, that is, to enhance, to prolong, to repeat. We named our concept the Need-Informational Theory of Emotions. According to this theory, motivation, emotion, and estimation of probability have different neuromorphological substrates. Activation through the hypothalamic motivatiogenic structures of the frontal parts of the neocortex orients the behavior to signals with a high probability of their reinforcement. At the same time the hippocampus is necessary for reactions to signals of low probability events, which are typical for the emotionally excited brain. By comparison of motivational excitation with available stimuli or their engrams, the amygdala selects a dominant motivation, destined to be satisfied in the first instance. In the cases of classical conditioning and escape reaction the reinforcement was related to involvement of the negative emotion's hypothalamic neurons, while in the course of avoidance reaction the positive emotion's neurons were involved. The role of the left and right frontal neocortex in the appearance or positive or negative emotions depends on these informational (cognitive) functions.

Animals↗
PubMedDate not supplied

[The brain mechanisms of emotions].

At the 23rd International Congress of Physiological Sciences (Tokyo, 1965) the results of experiment brought us to a conclusion that emotions were determined by the actual need and estimation of probability (possibility) of its satisfaction. Low probability of need satisfaction leads to negative emotions actively minimized by the subject. Increased probability of satisfaction, as compared to the earlier forecast, generates positive emotions which the subject tries to maximize, that is to enhance, to prolong, to repeat. We named our concept the Need-Informational Theory of Emotions. According to this theory, motivation, emotion and estimation of probability have different neuromorphological substrate. Activating by motivatiogenic structures of the hypothalamus the frontal parts of neocortex orients the behavior to signals with a high probability of their reinforcement. At the same time the hippocampus is necessary for reactions to signals of low probability events, which is typical for emotionally excited brain. By comparison of motivational excitation with available stimuli or their engrams the amygdala selects a dominant motivation, destined to be satisfied in the first instance. In the cases of classical conditioning and escape reaction the reinforcement was related to involvement of the negative emotion's hypothalamic neurons while in the course of avoidance reaction the positive emotion's neurons being involved. The role of the left and right frontal neocortex in the appearance of positive or negative emotions depends on this informational (cognitive) functions.

Animals↗
PubMed1978

The synaptic connexions to intercostal motoneurones as revealed by the average common excitation potential.

1. The hypothesis is advanced that the joint occurrence of unitary e.p.s.p.s evoked in motoneurones by branches of common stem presynaptic fibres causes, on average, transient depolarization in one motoneurone at the time of discharge in another motoneurone of the same pool. 2. The hypothesis was tested in anaesthetized, paralysed cats by averaging the naturally occurring synpatic noise of thoracic inspiratory motoneurones with an averager triggered by spikes from other inspiratory motoneurones. These spikes were obtained as efferent discharges in nerve filaments supplying the proximal regions of the external intercostal muscles. 3. A transient depolarization centred around the time of the trigger spikes was consistently observed and was designated the average common excitation (a.c.e.) potential. 4. The peak depolarization lay between -1.0 and +4.6 msec (mean +0.7 msec) with respect to the trigger spikes and the rise times of its most prominent component ranged from 4 to 16 msec (mean 8.4 msec). 5. The amplitudes of the a.c.e. potentials ranged from 6 to 104 muV (mean 32 muV) when the trigger spikes were derived from a filament in the same segment as the relevant motoneurones, and from 3 to 42 muV (mean 19 muV) when the filament was two segments rostral to the motoneurone. 6. Cells innervating the proximal region of the intercostal space gave larger a.c.e. potentials than those innervating more distal regions and also showed larger central respiratory drive potentials. 7. A.c.e. potentials were observed for either alpha or gamma spikes as triggers. The potentials were usually smaller for the gamma than for the alpha spikes, the mean ration being about 0.6. The presence of the a.c.e. potentials from the gamma spikes was taken as evidence for alpha-gamma coactivation by common presynaptic axons. 8. A theory is developed which quantitatively accounts for the main features of both the a.c.e. potential and the short term synchrony observed by Sears & Stagg (1976). 9. The theory includes the proposition that the raised probability of firing of a motoneurone due to a unitary e.p.s.p. has a time course which may be described by the sum of the e.p.s.p. time course and its time differential. Thus, via the measurements, the theory predicts at least to a first approximation the expected probability of firing due to e.p.s.p.s of various shapes and sizes.

Action Potentials↗
PubMed1991

Sodium channel inactivation from resting states in guinea-pig ventricular myocytes.

1. Unitary Na+ channel currents were recorded from isolated guinea-pig ventricular myocytes using the cell-attached patch-clamp technique with high [Na+] in the pipette to enhance the signal-to-noise ratio. 2. The probability that the channel enters the inactivated state (I) directly from resting states (C) was investigated over a wide range of membrane potentials. 3. At membrane potentials of -60 mV or more positive, Markov chain theory was used to estimate the probability of C----I from histograms of the number of channel openings per depolarizing period. Holding potentials at least as negative as -136 were required to ensure that all channels resided in C prior to depolarization. 4. At membrane potentials negative to -60 mV, a two-pulse protocol was employed to determine the probability of C----I from the fraction of blank sweeps during the pre-pulse with correction for missed events. 5. The probability of C----I was found to be steeply voltage dependent at negative potentials, falling from 0.87 +/- 0.03 (mean +/- S.D.) at -91 mV to 0.42 +/- 0.01 at -76 mV. At potentials positive to -60 mV, this probability was less steeply voltage dependent and decayed to near zero at 0 mV. 6. Under physiological conditions, C----I transitions may produce appreciable Na+ channel inactivation at diastolic potentials. At potentials above the action potential threshold, inactivation is much more likely to occur from the open state.

Action Potentials↗
PubMed1979

Some models of genetic selection.

This paper begins with a description of the classical theory of viability selection in which probabilities that individuals of various genotypes survive are in proportions that do not change with time and are independent of population structure. Salient features of viability selection with one and two loci are reviewed. This theory is intimately connected with the usual theory of mass selection in quantitative genetics. It is well known that the mean of the relative viabilities does not necessarily increase if there is viability selection at more than one locus. It also turns out that if there is selection for fecundity with one locus, the mean fecundity may steadily decrease or oscillate rather than increase. This and the fact that a Hardy-Weinberg structure may no longer exist at any stage of life may have a bearing on predicting progress from artificial selection on reproductive characters. Classical viability selection theory does not completely describe natural selection. Other possibilities are discussed. Among these is the density and frequency dependent selection induced when the population lives in a limited habitat. Implications in quantitative genetics are discussed.

Alleles↗
PubMed2003

Evolutionary dynamics of escape from biomedical intervention.

Viruses, bacteria, eukaryotic parasites, cancer cells, agricultural pests and other inconvenient animates have an unfortunate tendency to escape from selection pressures that are meant to control them. Chemotherapy, anti-viral drugs or antibiotics fail because their targets do not hold still, but evolve resistance. A major problem in developing vaccines is that microbes evolve and escape from immune responses. The fundamental question is the following: if a genetically diverse population of replicating organisms is challenged with a selection pressure that has the potential to eradicate it, what is the probability that this population will produce escape mutants? Here, we use multi-type branching processes to describe the accumulation of mutants in independent lineages. We calculate escape dynamics for arbitrary mutation networks and fitness landscapes. Our theory shows how to estimate the probability of success or failure of biomedical intervention, such as drug treatment and vaccination, against rapidly evolving organisms.

Biological Evolution↗
PubMed2006

Sensitivity analysis of Markov models for communities of competing sessile organisms.

1. Communities of competing sessile organisms are often modelled using Markov chains. Sensitivity analysis of the stationary distribution of these models tells us how we expect the abundance of each organism to respond to changes in interactions between species. This is important for conservation and management. 2. Markov models for such communities have usually been formulated in discrete time. Each column of the discrete-time transition matrix must sum to 1 (column stochasticity). Sensitivity analysis therefore involves defining a pattern of compensation that maintains column stochasticity as a single transition probability changes. There is little biological theory about the appropriate compensation pattern, but the usual choices involve changing only the elements of a single column of the transition matrix. 3. I argue that if the underlying dynamics occur in continuous time, each transition probability is the net outcome of direct and many indirect interactions. 4. Determining the consequences of changing a single direct interaction will often be of interest. I show how this can be achieved using a continuous-time model. The resulting discrete-time compensation pattern is quite different from those that have been considered elsewhere, with changes occurring in many columns. 5. I also show how to determine which direct interactions are being changed under any discrete-time compensation pattern.

Ecosystem↗
PubMed2006

Distinct neuropsychological processes may mediate decision-making under uncertainty with known and unknown probability in gain and loss frames.

Decision-making under uncertainty has been studied in psychiatry, economic psychology, and neuroeconomics. Psychiatric patients (e.g., drug addicts) often show low degrees of aversion to potential danger. Investigation into neuropsychological processing underlying decision under uncertainty is important for medical treatments of neuropsychiatric disorders. In economic decision theory, choices under uncertainty with and without known probabilities of outcomes have been discriminated. Regarding decision-making under uncertainty with known probabilities (risk), Kahnemann-Tversky's prospect theory revealed that people tend to avoid uncertainty in potential gains (i.e., risk-aversion in a gain-frame); on the contrary, prefer uncertainty in potential losses (i.e., risk-seeking in a loss-frame). Regarding choices between possible gains with known and unknown probabilities, Ellsberg demonstrated that, in a gain-frame, people tend to avoid uncertainty with unknown probabilities, more dramatically than uncertainty with known probabilities. This can be explained by risk/uncertainty aversion in the gain-frame, suggesting that uncertainty with known and unknown probabilities (i.e., risk and Knightian uncertainty, respectively) may possibly be processed by similar neuropsychological processing in the gain-frame. However, in spite of accumulating evidence in neuroimaging and neuroeconomic studies, it is still unknown whether probability and Knightian uncertainty in the loss-frame are mediated by similar neuropsychological processes as well. We propose that distinct neuropsychological processes may mediate potential losses with known and unknown probabilities, based on recent findings in neuroeconomics and our experiment. Importance of examining subjects' degree of Knightian uncertainty aversion for the prediction/treatment of drug addicts' risky behavior (e.g., needle-sharing) is also discussed.

Decision Making↗
PubMed1985

Packaged DNA. An elastic model.

We review and deepen a theory of elastic bending of DNA on a persistence length scale. In a regime of extensive charge neutralization the axis of the double helix is elastically unstable when straight. Its stable bent conformation allows nucleation of DNA toruses and in principle could direct the supercoiled (solenoid) form of a polynucleosome. The Euler theory of elastic instability of macroscopic rods gives a partial description of the intrinsic ability of DNA to form locally stable bends. A different, quasi-Eulerian theory can be based on what is probably the dominant bending mechanism of DNA in solution-flexible kinking at the sites of open base pairs. This predictive theory is in quantitative agreement with the observed value (about 16 nm) for the minimum radius of torus holes. Stability of the inner torus ring is achieved when DNA phosphate groups are about 90% neutralized by trivalent cations, another prediction that is consistent with the observed formation of toruses in these conditions. The predicted stable radius of curvature of charge-neutralized DNA is also equal to the radial dimension of a maximally contracted polynucleosome supercoil as measured by neutron scattering (17 nm), but further experimental investigation of the geometrical disposition of the spacer DNA regions in the solenoid will be necessary to rule out the possibility of accidental agreement for this complex system. We stress again the experimental reality and probable importance of open base pairs in the equilibrium solution conformation of DNA.

Adenine Nucleotides↗