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PubMed2005

On the use of the Price equation.

This paper distinguishes two categories of questions that the Price equation can help us answer. The two different types of questions require two different disciplines that are related, but nonetheless move in opposite directions. These disciplines are probability theory on the one hand and statistical inference on the other. In the literature on the Price equation this distinction is not made. As a result of this, questions that require a probability model are regularly approached with statistical tools. In this paper, we examine the possibilities of the Price equation for answering questions of either type. By spending extra attention on mathematical formalities, we avoid the two disciplines to get mixed up. After that, we look at some examples, both from kin selection and from group selection, that show how the inappropriate use of statistical terminology can put us on the wrong track. Statements that are 'derived' with the help of the Price equation are, therefore, in many cases not the answers they seem to be. Going through the derivations in reverse can, however, be helpful as a guide how to build proper (probabilistic) models that do give answers.

Animals↗
PubMed1991

A probabilistic view on steady-state enzyme reactions.

A new theoretical description of steady-state enzyme reactions is proposed. The description is based on the concepts of the probability theory instead of the conventional formalism of chemical kinetics. A general steady-state rate equation is obtained using a probabilistic model of the catalytic act. As a result, the classical problems of enzyme kinetics can be formulated and considered in a different aspect. It is shown that the new theory presents a clearer treatment of some commonly obscure questions, such as the steady-state establishment. The theory also gives additional possibilities in the interpretation of the experimental results of traditional methods and proposes certain new ways in experimental investigations of enzymes.

Animals↗
PubMed1992

Beyond positivism: a metaphysical basis for clinical practice?

Medicine does not have its own unified body of scientific knowledge. Instead, physicians who are oriented to research make sporadic incursions into the basic sciences such as genetics, biochemistry, immunology, epidemiology, physiology, pharmacology and so on. These latter, taken together, comprise biomedicine which is said to have adopted the positivist epistemology or the Cartesian/Newtonian one that regards the scientist as an uninvolved observer of nature. In effect, medical science has come to rest on a theory of knowledge which links meaning to probability and considers prediction as the scientist's chief task. Like its predecessor, the probability theory of meaning rejects metaphysical speculation and remains connected to observations made, directly or indirectly, by means of the five senses. Despite some brilliant successes touching on relatively uncommon disorders, biomedicine cannot explain most day-to-day clinical activity. An understanding of what transpires between patient and doctor, of its diagnostic potential and therapeutic weight requires hermeneutic, or phenomenological, inquiry which brings about changes in both parties to it. Such a science, as ontological speculation has been called, cannot be deciphered by an epistemology couched in the imagery of physics and chemistry.

Metaphysics↗
PubMed1992

[Medical informatics as a complementary method in medical education].

The practice of the decision making at the bed side especially highlights the place to be devoted to medical informatics both at the pre- and post-graduate levels. Still in a relatively recent past, say the 50s-60s, most of the medical educational efforts were delivered when watching and then imitating the medical behaviour of an older physician. The medical educators were aware that besides the formal lessons related to selected chapters of medical textbooks, there were an obvious need for better training in the ability to make sound clinical judgements. If this ability has been considered only as an artful and intuitive process neither subjected to theoretical analysis nor to be captured in a formal quantitative model, now things have changed to such an extent that it becomes broadly shared that a science of medical decision making can be reasonably founded and this threefold: 1) Upon a formulated logic, 2) The probability theory, and 3) A value theory. The first gives the hand to artificial intelligence (AI) technics, the third to medical information data bases dealing either with patients (like in hospital information systems) or with literature like MEDLINE or electronic "cookbooks". Basically the probabilistic theory is based here upon a priori probabilities related to patients informations and data and opens the way to bayesian decision making. After this little summary it is stressed that educational informatics in medicine would appear either very central or very marginal, if not optional.

Computer-Assisted Instruction↗
PubMed1998

Probabilistic analysis of functional magnetic resonance imaging data.

Probability theory is applied to the analysis of fMRI data. The posterior distribution of the parameters is shown to incorporate all the information available from the data, the hypotheses, and the prior information. Under appropriate simplifying conditions, the theory reduces to the standard statistical test, including the general linear model. The theory is particularly suited to handle the spatial variations in the noise present in fMRI, allowing the comparison of activated voxels that have different, and unknown, noise. The theory also explicitly includes prior information, which is shown to be critical in the attainment of reliable activation maps.

Humans↗
PubMed1979

Application of case series review results to the evaluation of individual cases in diagnostic radiology.

Probability theory provides a simple method for physicians to use their "intellectual linkages" to their past clinical experience in making current diagnoses. Only a pencil and paper are required for making a few likelihood calculations. To illustrate this method, evaluation was done of a new diagnostic sign (presence of knee ossification centers) for differentiating rubella from cytomegalovirus infection in young infants. Two practical questions can be answered by use of this method for calculating probabilities: (1) How certain can one be about either diagnosis when centers are present or absent? (2) How can other radiologists apply these results to their individual cases?

Cytomegalovirus Infections↗
PubMed1990

Probabilistic belief networks for genetic counseling.

This paper describes a program, GenInfer, which uses belief networks to calculate risks of inheriting genetic disorders. GenInfer is based on Pearl's (J. Pearl, Artif. Intell. 29 (1986) 241-288) algorithm for fusion and propagation in probabilistic belief networks. It is written in Common Lisp. GenInfer can calculate genotypes for any family affected with any single-gene inherited disorder. Besides considering both negative and positive information in the pedigree. GenInfer takes into account additional information about the specific disorder as well as supplementary information for family members. The output consists of genotype probabilities for all family members and estimated genetic risks for prospective children of the consultands. Belief networks provide a way to calculate probabilities for systems of conditionally dependent variables. The impacts of various pieces of information are propagated and fused in such a way that, when equilibrium is reached, each proposition can be assigned a degree of belief consistent with the axioms of probability theory. In Pearl's algorithm, information is communicated through the network by messages sent between nodes. Pearl's basic algorithm cannot directly handle multiple-connected networks, which arise in the genetic counseling domain whenever a family pedigree includes consanguinity or more than one child per couple. GenInfer makes use of two cycle breaking methods, clustering and conditioning, to handle these situations.

Bayes Theorem↗
PubMed2002

A Bayesian network model for protein fold and remote homologue recognition.

MOTIVATION: The Bayesian network approach is a framework which combines graphical representation and probability theory, which includes, as a special case, hidden Markov models. Hidden Markov models trained on amino acid sequence or secondary structure data alone have been shown to have potential for addressing the problem of protein fold and superfamily classification. RESULTS: This paper describes a novel implementation of a Bayesian network which simultaneously learns amino acid sequence, secondary structure and residue accessibility for proteins of known three-dimensional structure. An awareness of the errors inherent in predicted secondary structure may be incorporated into the model by means of a confusion matrix. Training and validation data have been derived for a number of protein superfamilies from the Structural Classification of Proteins (SCOP) database. Cross validation results using posterior probability classification demonstrate that the Bayesian network performs better in classifying proteins of known structural superfamily than a hidden Markov model trained on amino acid sequences alone.

Amino Acid Sequence↗
PubMed1998

Statistical distribution of factors and factor images in factor analysis of medical image sequences.

From a time or energy image sequence, factor analysis of medical image sequences (FAMIS) estimates factors, representing kinetics or spectra in a given physiological compartment, and associated factor images, showing the compartments corresponding to each curve. In this paper, we show that the statistical properties of factor images and associated factors can be determined using a well known result from elementary probability theory. Numerical experiments are conducted to demonstrate that the variance observed in factor images can be predicted when the statistical properties of the original data are known. It is shown how these theoretical results can be used to relax the non-negativity constraints during FAMIS oblique analysis and to improve the quantitative interpretation of the factor images by associating a confidence interval with each pixel value.

Biophysical Phenomena↗
PubMed2001

Risk perception and communication: recent developments and implications for anaesthesia.

This review begins by outlining the history of probability theory, exposing cultural differences between scientists and lay people in the way risks are viewed. The basic principles of the science of risk perception are described, and the various methods of communicating risk in health care, both verbal and numerical, are then discussed critically. These concepts are then applied to the practice of anaesthesia. Risk perception may affect anaesthetists' choice of career and may be involved in the genesis and evolution of critical incidents; we also discuss possibilities for training in risk perception issues. The place of risk communication in informed consent and its ethical implications are discussed.

Anesthesia↗
PubMed1994

The international normalized ratio and uncertainty. Validation of a probabilistic model.

The motivation behind the creation of the International Normalized Ratio (INR) was to improve interlaboratory comparison for patients on anticoagulation therapy. In principle, a laboratory that reports the prothrombin time (PT) as an INR can standardize its PT measurements to an international reference thromboplastin. Using probability theory, the authors derived the equation for the probability distribution of the INR based on the PT, the International Sensitivity Index (ISI), and the geometric mean PT of the reference population. With Monte Carlo and numeric integration techniques, the model is validated on data from three different laboratories. The model allows computation of confidence intervals for the INR as a function of PT, ISI, and reference mean. The probabilistic model illustrates that confidence in INR measurements degrades for higher INR values. This occurs primarily as a result of amplification of between-run measurement errors in the PT, which is inherent in the mathematical transformation from the PT to the INR. The probabilistic model can be used by any laboratory to study the reliability of its own INR for any measured PT. This framework provides better insight into the problems of monitoring oral anticoagulation.

Evaluation Studies as Topic↗
PubMed2005

Fuzzy-probabilistic model for risk assessment of radioactive material railway transportation.

Transportation of radioactive materials is obviously accompanied by a certain risk. A model for risk assessment of emergency situations and terrorist attacks may be useful for choosing possible routes and for comparing the various defence strategies. In particular, risk assessment is crucial for safe transportation of excess weapons-grade plutonium arising from the removal of plutonium from military employment. A fuzzy-probabilistic model for risk assessment of railway transportation has been developed taking into account the different natures of risk-affecting parameters (probabilistic and not probabilistic but fuzzy). Fuzzy set theory methods as well as standard methods of probability theory have been used for quantitative risk assessment. Information-preserving transformations are applied to realise the correct aggregation of probabilistic and fuzzy parameters. Estimations have also been made of the inhalation doses resulting from possible accidents during plutonium transportation. The obtained data show the scale of possible consequences that may arise from plutonium transportation accidents.

Body Burden↗
PubMed1998

A recipe for randomness.

Despite many diverse theories that address closely related themes-e. g., probability theory, algorithmic complexity, cryptoanalysis, and pseudorandom number generation-a near-void remains in constructive methods certified to yield the desired "random" output. Herein, we provide explicit techniques to produce broad sets of both highly irregular finite and normal infinite sequences, based on constructions and properties derived from approximate entropy (ApEn), a computable formulation of sequential irregularity. Furthermore, for infinite sequences, we considerably refine normality, by providing methods for constructing diverse classes of normal numbers, classified by the extent to which initial segments deviate from maximal irregularity.

Journal Article↗
PubMedDate not supplied

Models in radiotherapy: volume effects.

A model for the dependence of normal tissue radiation dose response functions on volume variations and dose inhomogeneities is derived using probability theory. Power law volume correction factors and the complication probability factor are shown to be special cases arising from approximations applied to this model. Both require the assumption of small probabilities of complication. Power law volume corrections are shown to require a homogeneous dose distribution. The general model is tissue specific and can be used to calculate probabilities of complication for individual organs or isoprobability doses for radiation injury. The model is applicable to both homogeneous and inhomogeneous dose distributions and has been used in computer determination of optimal treatment parameters. Experimental data are presented which are consistent with the general model alone and which demonstrate the limits of applicability of previous models.

Humans↗
PubMed1999

Naive probability: a mental model theory of extensional reasoning.

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it occurs. The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning.

Cognition↗
PubMed2002

Judgments under uncertainty: representativeness or potential surprise?

Tversky and Kahneman's (1983) account of conjunctive probability judgment in terms of the representativeness heuristic is questioned. Instead, potential surprise (Shackle, 1969) is proposed as an important mechanism underlying subjective probability judgment. Study 1 reveals that, consistent with Shackle's theory, probabilities assigned to conjunctions are predominantly determined by the magnitude of the smaller component event probability. Also consistent with Shackle, Study 2 shows that for disjunctions, this role is performed by the larger component. Study 3 again contrasts the relative roles played by the component events in determining the value assigned to the conjunction. The results of the study are consistent with two reasoning processes: one analytically based, in which due account is taken of both component events, the other heuristic in nature and consistent with Shackle's theory of potential surprise. The implications of these results for a range of different types of judgment, e.g. with regard to person perception, stereotyping, categorization, and typicality, are evaluated.

Adult↗
PubMedDate not supplied

Medical informatics and clinical decision making: the science and the pragmatics.

There are important scientific and pragmatic synergies between the medical decision making field and the emerging discipline of medical informatics. In the 1970s, the field of medicine forced clinically oriented artificial intelligence (AI) researchers to develop ways to manage explicit statements of uncertainty in expert systems. Classic probability theory was considered and discussed, but it tended to be abandoned because of complexities that limited its use. In medical AI systems, uncertainty was handled by a variety of ad hoc models that simulated probabilistic considerations. To illustrate the scientific interactions between the fields, the author describes recent work in his laboratory that has attempted to show that formal normative models based on probability and decision theory can be practically melded with AI methods to deliver effective advisory tools. In addition, the practical needs of decision makers and health policy planners are increasingly necessitating collaborative efforts to develop a computing and communications infrastructure for the decision making and informatics communities. This point is illustrated with an example drawn from outcomes management research.

Artificial Intelligence↗