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At least 685 records · Page 38Linked to original sources
PubMed2005

Model inference or model selection: discussion of Klugkist, Laudy, and Hoijtink (2005).

I. Klugkist, O. Laudy, and H. Hoijtink (2005) presented a Bayesian approach to analysis of variance models with inequality constraints. Constraints may play 2 distinct roles in data analysis. They may represent prior information that allows more precise inferences regarding parameter values, or they may describe a theory to be judged against the data. In the latter case, the authors emphasized the use of Bayes factors and posterior model probabilities to select the best theory. One difficulty is that interpretation of the posterior model probabilities depends on which other theories are included in the comparison. The posterior distribution of the parameters under an unconstrained model allows one to quantify the support provided by the data for inequality constraints without requiring the model selection framework.

Analysis of Variance↗
PubMed1999

An equilibrium statistical model for the spreading phase of open-ocean convection.

A "most probable state" equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. The simplest theory is formulated for a uniform cooling event over the entire basin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a stabilizing barotropic rim current and localized temperature anomaly.

Journal Article↗
PubMed2004

Local estimation of posterior class probabilities to minimize classification errors.

Decision theory shows that the optimal decision is a function of the posterior class probabilities. More specifically, in binary classification, the optimal decision is based on the comparison of the posterior probabilities with some threshold. Therefore, the most accurate estimates of the posterior probabilities are required near these decision thresholds. This paper discusses the design of objective functions that provide more accurate estimates of the probability values, taking into account the characteristics of each decision problem. We propose learning algorithms based on the stochastic gradient minimization of these loss functions. We show that the performance of the classifier is improved when these algorithms behave like sample selectors: samples near the decision boundary are the most relevant during learning.

Probability↗
PubMed1992

On the theory of partially inbreeding finite populations. III. Fixation probabilities under partial selfing when heterozygotes are intermediate in viability.

In a previous paper by the senior author, an approximation to the probability of survival was given for a mutant, which is originally present in a single heterozygote, in a population that reproduces partly by selfing and partly by random mating. The population was assumed to be very large, but the result obtained is general with regard to the level of dominance in viability. In this paper two errors which were made in that earlier work are corrected. A general approximate expression is then derived for the probability that an allele A is fixed in a partially self fertilizing population of size N, if its initial frequency is p, selection is weak and heterozygotes with the allele are exactly intermediate in viability compared with genotypes AA and AA. A rigorous proof is given for a special case that is a generalization of the classical binomial sampling model. In this case, but not in general, the approximate fixation probability is independent of the probability of reproduction by selfing. Some implications are discussed.

Alleles↗
PubMed2000

Scaling of avalanche queues in directed dissipative sandpiles

Using numerical simulations and analytical methods we study a two-dimensional directed sandpile automaton with nonconservative random defects (concentration c) and varying driving rate r. The automaton is driven only at the top row and driving rate is measured by the number of added particles per time step of avalanche evolution. The probability distribution of duration of elementary avalanches at zero driving rate is exactly given by P1(t,c)=t(-3/2) exp[t ln(1-c)]. For driving rates in the interval 0 server queue in the queue theory. We study scaling properties of the busy period and dissipated energy of sequences of noninterrupted activity. In the limit c-->0 and varying linear system size L<<1/c we find that at driving rates r</=L(-1/2) the distributions of duration and energy of the avalanche queues are characterized by a multifractal scaling and we determine the corresponding spectral functions. For L>>1/c increasing the driving rate somewhat compensates for the energy losses at defects above the line r approximately sqrt[c]. The scaling exponents of the distributions in this region of phase diagram vary approximately linearly with the driving rate. Using properties of recurrent states and the probability theory we determine analytically the exact upper bound of the probability distribution of busy periods. In the case of conservative dynamics c=0 the probability of a continuous flow increases as F(infinity) approximately r(2) for small driving rates.

Journal Article↗
PubMedDate not supplied

Decision analysis with cumulative prospect theory.

BACKGROUND: Individuals sometimes express preferences that do not follow expected utility theory. Cumulative prospect theory adjusts for some phenomena by using decision weights rather than probabilities when analyzing a decision tree. METHODS: The authors examined how probability transformations from cumulative prospect theory might alter a decision analysis of a prophylactic therapy in AIDS, eliciting utilities from patients with HIV infection (n = 75) and calculating expected outcomes using an established Markov model. They next focused on transformations of three sets of probabilities: 1) the probabilities used in calculating standard-gamble utility scores; 2) the probabilities of being in discrete Markov states; 3) the probabilities of transitioning between Markov states. RESULTS: The same prophylaxis strategy yielded the highest quality-adjusted survival under all transformations. For the average patient, prophylaxis appeared relatively less advantageous when standard-gamble utilities were transformed. Prophylaxis appeared relatively more advantageous when state probabilities were transformed and relatively less advantageous when transition probabilities were transformed. Transforming standard-gamble and transition probabilities simultaneously decreased the gain from prophylaxis by almost half. Sensitivity analysis indicated that even near-linear probability weighting transformations could substantially alter quality-adjusted survival estimates. CONCLUSION: The magnitude of benefit estimated in a decision-analytic model can change significantly after using cumulative prospect theory. Incorporating cumulative prospect theory into decision analysis can provide a form of sensitivity analysis and may help describe when people deviate from expected utility theory.

AIDS-Related Opportunistic Infections↗
PubMed1986

Application of information theory to decision analysis in potentially prostaglandin-responsive neonates.

To define settings in which use of prostaglandin E1 before transfer from a community hospital to a tertiary care center benefits neonates with possible heart disease, information theory was used to predict the probability of a favorable response to prostaglandin therapy from the limited information of clinical variables. Records of 250 patients, newborn to 7 days old, with suspected heart disease were reviewed to assess six clinical variables (cyanosis, respiratory distress, heart murmur, pulse contour, hepatomegaly and prematurity). According to the anatomic and hemodynamic cardiovascular condition, each case was categorized as to whether a favorable response to prostaglandin E1 could be anticipated. Information content of each clinical variable with respect to prostaglandin responsiveness was determined, and patients were classified according to the most informative clinical variable. Stepwise extraction of information proceeded until remaining clinical variables added no significant information. Bayes' rule gave estimates of probability of prostaglandin-responsive defect in final subgroups for use in decision analysis. Cyanosis, murmur, small volume pulses and prematurity gave information about prostaglandin-responsive defects. Decision analysis indicated that frequency of poor outcome is minimized by early prostaglandin treatment of cyanotic term infants with a murmur or poor pulses, regardless of how ill they appear, and by treating any critically ill term newborn who has either cyanosis or poor pulses. Acyanotic patients with normal pulses are best untreated with prostaglandin until after definitive diagnosis is made. Advantage to either course was not seen in some small subgroups. Information theory with decision analysis is a rigorous approach to identify relevant clinical variables and define their roles in critical decisions in pediatric cardiology.

Algorithms↗
PubMedDate not supplied

[The theory of functional systems and purposeful behavior].

The role of probability forecasting in the purposive behavior under conditions of subjective uncertainty is considered in terms of the theory of functional systems. Participation of the probability forecasting in the afferent synthesis, goal formation, formation of the acceptor of action result and action program, and, finally, in the action program actualization is substantiated. The model of behavior under conditions of subjective uncertainty is advanced. It includes all the classical elements of the model of behavioral act developed by P.K. Anokhin. In order to take into account the probability aspects of behavior, the role of probability forecasting is emphasized at every stage of the system functioning. In addition to the classical elements, two novel components are introduced. These are the "memory buffer" (results of searching reactions) and the apparatus of probability decisions about changes in the action program. By the memory buffer an apparatus is meant, which gathers and stores the information about the results of many behavioral acts performed during the actualization of the action program. This information is used in the process of making a probability decision as whether to alter or not the action program after each specific behavioral act. Such an approach integrates the probability forecasting and the theory of functional systems. The theory becomes universal, i.e., applicable not only to deterministic but also to probabilistic environments.

Animals↗