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Predicting conditional probability distributions: a connectionist approach.

Most traditional prediction techniques deliver a single point, usually the mean of a probability distribution. For multimodal processes, instead of predicting the mean, it is important to predict the full distribution. This article presents a new connectionist method to predict the conditional probability distribution in response to an input. The main idea is to transform the problem from a regression problem to a classification problem. The conditional probability distribution network can perform both direct predictions and iterated predictions, the latter task being specific for time series problems. We compare this new method to fuzzy logic and discuss important differences, and also demonstrate the architecture on two time series. The first is the benchmark laser series used in the Santa Fe competition, a deterministic chaotic system. The second is a time series from a Markov process which exhibits structure on two time scales. The network produces multimodal predictions for this series. We compare the predictions of the network with a nearest-neighbor predictor and find that the conditional probability network is more than twice as likely a model.

Neural Networks, Computer↗

Role of oxygen in the production of human decompression sickness.

In the calculation of decompression schedules, it is commonly assumed that only the inert gas needs to be considered; all inspired O2 is ignored. Animal experiments have shown that high O2 can increase risk of serious decompression sickness (DCS). A trial was performed to assess the relative risks of O2 and N2 in human no-decompression dives. Controlled dives (477) of 30- to 240-min duration were performed with subjects breathing mixtures with low (0.21-0.38 ATA) or high (1.0-1.5 ATA) Po2. Depths were chosen by a sequential dose-response format. Only 11 cases of DCS and 18 cases of marginal symptoms were recorded despite exceeding the presently accepted no-decompression limits by greater than 20%. Analysis by maximum likelihood showed a shallow dose-response curve for increasing depth. O2 was estimated to have zero influence on DCS risk, although data variability still allows a slight chance that O2 could be 40% as effective as N2 in producing a risk of DCS. Consideration of only inert gases is thus justified in calculating human decompression tables.

Decompression Sickness↗

A two-state stochastic model of REM sleep architecture in the rat.

Rapid eye movement (REM) sleep is a recurring state throughout the sleeping period. Based on the examination of 45 sleep records of 3-mo-old male rats during the middle of the light phase, a stochastic model is proposed for the sequence X(1),Y(2), X(2),Y(2),. of REM sleep durations X and inter-REM sleep waiting times Y experienced by a rat during a sleeping period. In our model the probability distribution of any variable in the sequence, given the past, is allowed to depend on only the immediately previous variable. The conditional distributions f(y(i) | x(i)) and g(x(i+1) | y(i)) do not depend on the index i. It is shown that the marginal distributions tend to stationarity. Aggregations of the data on a discrete time scale suggest that the conditional distributions be formulated as two-component mixtures. These component distributions are modeled as Poisson and their means are called the means of short and long waiting time and the means of short and long REM sleep duration. Associated with each mean is a probability weight. Parametric forms are given to the means and probability weights. The model estimated by maximum likelihood shows a good fit to data of the 3-mo-old rats. The model fit to a smaller data set obtained from rats aged 15-22 mo shows a significant shortening of the means for both short and long REM sleep bout durations compared with the means of the 3-mo-old rats. Neuronal correlates for the behavior of the model are discussed in the context of the reciprocal interaction model of REM sleep regulation.

Aging↗

Adjusting the outputs of a classifier to new a priori probabilities: a simple procedure.

It sometimes happens (for instance in case control studies) that a classifier is trained on a data set that does not reflect the true a priori probabilities of the target classes on real-world data. This may have a negative effect on the classification accuracy obtained on the real-world data set, especially when the classifier's decisions are based on the a posteriori probabilities of class membership. Indeed, in this case, the trained classifier provides estimates of the a posteriori probabilities that are not valid for this real-world data set (they rely on the a priori probabilities of the training set). Applying the classifier as is (without correcting its outputs with respect to these new conditions) on this new data set may thus be suboptimal. In this note, we present a simple iterative procedure for adjusting the outputs of the trained classifier with respect to these new a priori probabilities without having to refit the model, even when these probabilities are not known in advance. As a by-product, estimates of the new a priori probabilities are also obtained. This iterative algorithm is a straightforward instance of the expectation-maximization (EM) algorithm and is shown to maximize the likelihood of the new data. Thereafter, we discuss a statistical test that can be applied to decide if the a priori class probabilities have changed from the training set to the real-world data. The procedure is illustrated on different classification problems involving a multilayer neural network, and comparisons with a standard procedure for a priori probability estimation are provided. Our original method, based on the EM algorithm, is shown to be superior to the standard one for a priori probability estimation. Experimental results also indicate that the classifier with adjusted outputs always performs better than the original one in terms of classification accuracy, when the a priori probability conditions differ from the training set to the real-world data. The gain in classification accuracy can be significant.

Classification↗

A subjective distance between stimuli: quantifying the metric structure of representations.

As subjects perceive the sensory world, different stimuli elicit a number of neural representations. Here, a subjective distance between stimuli is defined, measuring the degree of similarity between the underlying representations. As an example, the subjective distance between different locations in space is calculated from the activity of rodent's hippocampal place cells and lateral septal cells. Such a distance is compared to the real distance between locations. As the number of sampled neurons increases, the subjective distance shows a tendency to resemble the metrics of real space.

Action Potentials↗

A rigorous complexity analysis of the (1 + 1) evolutionary algorithm for separable functions with Boolean inputs.

Evolutionary algorithms (EAs) are heuristic randomized algorithms which, by many impressive experiments, have been proven to behave quite well for optimization problems of various kinds. In this paper a rigorous theoretical complexity analysis of the (1 + 1) evolutionary algorithm for separable functions with Boolean inputs is given. Different mutation rates are compared, and the use of the crossover operator is investigated. The main contribution is not the result that the expected run time of the (1 + 1) evolutionary algorithm is theta (n ln n) for separable functions with n variables but the methods by which this result can be proven rigorously.

Algorithms↗

Patient-oriented performance measures of diagnostic tests. 2. Assignment potential and assignment strength.

Assignment Potential (AP) is a performance measure of a diagnostic test, characterizing the chance that, as a consequence of performing the test, the probability of disease will exceed a decision threshold, thereby permitting a management action to be taken. Another performance measure, Assignment Strength (AS) characterizes the average extent to which a decision threshold will be exceeded when the post-test probability of disease does exceed the threshold. Both AP and AS are functions of prior probability of disease and decision threshold, and can be represented as two-dimensional contour maps indicating their behavior throughout the entire probability and threshold space. AP and AS can be determined for both discrete-valued tests and tests with continuous spectra of results. The contour map displays facilitate determination of the values of these measures at any prior probability and threshold, as well as visual sensitivity analysis for ranges of prior probability and/or threshold. AP and AS may be useful to the clinician in prospective evaluation of a diagnostic test in situations where formal decision analysis is not feasible.

Diagnosis↗

Patient-oriented performance measures of diagnostic tests. 3. U-Factor.

When a clinician is faced with the problem of deciding whether to order a specific diagnostic test, the ideal information would be the utility of the "perform test" branch of the decision tree versus the utility of the "do not perform test" branch. This difference in utility is termed the Expected Utility of the Test ( EUT ). We propose a new performance measure of a test called the U-Factor (UF) which is related to EUT by a simple formula. UF depends on the prior probability of disease and on the decision thresholds at which one would be indifferent between any two immediately subsequent management options, and can be presented as a two-dimensional nomogram. UF is useful as a computational aid in a formal decision analysis, and may be useful as an informal measure of the value of a diagnostic test when a formal analysis is not feasible.

Costs and Cost Analysis↗

Probabilistic sensitivity analysis using Monte Carlo simulation. A practical approach.

The data for medical decision analyses are often unreliable. Traditional sensitivity analysis--varying one or more probability or utility estimates from baseline values to see if the optimal strategy changes--is cumbersome if more than two values are allowed to vary concurrently. This paper describes a practical method for probabilistic sensitivity analysis, in which uncertainties in all values are considered simultaneously. The uncertainty in each probability and utility is assumed to possess a probability distribution. For ease of application we have used a parametric model that permits each distribution to be specified by two values: the baseline estimate and a bound (upper or lower) of the 95 percent confidence interval. Following multiple simulations of the decision tree in which each probability and utility is randomly assigned a value within its distribution, the following results are recorded: (a) the mean and standard deviation of the expected utility of each strategy; (b) the frequency with which each strategy is optimal; (c) the frequency with which each strategy "buys" or "costs" a specified amount of utility relative to the remaining strategies. As illustrated by an application to a previously published decision analysis, this technique is easy to use and can be a valuable addition to the armamentarium of the decision analyst.

Decision Making↗

Holistic thinking is not the whole story: alternative or adjunct approaches for increasing the accuracy of legal evaluations.

There are a number of very helpful, but often underutilized, principles and procedures that can augment decision making in clinical and legal settings. Psychologists often restrict their range of decision-making strategies and options--at the cost of maximizing diagnostic and predictive accuracy--in part as the result of "ontological-epistemological one-worldedness" (O-E O-W). However, no philosophical, logical, or scientific necessity demands strict consistency between views regarding the nature of psychological phenomena and views about how to best assess or learn about those phenomena. Relaxing this unnecessary and largely psychologically-based O-E O-W may promote greater comfort with and utilization of the methods that are discussed in this article for increasing judgmental accuracy.

Decision Making↗

RNA analysis of B cell lines arrested at defined stages of differentiation allows for an approximation of gene expression patterns during B cell development.

The development of a mature B lymphocyte from a bone marrow stem cell is a highly ordered process involving stages with defined features and gene expression patterns. To obtain a deeper understanding of the molecular genetics of this process, we have performed RNA expression analysis of a set of mouse B lineage cell lines representing defined stages of B cell development using Affymetrix microarrays. The cells were grouped based on their previously defined phenotypic features, and a gene expression pattern for each group of cell lines was established. The data indicated that the cell lines representing a defined stage generally presented a high similarity in overall expression profiles. Numerous genes could be identified as expressed with a restricted pattern using dCHIP-based, quantitative comparisons or presence/absence-based, probabilistic state analysis. These experiments provide a model for gene expression during B cell development, and the correctly identified expression patterns of a number of control genes suggest that a series of cell lines can be useful tools in the elucidation of the molecular genetics of a complex differentiation process.

Animals↗

Coefficients of agreement between observers and their interpretation.

The measurement of agreement between ratings of patient symptomatology by two or more psychiatrists is discussed. It is noted that coefficients which allow for possible chance agreement are to be preferred, but they involve assumptions about the way in which chance factors may operate. Assumptions which involve prior probabilities of the incidence of a symptom appear to be too stringent, and a new coefficient, called the RE coefficient, is recommended in which is assumed to operate in a purely random way. Binary scales are discussed in detail, but methods of dealing with scales of wider range are also referred to.

Diagnosis, Differential↗

Validation of probabilistic linkage to match de-identified ambulance records to a state trauma registry.

OBJECTIVES: To validate the accuracy of using probabilistic linkage for matching de-identified ambulance records to a state trauma registry. METHODS: This was a retrospective cohort analysis. Three thousand nine hundred nineteen true matches between ambulance and state trauma registry data from 1998 to 2003 were identified by deterministic matching on trauma identification number and verified by human review. Two thousand thirty-eight ambulance records from trauma patients not meeting criteria for a true match, and an identical number of trauma registry records randomly selected from the one local county served by a different EMS provider, were included as nonmatches. There were 17 variables considered for linkage, which included the following: age, gender, race, county, hospital, date, rural setting, call and arrival times, mechanism, penetrating injury, vital signs, intubation, and intoxication. Probabilistic linkage was used to link the two data sets, using seven different combinations of common variables (maximum, 17; minimum, 4). The sensitivity and specificity of identifying true matches and nonmatches (95% confidence intervals [95% CI]) were calculated for each combination of variables. RESULTS: Using all 17 available variables, 3,766 of 3,919 true matches were appropriately linked (sensitivity, 96.1%; 95% CI = 95.4% to 96.7%), with eight mismatches (specificity, 99.6%; 95% CI = 99.2% to 99.8%). Sensitivity fell below 95% with < 15 variables; however, sensitivity was very dependent on the inclusion of variables with high discriminatory power. Specificity remained >98% regardless of the number of variables included. CONCLUSIONS: Probabilistic linkage is a valid method for matching ambulance records to a trauma registry without the use of patient identifiers; however, the sensitivity of identifying true matches is critically dependent on the number and type of common variables included in the analysis.

Ambulances↗

A computer program for pharmacokinetics based on maximum likelihood estimation using the gamma distribution with a probability density function: comparison with the normal distribution.

A computer program is described for maximum likelihood estimation within the gamma or normal distribution which can be used to estimate pharmacokinetic parameters. Pharmacokinetic analysis using this proposed program was investigated by the Monte Carlo method. The assumed pharmacokinetic models were a one-compartment intravenous model and an oral model. The simulated drug concentrations were generated using a 10% S.D. based on the gamma or normal distribution. The gamma or normal distribution was adopted as the probability density function (p.d.f.) to estimate model parameters. The Powell method was used to maximize the logarithmic likelihood. There were no differences in the estimated parameters in terms of statistical and frequency distributions between the gamma and normal distributions using the generated data and the p.d.f. distributions. However, the number of failures to calculate the parameters using the p.d.f. with the normal distribution was more than five times that using the gamma distribution. This result suggests that it may be necessary to evaluate the validity of results computed using the maximum likelihood estimation based on a normal distribution as a data error distribution and p.d.f.

Algorithms↗

Theoretical description of the direct exponential amplification and sequencing (DEXAS) method.

We present a theoretical description of the method of DNA sequencing with simultaneous exponential PCR amplification of the template (DEXAS). Based on the theory of probability, the formula determining the optimal ratio of concentrations of deoxy- and dideoxynucleotides in the reaction mixture is derived, as well as the length distribution of sequenced DNA fragments. The prediction of the number of mutations is given and the theoretically determined aspects of DEXAS are compared with the corresponding quantities of classical sequencing methods. Some other experimentally observed effects are also discussed.

DNA Mutational Analysis↗