Simultaneous linear prediction

Given a set of items (predictors) suppose one wishes to predict another set of items (predictands) in asimultaneous way. Such a situation may occur when the predictands are different measurable aspects of the same phenomenon. Alternatively one might wish to predict the success of an event (say a successfully performed task) which has many correlated or uncorrelated failure modes (say a set of possible mental or physical disabilities each of them by itself precluding the achievement of the said task.) In such a case a unidimensional prediction is of value only if prediction is simultaneous for all possible failure modes. A linear summarization of the predictors is suggested, which is unique and has maximum predictability value for all predictands simultaneously. Other summarizations or scores are found that give maximum explanation of residual measures on the predictands and that are uncorrelated. The set of those simultaneous linear predictions is compared to the set of the individual multiple regression predictions as used, for instance, in the same context by Horst [4] for each predictand given the original predictors. We suggest that this technique can be applied in particular to the summarization of a subset of items when the whole set of items constitutes the set of predictands.This work was initiated at Stanford University under contract 2-1-065 with U. S. Office of Education and was partly revised at the Université de Montréal.I wish to express my gratitude to Professor Herbert Solomon, Stanford University, for his unfailing assistance at all stages of my work.     

Simultaneous temporal processing

Seven experiments assessed the ability of rats to process temporal information from two internal clocks simultaneously and independently. In the first six experiments a light stimulus signalled an overall interval between the beginning of a trial and the availability of food reinforcement (e.g., a 50-s fixed interval). During the overall interval a sound stimulus was used to signal shorter intervals that divided the overall interval into equal segments. When there was a fixed temporal relation between the final segment signal and the availability of reinforcement, there was a double-scallop pattern of responding throughout the segmented overall interval; the function relating response rate to time during segment intervals was similar to the function relating response rate to time in unsegmented overall intervals; a change in response rate occurred at the time that a normally presented segment signal was omitted. Taken together, the results indicate that rats timed the overall interval and the segment intervals simultaneously and independently without interference. In Experiment 7 a light stimulus was used on some trials, and a sound stimulus was used on other trials to signal a discrete-trial 50-s peak procedure. When these two signals were presented in compound, there was a leftward shift of the response function, which suggests that rats timed both signals simultaneously. For all of the experiments a scalar timing model with specific stimulus integration rules is used to explain the results. The stimulus integration rule used in the first six experiments, in which there were two signals for the same reinforcement, was to respond if both the segment and the overall interval had exceeded a response threshold. The stimulus integration rule used in Experiment 7, in which there were two signals for different reinforcements, was to respond if the response threshold for either interval had been exceeded.     

Techniques for Simultaneous Inference

When more than one significance test is carried out on data from a single experiment, researchers are often concerned with the probability of one or more Type I errors over the entire set of tests. This article considers several methods of exercising control over that probability (the so-called family-wise Type I error rate), provides a schematic that can be used by a researcher to choose among the methods, and discusses applications to contingency tables.     

Simultaneous auditory discrimination.

Stimuli in many visual stimulus control studies typically are presented simultaneously; in contrast the stimuli in auditory discrimination studies are presented successively. Many everyday auditory stimuli that control responding occur simultaneously. This suggests that simultaneous auditory discriminations should be readily acquired. The purpose of the present experiment was to train rats in a simultaneous auditory discrimination. The apparatus consisted of a cage with two response levers mounted on one wall and a speaker mounted adjacent to each lever. A feeder was mounted on the opposite wall. In a go-right/go-left procedure, two stimuli were presented on each trial, a wide-band noise burst through one speaker and a 2-kHz complex signal through the other. The stimuli alternated randomly from side to side across trials, and the stimulus correlated with reinforcement for presses varied across subjects. The rats acquired the discrimination in 400 to 700 trials, and no response position preference developed during acquisition. The ease with which the simultaneous discrimination was acquired suggests that procedures, such as matching to sample, that require simultaneous presentation of stimuli can be used with auditory stimuli in animals having poor vision.     

Simultaneous Group and Insulin Therapy

Abstract

The concept of focus can provide a meaningful bridge between theory and practice. The authors’ aim in this paper is to demonstrate that for theory to be clinically useful, it should provide a sense of focus and organization for clinical work. They illustrate how their particular use of a self–psychological/intersubjective model leads to an emphasis on what they refer to as “sustained empathic focus.” The authors’ choice of concepts leads them consistently to stress the patient’s subjective experience and emerging vulnerability.     

Simultaneous time and size perception

Judgments of the apparent duration and size of visually presented circles vary directly with the duration and size of the presented stimuli. When the frequencies of stimulus duration (short vs. long) and stimulus area (small vs. large) are varied, perceived size and duration are directly related to the frequency of the lower attribute value (short or small). These data are compared to the predictions of different information-processing models. The model which accounts for the data best is one in which it is assumed that perceived size and perceived duration grow together over the course of time spent sampling size information, and that attribute frequency affects the rate of sampling and/or the point at which sampling stops.     

Causation as Simultaneous and Continuous

We propose that all actual causes are simultaneous with their direct effects, as illustrated by both everyday examples and the laws of physics. We contrast this view with the sequential conception of causation, according to which causes must occur prior to their effects. The key difference between the two views of causation lies in differing assumptions about the mathematical structure of time.     

Simultaneous grouping and auditory continuity

Are the conditions for illusory auditory continuity entirely local in frequency, or are judgments of continuity made on auditory objects? Listeners made continuous/pulsating judgments on a variety of complex tones that repeatedly alternated with a 100- to 500-Hz bandpass noise. A sufficiently quiet complex tone was heard as continuous when all its harmonics fell within the frequency range of the noise. Adding harmonics outside the noise's frequency range substantially reduced the impression of continuity, which was largely restored when these additional components were given a different fundamental frequency. Judgments of auditory continuity thus appear to be based on entire simultaneously grouped objects, rather than being determined solely by local criteria based on individual frequency channels.     

Simultaneous temporal and spatial processing

Rats searched for food that was contingent on time and place in an open field. One location was active at a time, the active location moved in a clockwise direction after each reward, and each location was repeated several times on each daily session. When a location was active, the first response after a fixed interval produced food. The intervals associated with each of the four locations were consistently 60, 30, 30 and 60 sec. For independent groups, inspecting an inactive location had no consequence (n = 7) or reduced the amount of food delivered at the active location (n = 6). The rates of inspecting active and inactive locations increased before the associated intervals elapsed, with preferential responding at the active locations. Rates of anticipation at active locations failed to superimpose when plotted as a function of proportional time. Simultaneous temporal and spatial processing contributed to the failure of proportional timing.     

The prediction of averages

Criterion measures are frequently obtained by averaging ratings, but the number and kind of ratings available may differ from individual to individual. This raises issues as to the appropriateness of any single regression equation, about the relation of variance about regression to number and kind of criterion observations, and about the preferred estimate of regression parameters. It is shown that if criterion ratings all have the same true score the regression equation for predicting the average is independent of the number and kind of criterion scores averaged.Two cases are distinguished, one where criterion measures are assumed to have the same true score, and the other where criterion measures have the same magnitude of error of measurement as well. It is further shown that the variance about regression is a function of the number and kind of criterion ratings averaged, generally decreasing as the number of measures averaged increases. Maximum likelihood estimates for the regression parameters are derived for the two cases, assuming a joint normal distribution for predictors and criterion average within each subpopulation of persons for whom the same type of criterion average is available.     

Dialogues on prediction errors

The recognition that computational ideas from reinforcement learning are relevant to the study of neural circuits has taken the cognitive neuroscience community by storm. A central tenet of these models is that discrepancies between actual and expected outcomes can be used for learning. Neural correlates of such prediction-error signals have been observed now in midbrain dopaminergic neurons, striatum, amygdala and even prefrontal cortex, and models incorporating prediction errors have been invoked to explain complex phenomena such as the transition from goal-directed to habitual behavior. Yet, like any revolution, the fast-paced progress has left an uneven understanding in its wake. Here, we provide answers to ten simple questions about prediction errors, with the aim of exposing both the strengths and the limitations of this active area of neuroscience research.     

Reichenbach's concept of prediction

Reichenbach emphasizes the central importance of prediction, which is—for him—the principal aim of science. This paper offers a critical reconstruction of his concept of prediction, taking into account the different periods of his thought. First, prediction is studied as a key factor in rejecting the positivism of the Vienna Circle. This part of the discussion concentres on the general features of prediction before Experience and Prediction (EP) (section 1). Second, prediction is considered in the context of Reichenbach's disagreements with his contemporaries—Carnap and Popper—(section 2). Pointing out these differences gives an additional basis for understanding how Reichenbach saw “prediction” in the period when EP was written. Third, Reichenbach's theoretical framework of prediction is analysed following EP. This analysis studies the semantical, logical, epistemological and methodological bases of his concept of prediction (section 3). Fourth, Reichenbach's conception of prediction, based on an objectivist interpretation of probabilities, is compared with the perspective on prediction of subjective Bayesians (the present personalists). This comparison (section 4) illustrates Reichenbach's views regarding the links of prediction with probability. Fifth, innovations and elements of continuity after EP are noted which give a more complete picture of Reichenbach's thought on prediction (section 5). This contributes to a comprehensive characterization of his concept of prediction. Finally, there is an assessment of his whole view of the matter and a presentation of the ingredients for a satisfactory alternative (section 6).     

The prediction of choice

This paper is concerned with a central concept in social measurement such as opinion polls, the measurement of attitudes, the prediction of political elections, the measurement of moral values, the measurement of consumer preferences, the measurement of utility, and the measurement of aesthetic values. The concept is that of the discriminal dispersion and its interesting effects in the prediction of choice.