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Generation of curves using incremental steps along fixed coordinate axes is important in such diverse areas as computer displays, digital plotters, and numerical control. Direct implementation of a nonparametric representation of a curve, f(x, y) = 0, has been shown to be attractive for digital generation. The algorithm in this paper is developed directly from the nonparametric representation of the curve, allows steps to be taken to any point adjacent to the current one, and uses decision variables closely related to an error criterion. Consequently, the algorithm is more general and produces curves closer to the actual curve than do previously reported algorithms.

Clozentropy testng and analysis techniques were adapted to non‐verbal material. An easily constructed, highly general test analyzes the ability of various viewers to predict what will happen next in various films. Validation showed significant differences in both entropy patterns and correct responses for (1) sophisticated and naive viewers, (2) simple and complex films, and (3) general and specific levels of prediction. The results suggest that this is a useful technique for the empirical analysis of visual communication.

Individually tailored behavioral ratings were introduced as a possible alternative to time sampling or counting each occurrence of the behavior. Interrater reliability was found to be good for the more specific behavior categories and reliability between ratings obtained from direct observation and those based on unit records was acceptable. The usefulness of individually tailored behavioral rating scales in demonstrating behavior change is demonstrated through the presentation of a representative case.

Planning pedestrian traffic in the city involves a better understanding of pedestrians' behavior and their perception of the urban environment. Lynch's (1961) studies proposed a qualitative method. An alternative method, essentially quantitative, is proposed here: pedestrians surveyed are asked to locate on a paper some well-known landmarks (six in all). Distances between each pair of them are measured. The model allows (1) interpretation of the degree of agreement between mental maps, and (2) a study of the ‘mean’ map. Perception seems to make space more symmetrical. Distortions can be explained by two effects: differences in transportation modes, and a particular knowledge of the neighborhood. The mental map recovered through multidimensional scaling is compared with the topographic one. It does not have the metric topology.

Some of the unsolved problems in the application of secondary task techniques include: (a) the evaluation of relative changes in performance in dual task situations; (b) the prediction of possible interactions between different tasks and their components; and (c) the extent of voluntary control of capacity allocation. The present paper describes a three-phase experiment in which an effort was made to attack these problems by a new methodological approach. The three successive phases included separate performance of the experimental tasks (one dimensional compensatory tracking and a digit processing, reaction time task) with adaptive adjustment of difficulty, simultaneous performance of the tasks with equal task priorities, and simultaneous performance with several manipulations of the two task priorities. The results have demonstrated the usefulness of the general methodological approach for the assessment of capacity limitations as well as for the evaluation of possible interactions between tasks. With regard to the allocation of capacity, the experimental results proved that, in general, subjects were able to adjust their allocation of capacity to the various changes in task priorities.

Articles, books, and technical reports on the theoretical and experimental estimation of probability of misclassification are listed for the case of correctly labeled or preclassified training data. By way of introduction, the problem of estimating the probability of misclassification is discussed in order to characterize the contributions of the literature.

This paper presents a two-dimensional classification of decision making based on two continuous variables which interact, namely, degree of subjectivity (objectivity) of attitude and degree of dissimilarity (similarity) of function of choice alternatives. On the basis of this typology two new ways of dissonance resolution are proposed.

This paper presents a formal analysis of the problem of determining the inferential impact of the information in a composite report from a collection of unreliable observers or sensors. Each sensor reports one of a finite number of possible states of a data system linked probabilistically with an ``objective system'' whose condition is to be inferred from the data state. The principal assumptions are that the sensors do not ``collaborate'' in making their reports and that their reports are conditioned only by the existing data state and not by the actual, unobservable state of the objective system. Use of the notion of conditional independence to express these assumptions gives the analytic expressions a tractable form which sheds light on various inference issues. The paper also briefly discusses current empirical research on the question of how well people actually adjust the impact of inferential evidence to correspond to the unreliability of the sources of information.

This is largely a review paper, describing various statistical methods for analysing interactions in general and genotype-environment interactions in particular, and giving nearly 100 references to previous work. The joint regression analysis approach introduced by Yates and Cochran (1938) is considered in some detail; alternatives to regression are discussed, as are various stability parameters. Much work has been done on statistical methods for testing for interactions in general, and this also is reviewed, from Tukey's (1949) one degree of freedom for non-additivity to Milliken and Graybill's (1970) generalisation to testing for various types of possible interaction. The difficulties of testing and inference in the presence of interaction are discussed. Data from a two-way table may be regarded as a multivariate set, as first shown by Williams (1952) and later extended by others, particularly Mandel (1969b and 1971 ). These methods are only just beginning to be used in studies of genotype-environment interactions, and several recent references are given. External measurements may be used to measure the environment and these may be either physical or biological. Again, the appropriate methods of analysis are fairly new. The interpretation of interactions is considered in relation to the use to be made of the results. It is suggested that various multivariate techniques may be used to assist in the elucidation of interactions, especially when these are not easy to explain by simpler methods of analysis.

There are two general ways to terminate the Bayesian tailored testing process:, according to the standard error of the estimate (S.E.E.) or according to the number of items administered. In this study tailoring was simulated with 100 Monte Carlo "examinees" for four different item banks. The estimate of ability obtained through tailoring was compared with the known true ability of each "examinee" as each S.E.E. level was reached and as each item was administered. As expected, the S.E.E. was a good index of validity regardless of the characteristics of the items. The relationship between the number of items administered and validity was shown to be dependent on the parameters of the items.

An attempt is made in this paper to find mosaic distribution patterns of neuron ensembles in cortical structures that can reflect changes in the functional state of the brain cortex and different types of specific activity. An indirect statistical method of defining ensemble distribution patterns in different functional states of the brain is used, and the whole pattern of neuronal responses is constructed by means of a computer.

SUMMARY Results in the theory of optimum regression designs are used to develop experimental designs for discriminating between several regression models. An extension of the Kiefer-Wolfowitz general equivalence theorem is used to establish properties of the procedures. A sequential data-dependent strategy is described and its properties investigated for specific examples. In conclusion, some difficulties in the Bayesian analysis of discrimination experiments are considered.

Threshold-type retrieval functions have been suggested by many people and used widely in clustering algorithms. In this paper, a discriminating capacity is defined for these retrieval functions. Explicit methods for computation are presented. The discriminating capacity is useful as a quantitative measure for the retrieval power of each function and can serve as a guide for selection.

Pattern recognition systems using information from the pattern which follows the present pattern are discussed. Parametric learning methods in the supervised and unsupervised machines are proposed and compare favorably with conventional methods. Furthermore, a semilinear machine with a nonparametric learning method is considered. The results of computer experiments with artificially generated data and with handprinted alphanumeric characters are given to show that the approach we adopt is quite useful for recognition of Markovian patterns.

The necessity arises in a variety of tasks to classify items on the basis of the presence of one of a number of criterial sets of co-related feature values. Such sets are called class characteristics. Because such classification problems require the identification of characteristics on the basis of limited training information, they entail a difficult search problem. Consideration of the differences between the theoretical models underlying characteristic and volume pattern generators suggests a schematic approach. Schemata, sets of commonly co-occuring features values, are probabilistic indicators of class membership whenever the characteristics are unknown but the characteristic model prevails. Formal and algorithmic solutions to the classification problem when exemplars are simple (consist only of M feature or attribute values) are described. The relevance of these procedures to problems involving general (relational) data structures is also indicated.

As a simple example of a neuronal network in which synaptic connectivity among neurons is probabilistic, Marr's model for the granular layer of cat cerebellar cortex is examined. The mean and variance are computed for the fraction of granule cells activated, and for the extent of pattern separation by granule cells, for various mossy fiber inputs and various values of connectivity and electrical parameters of the network structure. Results suggest different functions for the network, and different optimal ranges for its parameters, depending on whether Golgi cells are present or absent. The model network does not perform the functions originally prescribed for it with high reliability.

In this paper, an attempt has been made to synthesize some of the current thinking in the area of criterion-referenced testing as well as to provide the beginning of an integration of theory and method for such testing. Since criterion-referenced testing is viewed from a decision-theoretic point of view, approaches to reliability and validity estimation consistent with this philosophy are suggested. Also, to improve the decision-making accuracy of criterion-referenced tests, a Bayesian procedure for estimating true mastery scores has been proposed. This Bayesian procedure uses information about other members of a student's group (collateral information), but the resulting estimation is still criterion referenced rather than norm referenced in that the student is compared to a standard rather than to other students. In theory, the Bayesian procedure increases the “effective length” of the test by improving the reliability, the validity, and more importantly, the decision-making accuracy of the criterion-referenced test scores.

Traditional research on the methods used in teaching developmental reading at the higher educational levels has focused on either an examination of one method or a comparison of different methods. An important problem which has been largely ignored is that of developing rationales and methods for combining different methods on an individualized basis. Linear programming provides a mathematical model for determining an optimal combination of available methods in accordance with the student's original levels of input, expected gains, and goals. The study reported herein tested an application of the Linear Programming Model at the Reading Clinic of Drew University. Results, while not conclusive, indicate that this approach yields greater gains in speed scores than a traditional approach for this population.

The degree of complexity of a critical path network may be classified by calculating a Coefficient of Network Complexity. It is defined as the quotient of activities squared divided by events or preceding work items squared divided by work items. Three distinct contributions are offered. First, the CNC may serve as an indicator of the attention spent in planning the project. Second, the CNC may be used to derive a predictor of network computer processing time. Third, the CNC value suggests the appropriate processing scheme.

Hydrologic systems, like most environmental systems, are usually characterized by partial differential equations. In order to develop a suitable mathe matical model for the analysis of such systems, it, is first necessary to make use of observed data in order to identify or estimate the system parameters. The digital simulation language PDEL has been ex tended so as to facilitate this type of parameter identification. The extended version of the lan guage has been named PDEL-ID. In this paper, two hydrologic modeling problems taken from recent water-resource studies are used as examples to illustrate the parameter identification facilities of PDEL. The solution of these two problems demon strates that little programming effort and virtually no knowledge of optimization techniques are required.

Operant Conditioning procedures have diffused to applied educational settings where results are not descriptively obvious. Inferential statistics using Multiple Linear Regression Analysis (MLR) to partial variance to answer specific behavioral modification research questions are presented. Four applications of MLR to typical behavioral modification designs are illustrated. The examples represent the case where the research questions dictate the statistical design. Assumptions regarding individual subject design and repeated measurement problems are presented and are seen as minor sources of difficulty for use of inferential statistics in behavioral modification studies.

An inductive inference problem will often be structured so that the target variable (hypotheses) are logically distant from the observable events (data). In this situation it may be difficult or impossible to assess the probabilistic connection between them, but it may be possible to decompose the problem through the use of intermediate or explanatory variables. That is, it will often be possible to assess the likelihood of the observed data given some intermediate variable, and the likelihood of that intermediate variable given another, and so on, until the hypotheses of interest are reached. Inferences which incorporate one or more intermediate variables are called hierarchical, cascaded, or multistage inferences. The present paper presents a normative model for the solution of the general hierarchical inference problem. The formulation begins with a formal description of the hierarchical inference tree, including a discussion of various simplifying conditional independence assumptions. The solution is first derived for three special case models of differing structure, and then the algorithm for the general solution is given for two cases: one in which the conditional independence assumptions have been made and one in which they have not.

Heuristic procedures are presented which have been developed to perform inferences by generalizing from available information. The procedures make use of a similarity structure which is imposed on the data base using nonnumerical clustering algorithms. They are implemented in a model fact retrieval system which uses a formal query language and a property-list data structure. A program of experiments is described wherein the procedures are used with test data bases which are altered by deleting part of the data and by purposely introducing false data. It is found that the system can infer the correct response under a variety of conditions involving incomplete and inconsistent data.

This paper deals with a central problem of the analysis of communication processes. After establishing a behavioral catalog, the question arises, which units of this catalog are distinguished in respect to their function in the communication process and which are not. The latter ones should be combined into classes, which increases the predictability of the successively occurring behavioral events. A statistical method is presented and illustrated by data coming from observations of the social behavior of squirrel monkeys, which enables us to check whether or not a particular classification of catalog units increases this predictability.

This paper describes an algorithm for the unsupervised selection of gains for a Root Locus analysis. This algorithm includes breakaway point gains, critical gains, and additive increments.

Summary The state of the art in identification of biological specimens by computer is reviewed. Current methods cover construction of diagnostic keys, matching or comparison methods, and probabilistic methods related to Bayes' theorem. There are also methods for reducing the number of characters that need to be used. The methods are compared and actual and possible progress is discussed.

Little attention has been given to the selection of the most effective agents for the biological control of weeds. The consequence has been a needlessly high failure rate and cost. Seven methods for their selection are discussed and a scoring system proposed as a means of incorporating their best features.

In a longitudinal study of 192 first-graders, the author examined the predictive efficiency of a newly developed measure of visual recognition memory in predicting end of first-grade reading achievement when analyzed in conjunction with a standardized, conventional reading readiness test. Results obtained from extensive regression analyses failed to substantiate any practical predictive utility for the instrument when used with a fairly homogeneous sample.

We show that least-squares filtered and smoothed estimates of a random process given observations of another colored noise process can be expressed as certain linear combinations of the state vector of the so-called innovations representation (IR) of the observed process. The IR of a process is a representation of it as the response of a causal and causally invertible linear filter to a white-noise "innovations" process. For nonstationary colored noise processes, the IR may not always exist and a major part of this paper is devoted to the problem of identifying a proper class of such processes and of giving effective recursive algorithms for their determination. The IR can be expressed either in terms of the parameters of a known lumped model for the process or in terms of its covariance function. In the first case, our results on estimation encompass most of those found in the previous literature on the subject; in the second case, there seems to be no prior literature. Finally, we may note that our proofs rely on, and exploit in both directions, the intimate relation that exists between least-squares estimation and the innovations representation.

A problem of prognosticating a disease course is shown to be reduced to spreading a continuous mapping specified over a set of vectors the components of which equal 0 or 1.