Generalized Inference Method Research Articles

Hold-out strategy for selecting learning models: Application to categorization subjected to presentation orders

In this article, we develop a new general inference method for selecting learning models. The method relies upon a specific hold-out cross-validation, which takes into account the dependency within the data. This allows us to retrieve the model that best fits the learning strategy of a single individual. The novelty of our approach lies on the choice of the testing set, both in the experimental design and in the data analysis. This individual approach is then applied to two category learning models (ALCOVE and Component-cue) on data-sets manipulating presentation order, after verification of the reliability of our method. We found that both models performed equally well during transfer, but Component-cue best fits the majority of participants during learning. To further analyze these models, we also investigated a potential relation between the underlying mechanisms of the models and the actual types of presentation order assigned to participants.

Interval estimation for the difference of two correlated gamma means: a generalized inference method and hybrid methods

Gamma distribution plays an important role in applied fields due to its flexibility of accommodating right-skewed data. Although inference methods for single gamma mean and for difference of two independent gamma means have been well studied, inference methods for difference of two correlated gamma means are sparse. This paper considers the problem of interval estimation for the difference of two correlated gamma means. We propose several inference methods including a method based on the concepts of generalized inference and two hybrid methods based on the method of variance estimates recovery. An extensive Monte Carlo simulation study was conducted to assess the performance of the proposed methods in terms of coverage probabilities and average lengths of the estimated intervals. Two real data examples from medical and engineering studies are analyzed using the proposed methods.

Inference for partially observed epidemic dynamics guided by Kalman filtering techniques

Despite the recent development of methods dealing with partially observed epidemic dynamics (unobserved model coordinates, discrete and noisy outbreak data), limitations remain in practice, mainly related to the quantity of augmented data and calibration of numerous tuning parameters. In particular, as coordinates of dynamic epidemic models are coupled, the presence of unobserved coordinates leads to a statistically difficult problem. The aim is to propose an easy-to-use and general inference method that is able to tackle these issues. First, using the properties of epidemics in large populations, a two-layer model is constructed. Via a diffusion-based approach, a Gaussian approximation of the epidemic density-dependent Markovian jump process is obtained, representing the state model. The observational model, consisting of noisy observations of certain model coordinates, is approximated by Gaussian distributions. Then, an inference method based on an approximate likelihood using Kalman filtering recursion is developed to estimate parameters of both the state and observational models. The performance of estimators of key model parameters is assessed on simulated data of SIR epidemic dynamics for different scenarios with respect to the population size and the number of observations. This performance is compared with that obtained using the well-known maximum iterated filtering method. Finally, the inference method is applied to a real data set on an influenza outbreak in a British boarding school in 1978.

Inference for the common mean of several Birnbaum–Saunders populations

ABSTRACTThe Birnbaum–Saunders distribution is a widely used distribution in reliability applications to model failure times. For several samples from possible different Birnbaum–Saunders distributions, if their means can be considered as the same, it is of importance to make inference for the common mean. This paper presents procedures for interval estimation and hypothesis testing for the common mean of several Birnbaum–Saunders populations. The proposed approaches are hybrids between the generalized inference method and the large sample theory. Some simulation results are conducted to present the performance of the proposed approaches. The simulation results indicate that our proposed approaches perform well. Finally, the proposed approaches are applied to analyze a real example on the fatigue life of 6061-T6 aluminum coupons for illustration.

Alternative Confidence Intervals on Variance Components in a Simple Regression Model with a Balanced Two-Fold Nested Error Structure

In applications using a linear regression model with a balanced two-fold nested error structure, interest focuses on inferences concerning variability of the effects associated with the levels of nesting. This article proposes confidence intervals on the variance components associated with the primary and secondary levels in the model. In order to construct the confidence intervals we use a modified large sample method, generalized inference method, and Satterthwaite approximation. Computer simulation is performed to compare the proposed confidence intervals. A numerical example is provided to demonstrate the intervals.

Generalized Inference for Measuring Process Yield With the Contamination of Measurement Errors—Quality Control for Silicon Wafer Manufacturing Processes in the Semiconductor Industry

The yield index Spk provides an exact measure of process yield for normally distributed processes, and it has been popularly accepted by many engineers and shop floor controllers as communication tools for evaluating and improving the manufacturing quality. Most research works related to Spk are carried out under the assumption of no gauge measurement errors. Unfortunately, such an assumption does not accommodate real situations closely even with modern and highly sophisticated measuring instruments. Conclusions drawn from process capability analysis without considering measurement errors are hence unreliable. Recently, Wang studied the impact of the process yield estimation and judgment on the true process yield in the presence of measurement errors and indicated that the presence of measurement errors in the data leads to different behaviors of the estimator according to the entity of the contamination degree. To remedy this, this paper applies the concept of generalized pivotal quantities to construct generalized confidence intervals for Spk with consideration of measurement errors. A series of simulations was undertaken to evaluate the performance of the proposed generalized inference method. The results reveal that the generalized inference method performs very well for measuring process yield in the presence of measurement errors.

Information-geometric approach to inferring causal directions

While conventional approaches to causal inference are mainly based on conditional (in)dependences, recent methods also account for the shape of (conditional) distributions. The idea is that the causal hypothesis “X causes Y” imposes that the marginal distribution PX and the conditional distribution PY|X represent independent mechanisms of nature. Recently it has been postulated that the shortest description of the joint distribution PX,Y should therefore be given by separate descriptions of PX and PY|X. Since description length in the sense of Kolmogorov complexity is uncomputable, practical implementations rely on other notions of independence. Here we define independence via orthogonality in information space. This way, we can explicitly describe the kind of dependence that occurs between PY and PX|Y making the causal hypothesis “Y causes X” implausible. Remarkably, this asymmetry between cause and effect becomes particularly simple if X and Y are deterministically related. We present an inference method that works in this case. We also discuss some theoretical results for the non-deterministic case although it is not clear how to employ them for a more general inference method.

Inferences on the common mean of several inverse Gaussian populations

This paper presents procedures for hypothesis testing and interval estimation for the common mean of several inverse Gaussian populations when the scalar parameters are unknown and unequal. The proposed approaches are hybrids between the generalized inference method and the large-sample theory. Some simulation results are presented to compare the performance of the proposed approaches with that of the existing approach. The simulation results indicate that one of the proposed approaches performs better than the existing approach in most cases. Furthermore, our approaches can be simply carried out by a few simulation steps. Finally, the proposed approaches are illustrated by using three examples.

A Generalized Inference Method for Fuzzy Quantified and Truth-Qualified Natural Language Propositions

We propose a generalized inference method for constructing natural language communication. The method is used to obtain fuzzy quantifierQ’ when “QAareFis τ →Q’(m’A) aremFism’’τ” is inferred (Q, Q’: fuzzy quantifiers,A: fuzzy subject,m, m’, m’’: modifiers,F: fuzzy predicate, τ: truth qualifier). We show thatQ’ is resolved step by step for a non-increasing type (few, ...) and a non-decreasing type (most, ...).

Applying Bootstrap method to the types I–II errors in the measurement system

AbstractThis paper attempts to evaluate different methods of calculating the type‐I and type‐II errors in the measurement system. Furthermore, we apply the Bootstrap method to construct the confidence intervals for the type‐I and type‐II errors. Also, the proposed method is compared with the generalized inference method. Several factors such as the sample size, the measurement error, the process mean, and the process variation are simulated to validate the performance. The simulation results show that both methods almost have the same performance. In addition, we develop a computer program that can evaluate the error of measurement system without changing information or data. Two case studies of the nano measurement data are used to demonstrate the application. The simulation results indicate that the sample size has an influence for all cases. The type‐I and type‐II errors are decreased when the measurement error is increased. The type‐I and type‐II errors are affected by the measurement error, the process mean, and the process deviation. The case studies show that the development of nano technology requires the immediate attention of the measurement capability. Copyright © 2007 John Wiley & Sons, Ltd.

Tuning and analysis of a fuzzy PI controller based on gain and phase margins

The nonlinearity of the simplest fuzzy PI controller with different inference methods has been discussed and it shows that Mamdani's minimum inference method is the most general inference method for the fuzzy PI controller. In addition, a novel tuning method based on gain and phase margins has been proposed to determine the weighting coefficients of the fuzzy PI controllers. With the proposed tuning formula, the nature of the fuzzy PI controller has been analyzed and it shows the desired characteristics in terms of gain and phase margins when controlling linear plants. Numerical simulations are presented to show the validity of the proposed tuning method.

Mental Spaces from a Functional Perspective

In his book Mental Spaces, Fauconnier develops a powerful theory of human knowledge representation and linguistic processing that handles a variety of problems in linguistics and the philosophy of language in a simple, uniform, and intuitively plausible way. However, he has little to say about the structure or general role of mental spaces in cognition. The present paper proposes that mental spaces are a means of organizing knowledge in support of a general inference method, simulative reasoning, found in various guises both in logic and in Artificial Intelligence. The structuring required to fulfill this role allows us to make a wide variety of predictions which seem to be borne out by evidence from natural language. In attributing a specific function to mental spaces, this paper suggests that the theory of mental spaces defines a potentially significant paradigm for knowledge representation in Artificial Intelligence.

On the Inference and Decision Models of Statistics

On the Inference and Decision Models of Statistics