Identification and Estimation of Graphical Models with Nonignorable Nonresponse

We study the identification and estimation of graphical models with nonignorable nonresponse. An observable variable correlated to nonresponse is added to identify the mean of response for the unidentifiable model. An approach to estimating the marginal mean of response is proposed, based on simulation imputation methods which are introduced for a variety of models including linear, generalized linear, and monotone nonlinear models. The proposed mean estimators are N -consistent, where N is the sample size. Finite sample simulations confirm the effectiveness of the proposed method. Sensitivity analysis for the untestable assumption on our augmented model is also conducted. A real data example is employed to illustrate the use of the proposed methodology.

Solving the problem of mathematical models overparameterization for some nonlinear oscillating systems

This study proposes a numerical-analytical method that allows us to simplify the model, which is obtained on the basis of the single observable variable of an object under the study, and which may be overparameterized. As a model, we consider a system of ordinary differential equations with polynomial right-hand sides. To solve this problem, the so-called differential model is used, that is, a system in which unknown variables are replaced by derivatives of the observed variable, and which is derived on the basis of a system under the study so that the observed variables of these systems coincide. The method of simplification of a system under the study is based on the fact that using a numerical method, a simpler differential model can be obtained. Next, an analytical transition from a simplified differential model to a simplified original system is performed. In this case, the time series error remains within given limits even for systems with deterministic chaos, despite their high sensitivity to the initial conditions.

IDENTIFICATION OF REGRESSION MODELS WITH A MISCLASSIFIED AND ENDOGENOUS BINARY REGRESSOR

We study identification in nonparametric regression models with a misclassified and endogenous binary regressor when an instrument is correlated with misclassification error. We show that the regression function is nonparametrically identified if one binary instrument variable and one binary covariate satisfy the following conditions. The instrumental variable corrects endogeneity; the instrumental variable must be correlated with the unobserved true underlying binary variable, must be uncorrelated with the error term in the outcome equation, but is allowed to be correlated with the misclassification error. The covariate corrects misclassification; this variable can be one of the regressors in the outcome equation, must be correlated with the unobserved true underlying binary variable, and must be uncorrelated with the misclassification error. We also propose a mixture-based framework for modeling unobserved heterogeneous treatment effects with a misclassified and endogenous binary regressor and show that treatment effects can be identified if the true treatment effect is related to an observed regressor and another observable variable.

On the Observability Requirement in Economics as an Axiomatic Science

This paper points out as the only social science that is axiomatic, economics has the power of predicting beyond interpreting. It then explains that in hypothesis testing, the law of demand is the only indispensable axiom in economics, and that quantity demanded is the only non-observable variable that must be retained. After reviewing his disagreements with his peers and colleagues, and his success in predicting the transformation of China, the author argues that the profession has gone astray with the surge in the use of non-observables.

Reliability analysis of non-destructive testing models within a probabilistic approach

The diagnosis of reinforced concrete is essential to detect the degradation and thus maintain the structural performance of civil engineering structures. This paper aims to establish a mathematical relationship between the ultrasonic pulse velocity UPV (considered as an observable variable) and two concrete properties indicators (compressive strength fc and water content W) within a probabilistic framework. Synthetic simulations are proposed to derive a conversion model between the statistical properties of the output and the input parameters for a reinforced concrete structure by taking into account spatial variability of concrete.

Reconstruction of the Lorenz system using the method of perspective coefficients

Reconstruction of the Lorenz ordinary differential equations system is performed by using perspective coefficients method. Four systems that have structures different from Lorenz system and can reproduce time series of one variable of Lorenz system were found. In many areas of science, the problem of identifying a system of ordinary differential equations (ODE) from a time series of one observable variable is relevant. If the right-hand sides of an ODE system are polynomials, then solving such a problem only by numerical methods allows to obtain a model containing, in most cases, redundant terms and not reflecting the physics of the process. The preliminary choice of the structure of the system allows to improve the precision of the reconstruction. Since this study considers only the single time series of the observable variable, and there are no additional requirements for candidate systems, we will look only for systems of ODE's that have the least number of terms in the equations. We will look for candidate systems among particular cases of the system with quadratic polynomial right-hand sides. To solve this problem, we will use a combination of analytical and numerical methods proposed in [12, 11]. We call the original system (OS) the ODE system, which precisely describes the dynamics of the process under study. We also use another type of ODE system-standard system (SS), which has the polynomial or rational function only in one equation. The number of OS variables is equal to the number of SS variables. The observable variable of the SS coincides with the observable variable of the OS. The SS must correspond to the OS. Namely, all the SS coefficients can be analytically expressed in terms of the OS coefficients. In addition, there is a numerical method [12], which allows to determine the SS coefficients from a time series. To find only the simplest OS, one can use the perspective coefficients method [10], which means the following. Initially, the SS is reconstructed from a time series using a numerical method. Then, using analytical relations and the structure of the SS, we determine which OS coefficients are strictly zero and strictly non-zero and form the initial system (IS), which includes only strictly non-zero coefficients. After that, the IS is supplemented with OS coefficients until the corresponding SS coincides with the SS obtained by a numerical method. The result will be one or more OS’s. Using this approach, we have found 4 OS structures with 7 coefficients that differ from the Lorenz system [17], but are able to reproduce exactly the time series of X variable of the Lorenz system. Numerical values of the part of the coefficients and relations connecting the rest of the coefficients were found for each OS

Development of a Causal Relationship Model of Behavior in Household Disposal of Used Batteries in a Rural Community Banpru Town Municipality, Hatyai District, Songkhla Province

This research aimed to develop a causal relationship model of the behavior of a Thai rural community in disposing of used batteries. The variables studied were 1) the household latent variable (three observable variables); 2) the social latent variable (six observable variables); 3) the intention latent variable (three observable variable); and 4) the behavior latent variable (three observable variables). Six hundred households were surveyed using a questionnaire. The questionnaire developed was validated by seven experts and its reliability was established by testing it with a sample group. Results showed that the modified model do present a good overall level of fit. The House and social positively and directly influenced intention. Intention positively and directly influenced behavior. The theoretical and practical implications relating specifically to intention to the behavior in disposing of used dry batteries by households are emphasized. The modified model indicated eighty-nine percent of the variance in the behavior in disposing of used dry batteries by households was explained by the intention factors. The most direct effect on behavior was the intention factors with 0.89 of effect size. The factors with indirect effects on behavior were household and social factors with an effect size of 0.52 and 0.35.

Hypothesis testing and advanced distinguishers in differential cryptanalysis of block ciphers

Distinguishing distributions is a major part during cryptanalysis of symmetric block ciphers. The goal of the cryptanalyst is to distinguish two distributions; one that characterizes the number of certain events which occur totally at random and another one that characterizes same type of events but due to propagation inside the cipher. This can be realized as a hypothesis testing problem, where a source is used to generate independent random samples in some given finite set with some distribution P, which is either R or W, corresponding to propagation inside the cipher or a random permutation respectively. Distinguisher’s goal is to determine which one is most likely the one which was used to generate the sample. In this paper, we study a general hypothesis-testing based approach to construct statistical distinguishers using truncated differential properties. The observable variable in our case is the expected number of pairs that follow a certain truncated differential property of the form ΔX → ΔY after a certain number of rounds. As a proof of concept, we apply this methodology to GOST and SIMON64/128 block ciphers and present distinguishers on 20 and 22 rounds respectively.

Real Time Dynamic System Stochastic Identification in Video Capture for Data Compression, Image Interpolation, Prediction, and Augmented Reality

In computer vision, cameras more and more accurate, fast, 3D featured are used. These still evolutions generate more data, which is an issue for users to store it with standard compression for example for recording proof in case of products manufacture defective. The aim of this work is to develop a specific solution adapted for vision systems which have a known scenario and can be described by dynamic models. In this framework, Kalman filters are used for data compression, observable variable prediction, and augmented reality. The developed concepts are tested with a scenario of a ruler on a table. The experiment aims to check the data compression level, the estimation of the friction forces coefficient of the ruler and the prediction of the stop position.