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Computer simulators are often used as a substitute of complex real-life phenomena which are either expensive or infeasible to experiment with. This paper focuses on how to efficiently solve the inverse problem for an expensive to evaluate time series valued computer simulator. The research is motivated by a hydrological simulator which has to be tuned for generating realistic rainfall-runoff measurements in Athens, Georgia, USA. Assuming that the simulator returns g(x,t) over L time points for a given input x, the proposed methodology begins with a careful construction of a discretization (time-) point set (DPS) of size $k << L$, achieved by adopting a regression spline approximation of the target response series at k optimal knots locations $\{t^*_1, t^*_2, ..., t^*_k\}$. Subsequently, we solve k scalar valued inverse problems for simulator $g(x,t^*_j)$ via the contour estimation method. The proposed approach, named MSCE, also facilitates the uncertainty quantification of the inverse solution. Extensive simulation study is used to demonstrate the performance comparison of the proposed method with the popular competitors for several test-function based computer simulators and a real-life rainfall-runoff measurement model., Comment: 33 pages

This study uses patent renewal information to estimate private value of patents by technology and ownership status. Patent value refers to the economic reward that the inventor extracts from the patent by making, using or selling an invention. Thus, we measure the value of patent right (private value of patent) from the patentee perspective. Our empirical analysis comprises of 555 patents with application year during 1999 to 2002. The term of these patents either ended in 2018 or lapsed due to non-payment of renewal fee. We model renewal decision of patentee as ordered probit where patent renewal fee increases with the age of patent. Variables such as patent family size, technological scope, number of inventors and grant lag are used as explanatory variables in the corresponding regression. Hence, this paper combines the patentee renewal decision along with patents characteristics and renewal cost schedule to estimate the initial rent distribution. We find that a large number of patents expire at an early stage leaving few patents with high value corroborating the results of studies using European, American and Chinese data. As expected, certain technology class patents enjoy high valuation.

This study assesses the degree to which the social value of patents can be connected to the private value of patents across discrete and complex innovation. The underlying theory suggests that the social value of cumulative patents is less related to the private value of patents. We use the patents applied between 1995 to 2002 and granted on or before December 2018 from the Indian Patent Office (IPO). Here the patent renewal information is utilized as a proxy for the private value of the patent. We have used a variety of logit regression model for the impact assessment analysis. The results reveal that the technology classification (i.e., discrete versus complex innovations) plays an important role in patent value assessment, and some technologies are significantly different than the others even within the two broader classifications. Moreover, the non-resident patents in India are more likely to have a higher value than the resident patents. According to the conclusions of this study, only a few technologies from the discrete and complex innovation categories have some private value. There is no evidence that patent social value indicators are less useful in complicated technical classes than in discrete ones.

The purpose of this paper is to use patent level characteristics to estimate the survival of resident patents (filed at the Indian Patent Office (IPO) and assigned to firms in India). This study uses the renewal information of firm-level patents applied during 1st January 1995 and 31st December 2005, which were eventually granted. The data provided by IPO consists of 2025 resident patents assigned to 266 firms (foreign subsidiary firms and domestic firms). The survival analysis is carried out via Kaplan-Meier estimation and Cox proportional hazard regression. The outcomes of this study suggest that the survival length of patents significantly depends on their technological scope and inventor size. Moreover, the patents of the firms taking tax credit benefits exhibit lower survival rate as compared to patents of remaining firms. The study also finds that the patents filed by foreign firms with DSIR affiliation are getting more benefit from the R&D tax incentive policy.

Over the last two decades, the science has come a long way from relying on only physical experiments and observations to experimentation using computer simulators. This chapter focusses on the modelling and analysis of data arising from computer simulators. It turns out that traditional statistical metamodels are often not very useful for analyzing such datasets. For deterministic computer simulators, the realizations of Gaussian Process (GP) models are commonly used for fitting a surrogate statistical metamodel of the simulator output. The chapter starts with a quick review of the standard GP based statistical surrogate model. The chapter also emphasizes on the numerical instability due to near-singularity of the spatial correlation structure in the GP model fitting process. The authors also present a few generalizations of the GP model, reviews methods and algorithms specifically developed for analyzing big data obtained from computer model runs, and reviews the popular analysis goals of such computer experiments. A few real-life computer simulators are also briefly outlined here.

Gaussian process (GP) based statistical surrogates are popular, inexpensive substitutes for emulating the outputs of expensive computer models that simulate real-world phenomena or complex systems. Here, we discuss the evolution of dynamic GP model - a computationally efficient statistical surrogate for a computer simulator with time series outputs. The main idea is to use a convolution of standard GP models, where the weights are guided by a singular value decomposition (SVD) of the response matrix over the time component. The dynamic GP model also adopts a localized modeling approach for building a statistical model for large datasets. In this chapter, we use several popular test function based computer simulators to illustrate the evolution of dynamic GP models. We also use this model for predicting the coverage of Malaria vaccine worldwide. Malaria is still affecting more than eighty countries concentrated in the tropical belt. In 2019 alone, it was the cause of more than 435,000 deaths worldwide. The malice is easy to cure if diagnosed in time, but the common symptoms make it difficult. We focus on a recently discovered reliable vaccine called Mos-Quirix (RTS,S) which is currently going under human trials. With the help of publicly available data on dosages, efficacy, disease incidence and communicability of other vaccines obtained from the World Health Organisation, we predict vaccine coverage for 78 Malaria-prone countries.

Factorial designs are often used in various industrial and sociological experiments to identify significant factors and factor combinations that may affect the process response. In the statistics literature, several studies have investigated the analysis, construction, and isomorphism of factorial and fractional factorial designs. When there are multiple choices for a design, it is helpful to have an easy-to-use tool for identifying which are distinct, and which of those can be efficiently analyzed/has good theoretical properties. For this task, we present an R library called IsoCheck that checks the isomorphism of multi-stage 2^n factorial experiments with randomization restrictions. Through representing the factors and their combinations as a finite projective geometry, IsoCheck recasts the problem of searching over all possible relabelings as a search over collineations, then exploits projective geometric properties of the space to make the search much more efficient. Furthermore, a bitstring representation of the factorial effects is used to characterize all possible rearrangements of designs, thus facilitating quick comparisons after relabeling. We present several examples with R code to illustrate the usage of the main functions in IsoCheck. Besides checking equivalence and isomorphism of 2^n multi-stage factorial designs, we demonstrate how the functions of the package can be used to create a catalog of all non-isomorphic designs, and subsequently rank these designs based on a suitably defined ranking criterion. IsoCheck is free software and distributed under the General Public License and available from the Comprehensive R Archive Network., Comment: 21 pages

In this paper we consider a dynamic computer simulator that produces a time-series response $y_t(x)$ over $L$ time points, for every given input parameter $x$. We propose a method for solving inverse problems, which refer to the finding of a set of inputs that generates a pre-specified simulator output. Inspired by the sequential approach of contour estimation via expected improvement criterion developed by Ranjan et al. (2008, DOI: 10.1198/004017008000000541), our proposed method discretizes the target response series on $k \; (\ll L)$ time points, and then iteratively solves $k$ scalar-valued inverse problems with respect to the discretized targets. We also propose to use spline smoothing of the target response series to identify the optimal number of knots, $k$, and the actual location of the knots for discretization. The performance of the proposed methods is compared for several test-function based computer simulators and the motivating real application that uses a rainfall-runoff measurement model named Matlab-Simulink model.

Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known as experimental design, that is, how to select the input settings where the computer simulator is run and the corresponding response is collected. Extra care should be taken in the selection process because computer simulators can be computationally expensive to run. The selection shall acknowledge and achieve the goal of the analysis. This article focuses on the goal of producing more accurate prediction which is important for risk assessment and decision making. We propose two new methods of design approaches that sequentially select input settings to achieve this goal. The approaches make novel applications of simultaneous and sequential contour estimations. Numerical examples are employed to demonstrate the effectiveness of the proposed approaches., Comment: 24 pages

A comprehensive understanding of the population growth of a variety of pests is often crucial for efficient crop management. Our motivating application comes from calibrating a two-delay blowfly (TDB) model which is used to simulate the population growth of Panonychus ulmi (Koch) or European red mites that infest on apple leaves and diminish the yield. We focus on the inverse problem, that is, to estimate the set of parameters/inputs of the TDB model that produces the computer model output matching the field observation as closely as possible. The time series nature of both the field observation and the TDB outputs makes the inverse problem significantly more challenging than in the scalar valued simulator case. In spirit, we follow the popular sequential design framework of computer experiments. However, due to the time-series response, a singular value decomposition based Gaussian process model is used for the surrogate model, and subsequently, a new expected improvement criterion is developed for choosing the follow-up points. We also propose a new criterion for extracting the optimal inverse solution from the final surrogate. Three simulated examples and the real-life TDB calibration problem have been used to demonstrate higher accuracy of the proposed approach as compared to popular existing techniques., Comment: 36 pages

Calibration of hydrological time-series models is a challenging task since these models give a wide spectrum of output series and calibration procedures require significant amount of time. From a statistical standpoint, this model parameter estimation problem simplifies to finding an inverse solution of a computer model that generates pre-specified time-series output (i.e., realistic output series). In this paper, we propose a modified history matching approach for calibrating the time-series rainfall-runoff models with respect to the real data collected from the state of Georgia, USA. We present the methodology and illustrate the application of the algorithm by carrying a simulation study and the two case studies. Several goodness-of-fit statistics were calculated to assess the model performance. The results showed that the proposed history matching algorithm led to a significant improvement, of 30% and 14% (in terms of root mean squared error) and 26% and 118% (in terms of peak percent threshold statistics), for the two case-studies with Matlab-Simulink and SWAT models, respectively.

In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining features of the relationship between the return and its volatility. Among one of the earliest SVM, Taylor (1982) proposed a hierarchical model, where the current return is a function of the current latent volatility, which is further modeled as an auto-regressive process. In an attempt to make the SVMs more appropriate for complex realistic market behavior, a leverage parameter was introduced in the Taylor SVM, which however led to the violation of the efficient market hypothesis (EMH, a necessary mean-zero condition for the return distribution that prevents arbitrage possibilities). Subsequently, a host of alternative SVMs had been developed and are currently in use. In this paper, we propose mean-corrections for several generalizations of Taylor SVM that capture the complex market behavior as well as satisfy EMH. We also establish a few theoretical results to characterize the key desirable features of these models, and present comparison with other popular competitors. Furthermore, four real-life examples (Oil price, CITI bank stock price, Euro-USD rate, and S&P 500 index returns) have been used to demonstrate the performance of this new class of SVMs., Comment: 35 pages

The recent accelerated growth in the computing power has generated popularization of experimentation with dynamic computer models in various physical and engineering applications. Despite the extensive statistical research in computer experiments, most of the focus had been on the theoretical and algorithmic innovations for the design and analysis of computer models with scalar responses. In this paper, we propose a computationally efficient statistical emulator for a large-scale dynamic computer simulator (i.e., simulator which gives time series outputs). The main idea is to first find a good local neighbourhood for every input location, and then emulate the simulator output via a singular value decomposition (SVD) based Gaussian process (GP) model. We develop a new design criterion for sequentially finding this local neighbourhood set of training points. Several test functions and a real-life application have been used to demonstrate the performance of the proposed approach over a naive method of choosing local neighbourhood set using the Euclidean distance among design points., Comment: 32 pages, 7 figures

For an expensive to evaluate computer simulator, even the estimate of the overall surface can be a challenging problem. In this paper, we focus on the estimation of the inverse solution, i.e., to find the set(s) of input combinations of the simulator that generates (or gives good approximation of) a pre-determined simulator output. Ranjan et al. (2008) proposed an expected improvement criterion under a sequential design framework for the inverse problem with a scalar valued simulator. In this paper, we focus on the inverse problem for a time-series valued simulator. We have used a few simulated and two real examples for performance comparison., Comment: 23 pages (submitted to OJS)

In an efficient stock market, the log-returns and their time-dependent variances are often jointly modelled by stochastic volatility models (SVMs). Many SVMs assume that errors in log-return and latent volatility process are uncorrelated, which is unrealistic. It turns out that if a non-zero correlation is included in the SVM (e.g., Shephard (2005)), then the expected log-return at time t conditional on the past returns is non-zero, which is not a desirable feature of an efficient stock market. In this paper, we propose a mean-correction for such an SVM for discrete-time returns with non-zero correlation. We also find closed form analytical expressions for higher moments of log-return and its lead-lag correlations with the volatility process. We compare the performance of the proposed and classical SVMs on S&P 500 index returns obtained from NYSE., Comment: 15 pages; 5 figures, submitted to IJSP

A computer code or simulator is a mathematical representation of a physical system, for example a set of differential equations. Running the code with given values of the vector of inputs, x, leads to an output y(x) or several such outputs. For instance, one application we use for illustration simulates the average tidal power, y, generated as a function of the turbine location, x = (x1, x2), in the Bay of Fundy, Nova Scotia, Canada (Ranjan et al. 2011). Performing scientific or engineering experiments via such a computer code is often more time and cost effective than running a physical experiment. Choosing new runs sequentially for optimization, moving y to a target, etc. has been formalized using the concept of expected improvement (Jones et al. 1998). The next experimental run is made where the expected improvement in the function of interest is largest. This expectation is with respect to the predictive distribution of y from a statistical model relating y to x. By considering a set of possible inputs x for the new run, we can choose that which gives the largest expectation., Comment: 14 pages, 3 figures. in Chapter 7 - Statistics in Action: A Canadian Outlook (ISBN 9781482236231 - CAT# K23109), Edited by Jerald F . Lawless Chapman and Hall/CRC, 2014

Constrained blackbox optimization is a difficult problem, with most approaches coming from the mathematical programming literature. The statistical literature is sparse, especially in addressing problems with nontrivial constraints. This situation is unfortunate because statistical methods have many attractive properties: global scope, handling noisy objectives, sensitivity analysis, and so forth. To narrow that gap, we propose a combination of response surface modeling, expected improvement, and the augmented Lagrangian numerical optimization framework. This hybrid approach allows the statistical model to think globally and the augmented Lagrangian to act locally. We focus on problems where the constraints are the primary bottleneck, requiring expensive simulation to evaluate and substantial modeling effort to map out. In that context, our hybridization presents a simple yet effective solution that allows existing objective-oriented statistical approaches, like those based on Gaussian process surrogates and expected improvement heuristics, to be applied to the constrained setting with minor modification. This work is motivated by a challenging, real-data benchmark problem from hydrology where, even with a simple linear objective function, learning a nontrivial valid region complicates the search for a global minimum., Comment: 22 Pages, 2 additional supplementary, 5 figures

Factorial designs with randomization restrictions are often used in industrial experiments when a complete randomization of trials is impractical. In the statistics literature, the analysis, construction and isomorphism of factorial designs has been extensively investigated. Much of the work has been on a case-by-case basis -- addressing completely randomized designs, randomized block designs, split-plot designs, etc. separately. In this paper we take a more unified approach, developing theoretical results and an efficient relabeling strategy to both construct and check the isomorphism of multi-stage factorial designs with randomization restrictions. The examples presented in this paper particularly focus on split-lot designs., Comment: 25 pages (accepted in Journal of Statistical Theory and Practice)

Gaussian Process (GP) models are popular statistical surrogates used for emulating computationally expensive computer simulators. The quality of a GP model fit can be assessed by a goodness of fit measure based on optimized likelihood. Finding the global maximum of the likelihood function for a GP model is typically very challenging as the likelihood surface often has multiple local optima, and an explicit expression for the gradient of the likelihood function is typically unavailable. Previous methods for optimizing the likelihood function (e.g. MacDonald et al. (2013)) have proven to be robust and accurate, though relatively inefficient. We propose several likelihood optimization techniques, including two modified multi-start local search techniques, based on the method implemented by MacDonald et al. (2013), that are equally as reliable, and significantly more efficient. A hybridization of the global search algorithm Dividing Rectangles (DIRECT) with the local optimization algorithm BFGS provides a comparable GP model quality for a fraction of the computational cost, and is the preferred optimization technique when computational resources are limited. We use several test functions and a real application from an oil reservoir simulation to test and compare the performance of the proposed methods with the one implemented by MacDonald et al. (2013) in the R library GPfit. The proposed method is implemented in a Matlab package, GPMfit.

Gaussian process (GP) models are commonly used statistical metamodels for emulating expensive computer simulators. Fitting a GP model can be numerically unstable if any pair of design points in the input space are close together. Ranjan, Haynes, and Karsten (2011) proposed a computationally stable approach for fitting GP models to deterministic computer simulators. They used a genetic algorithm based approach that is robust but computationally intensive for maximizing the likelihood. This paper implements a slightly modified version of the model proposed by Ranjan et al. (2011), as the new R package GPfit. A novel parameterization of the spatial correlation function and a new multi-start gradient based optimization algorithm yield optimization that is robust and typically faster than the genetic algorithm based approach. We present two examples with R codes to illustrate the usage of the main functions in GPfit. Several test functions are used for performance comparison with a popular R package mlegp. GPfit is a free software and distributed under the general public license, as part of the R software project (R Development Core Team 2012)., Comment: 20 pages, 17 images

Latin hypercube designs (LHDs) with space-filling properties are widely used for emulating computer simulators. Over the last three decades, a wide spectrum of LHDs have been proposed with space-filling criteria like minimum correlation among factors, maximin interpoint distance, and orthogonality among the factors via orthogonal arrays (OAs). Projective geometric structures like spreads, covers and stars of PG(p-1,q) can be used to characterize the randomization restriction of multistage factorial experiments. These geometric structures can also be used for constructing OAs and nearly OAs (NOAs). In this paper, we present a new class of space-filling LHDs based on NOAs derived from stars of PG(p-1, 2)., Comment: 16 pages (accepted in SPL)

Classification of satellite images is a key component of many remote sensing applications. One of the most important products of a raw satellite image is the classified map which labels the image pixels into meaningful classes. Though several parametric and non-parametric classifiers have been developed thus far, accurate labeling of the pixels still remains a challenge. In this paper, we propose a new reliable multiclass-classifier for identifying class labels of a satellite image in remote sensing applications. The proposed multiclass-classifier is a generalization of a binary classifier based on the flexible ensemble of regression trees model called Bayesian Additive Regression Trees (BART). We used three small areas from the LANDSAT 5 TM image, acquired on August 15, 2009 (path/row: 08/29, L1T product, UTM map projection) over Kings County, Nova Scotia, Canada to classify the land-use. Several prediction accuracy and uncertainty measures have been used to compare the reliability of the proposed classifier with the state-of-the-art classifiers in remote sensing., Comment: 31 pages, 6 figures, 4 tables

The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central processing units (CPUs), and thus provide a great deal of promise for computationally intensive statistical applications. Fitting complex statistical models with a large number of parameters and/or for large datasets is often very computationally expensive. In this study, we focus on Gaussian process (GP) models -- statistical models commonly used for emulating expensive computer simulators. We demonstrate that the computational cost of implementing GP models can be significantly reduced by using a CPU+GPU heterogeneous computing system over an analogous implementation on a traditional computing system with no GPU acceleration. Our small study suggests that GP models are fertile ground for further implementation on CPU+GPU systems., Comment: 11 pages, 2 figures

In computer experiments, a mathematical model implemented on a computer is used to represent complex physical phenomena. These models, known as computer simulators, enable experimental study of a virtual representation of the complex phenomena. Simulators can be thought of as complex functions that take many inputs and provide an output. Often these simulators are themselves expensive to compute, and may be approximated by "surrogate models" such as statistical regression models. In this paper we consider a new kind of surrogate model, a Bayesian ensemble of trees (Chipman et al. 2010), with the specific goal of learning enough about the simulator that a particular feature of the simulator can be estimated. We focus on identifying the simulator's global minimum. Utilizing the Bayesian version of the Expected Improvement criterion (Jones et al. 1998), we show that this ensemble is particularly effective when the simulator is ill-behaved, exhibiting nonstationarity or abrupt changes in the response. A number of illustrations of the approach are given, including a tidal power application., Comment: 21 pages

For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are commonly used to model such simulator outputs. Fitting a GP model to $n$ data points requires the computation of the inverse and determinant of $n \times n$ correlation matrices, $R$, that are sometimes computationally unstable due to near-singularity of $R$. This happens if any pair of design points are very close together in the input space. The popular approach to overcome near-singularity is to introduce a small nugget (or jitter) parameter in the model that is estimated along with other model parameters. The inclusion of a nugget in the model often causes unnecessary over-smoothing of the data. In this paper, we propose a lower bound on the nugget that minimizes the over-smoothing and an iterative regularization approach to construct a predictor that further improves the interpolation accuracy. We also show that the proposed predictor converges to the GP interpolator., Comment: 26 pages, 12 figures

Deterministic computer simulations are often used as a replacement for complex physical experiments. Although less expensive than physical experimentation, computer codes can still be time-consuming to run. An effective strategy for exploring the response surface of the deterministic simulator is the use of an approximation to the computer code, such as a Gaussian process (GP) model, coupled with a sequential sampling strategy for choosing design points that can be used to build the GP model. The ultimate goal of such studies is often the estimation of specific features of interest of the simulator output, such as the maximum, minimum, or a level set (contour). Before approximating such features with the GP model, sufficient runs of the computer simulator must be completed. Sequential designs with an expected improvement (EI) function can yield good estimates of the features with a minimal number of runs. The challenge is that the expected improvement function itself is often multimodal and difficult to maximize. We develop branch and bound algorithms for efficiently maximizing the EI function in specific problems, including the simultaneous estimation of a minimum and a maximum, and in the estimation of a contour. These branch and bound algorithms outperform other optimization strategies such as genetic algorithms, and over a number of sequential design steps can lead to dramatically superior accuracy in estimation of features of interest., Comment: 26 pages, 14 figures, preprint submitted to the Journal of Statistical Planning and Inference

Regular factorial designs with randomization restrictions are widely used in practice. This paper provides a unified approach to the construction of such designs using randomization defining contrast subspaces for the representation of randomization restrictions. We use finite projective geometry to determine the existence of designs with the required structure and develop a systematic approach for their construction. An attractive feature is that commonly used factorial designs with randomization restrictions are special cases of this general representation. Issues related to the use of these designs for particular factorial experiments are also addressed., Comment: Published in at http://dx.doi.org/10.1214/08-AOS644 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Identifying promising compounds from a vast collection of feasible compounds is an important and yet challenging problem in the pharmaceutical industry. An efficient solution to this problem will help reduce the expenditure at the early stages of drug discovery. In an attempt to solve this problem, Mandal, Wu and Johnson [Technometrics 48 (2006) 273--283] proposed the SELC algorithm. Although powerful, it fails to extract substantial information from the data to guide the search efficiently, as this methodology is not based on any statistical modeling. The proposed approach uses Gaussian Process (GP) modeling to improve upon SELC, and hence named $\mathcal{G}$-SELC. The performance of the proposed methodology is illustrated using four and five dimensional test functions. Finally, we implement the new algorithm on a real pharmaceutical data set for finding a group of chemical compounds with optimal properties., Comment: Published in at http://dx.doi.org/10.1214/08-AOAS199 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)