Estimates In Order Research Articles

The order estimation for hidden Markov models

The hidden Markov model has been successfully applied to many fields. In this paper, we provide a novel method to estimate the order of finite state stationary hidden Markov models. Our method relies on the fact that return times of a fixed observation are identical distribution if starting points correspond to the unique hidden state. We obtain the order estimator by clustering all return times of different starting points, and prove that the estimator is strong consistent. The results of numerical experiments show that the proposed method has a better performance compared to the previous, its accuracy is greatly improved, and its computational complexity is significantly reduced. Finally, we give the application of our method to a real-life data set.

Enhancing piecewise‐defined surrogate response surfaces with adjoints on sets of unstructured samples to solve stochastic inverse problems

SummaryMany approaches for solving stochastic inverse problems suffer from both stochastic and deterministic sources of error. The finite number of samples used to construct a solution is a common source of stochastic error. When computational models are expensive to evaluate, surrogate response surfaces are often employed to increase the number of samples available for approximating the solution. This leads to a reduction in finite sampling errors while the deterministic error in the evaluation of each sample is potentially increased. The pointwise accuracy of sampling the surrogate is primarily impacted by two sources of deterministic error: the local order of accuracy in the surrogate and the numerical error from the numerical solution of the model. In this work, we use adjoints to simultaneously give a posteriori error and derivative estimates in order to construct low‐order, piecewise‐defined surrogates on sets of unstructured samples. Several examples demonstrate the computational gains of this approach in obtaining accurate estimates of probabilities for events in the design space of model input parameters. This lays the groundwork for future studies on goal‐oriented adaptive refinement of such surrogates.

Extending composite loss models using a general framework of advanced computational tools

ABSTRACTComposite models have a long history in actuarial science because they provide a flexible method of curve-fitting for heavy-tailed insurance losses. The ongoing research in this area continuously suggests methodological improvements for existing composite models and considers new composite models. A number of different composite models have been previously proposed in the literature to fit the popular data set related to Danish fire losses. This paper provides the most comprehensive analysis of composite loss models on the Danish fire losses data set to date by evaluating 256 composite models derived from 16 parametric distributions that are commonly used in actuarial science. If not suitably addressed, inevitable computational challenges are encountered when estimating these composite models that may lead to sub-optimal solutions. General implementation strategies are developed for parameter estimation in order to arrive at an automatic way to reach a viable solution, regardless of the specific head and/or tail distributions specified. The results lead to an identification of new well-fitting composite models and provide valuable insights into the selection of certain composite models for which the tail-evaluation measures can be useful in making risk management decisions.

A review of the development of airflow models used in building load calculation and energy simulation

Various modeling approaches have been developed and applied to predict the heat and mass transfer phenomena within buildings. As the theoretical basis, these transfer phenomena play a significant role in the estimation and prediction of building load and energy consumption. In consideration of the complexity of the phenomena observed, the results expected, the parameters investigated, and the degree of accuracy required, these modeling approaches can be represented with three models: Multi-zone models, Zonal models, and Computational Fluid Dynamics (CFD) models. In the application of these models in building load and energy simulation, selecting an appropriate model is an essential step, which mainly depends on four factors, including the level of accuracy needed, the problem to be solved, the computational time and resources that can be affordable, as well as the level of experience the users have. The importance of utilizing an appropriate model, however, is usually ignored by designers, engineers, and researchers. Therefore, in this paper, a literature review is carried out including the basic theories and the development and application of these modeling approaches used in building load and energy simulations. The major objective of this paper is to give building designers and/or researchers a better understanding of the models used for building load estimation and energy simulation in order to provide a reference for them to select an appropriate model for their needs. The study primarily reveals that the use of zonal/CFD modeling approaches in building simulation still rests on the theory research stage, but these modeling approaches define the direction for future development in building load estimation and energy modeling. Compared to CFD models, which use large memory and computer resources, zonal models could be a more possible substitute for single-/multi-zone models in building energy simulation in consideration of the current development of computer techniques and the unpopularity of high performance computing.

Exploring Bayesian parameter estimation for chiral effective field theory using nucleon–nucleon phase shifts

We recently developed a Bayesian framework for parameter estimation in general effective field theories. Here we present selected results from using that framework to estimate parameters with a nucleon–nucleon (NN) potential derived using chiral effective field theory (χEFT): the semi-local NN potential of Epelbaum, Krebs, and Meißner (EKM). There are many NN scattering data, up to high energies, and with rather small errors. Imposing a penalty for unnatural low-energy constants (LECs) therefore has a small effect on the fits, unless only a small fraction of the NN data is used in the fit. In contrast, we have found that including an estimate of higher orders in χEFT plays an important role in robust parameter estimation. We present two case studies where our Bayesian machinery illuminates physics issues. The first involves the EKM potential at fourth order in the χEFT expansion: the two-dimensional posterior probability density function (pdf) for the fourth-order s-wave LECs obtained from the Nijmegen PWA93 phase shifts indicates these parameters in the NN potential are degenerate. We trace this feature of the pdf to the presence of an operator in the fourth-order NN potential that vanishes on-shell. The second case study examines the stability of LEC extractions as more data at higher energies are included in the fit. We show that as long as χEFT truncation errors are properly accounted for in the parameter estimation, the LEC values extracted using our Bayesian approach are not sensitive to the maximum energy chosen for the fit. Uncorrelated and fully correlated models for the truncation errors are compared, pointing the way to the use of Gaussian processes to more generally model the correlation structure.

Achieving Inclusive Growth in Nigeria through Exports: An Empirical Investigation

The study investigated the effectiveness of export in the attainment of inclusive growth in Nigeria. The study functionally expressed inclusive growth as a function of oil export, non oil export, investment and foreign direct investment. In order to achieve the objectives of the study, a number of literature were reviewed, however, there were empirical regularities in the literature embracing inclusive growth as critical determinant of sustainable growth. Within the context of secondary data which spanned the period 1970-2016, the study utilized econometric technique to analyze inclusive growth model. In the model, real per capita income (proxy inclusive growth) is expressed as a function of oil exports, non oil export, investment and foreign direct investment. In particular, a number of diagnostic tests were carried out on the data before estimation in order to prevent spurious results. These include the unit root test, co-integration test and vector error correction tests. The stationarity test indicated that the data were stationary at first difference, while the co-integration test suggested long run co movement among the variables. In addition, the vector error correction model indicated the relationships among the inclusive growth fundamentals. Findings from the results indicated that in the long run, the coefficients of oil and non oil exports have negative effect on inclusive growth (proxied by real GDP per capita) while investment and foreign direct investment impacted positively on inclusive growth, while in the short run, oil exports and non oil export positively and significantly influenced inclusive growth in Nigeria. This study further suggested that government should intensify policy towards stimulating oil export and promote foreign investment inflows. More so, policy thrust should also embrace diversification of the economic base from monolithic base structure to agriculture.

Instability, imprecision and inconsistent use of equilibrium real interest rate estimates

The debate on monetary and fiscal policy is heavily influenced by estimates of the equilibrium real interest rate. In particular, this concerns estimates derived from a simple aggregate demand and Phillips curve model with time-varying components as proposed by Laubach and Williams (2003). For example, Summers (2014a) refers to these estimates as important evidence for a secular stagnation and the need for fiscal stimulus. Yellen (2015, 2017) has made use of such estimates in order to explain and justify why the Federal Reserve has held interest rates so low for so long. First, we re-estimate the United States equilibrium rate with the methodology of Laubach and Williams (2003). Then, we build on their approach and an alternative specification to provide new estimates for the United States, Germany, the euro area and Japan. Third, we subject these estimates to a battery of sensitivity tests. Due to the great uncertainty and sensitivity that accompany these equilibrium rate estimates, the observed decline in the estimates is not a reliable indicator of a need for expansionary monetary and fiscal policy. Yet, if these estimates are employed to determine the appropriate monetary policy stance, such estimates are better used together with the consistent estimate of the level of potential output.

Solving IQ Mismatch Problem for Two-Path Successive Relaying OFDMA Uplink Systems With Direct Conversion Transceivers

In this letter, the properties of two-path successive relaying systems are exploited to develop an iterative decision directed algorithm to estimate in-phase/quadrature-phase mismatch parameters occurring at the transmitters, relays, and destination for the uplink orthogonal frequency-division multiple access transmission. These parameters along with the actual channel taps of different links are treated as a single unknown parameter to be estimated. A space-alternating generalized expectation-maximization tool is employed to compute the maximum-likelihood estimate. The proposed algorithm iterates between data detector and estimator in order to refine the estimation process. Simulation results confirm the effectiveness of the proposed estimator.

Envelopes and vertical amplitudes of disc-crossing orbits

We recently found that regular orbits in axially symmetric galactic disks have their envelopes $Z(R)$ accurately described by the relation $Z(R)\propto[\Sigma_I(R)]^{-1/3}$, if their amplitudes are comparable to the disk thickness, where $\Sigma_I$ is the surface density of the disk (integrated over its whole vertical range). Moreover, the usual adiabatic approximation gives a good description of the orbits' envelopes for low vertical amplitudes. However, these two approaches are apparently disconnected, since their expressions differ qualitatively. Our purpose in this paper is to fill this gap by extending these previous formulae to regular orbits with arbitrary vertical amplitudes inside the disk. We compare existing $Z(R)$ estimates: the razor-thin disk case, the adiabatic approximation (low-amplitude orbits in three-dimensional disks), and the integrated surface-density estimate (high-amplitude orbits in three-dimensional disks) in order to establish a connection between them. The formula presented here links the aforementioned results in an elegant and continuous way, being valid for vertical amplitudes throughout the whole vertical extension of the disk and with an expression which has the same form for all regimes. The advantage of the present formalism is the dependence of $Z(R)$ only on observable quantities, namely the disk's vertically integrated surface density, without the need to obtain the gravitational potential for the system.

Estimation of normal means in the tree order model by the weighting methods

Consider k + 1 independent normal populations with the tree order restriction on the mean parameters. For the tree order model, the restricted estimator of control group parameter is dominated by the unrestricted estimator when the number of treatment groups is large. We discuss two techniques for reducing of mean squared error via to the two weighting methods which are dissimilarity and conditional Bayesian criteria. Based on the bias and mean squared error criteria, the performance of the proposed estimators is compared with the alternative estimators in order to search for a better estimator. Although the superior estimator that uniformly dominates the others does not exist in general, but the proposed estimators dominate the corresponding unrestricted estimator and compete very well with the other alternative estimators introduced by the authors.

A Polynomial Least Squares Multiple-Model Estimator: Simple, Optimal, Adaptive, and Practical

Original polynomial least squares (LS) fits data by constructing coefficients that minimize the sum of squared deviations of deterministic samples from assumed polynomials. Contemporary LS estimates existing polynomial coefficients by filtering out corrupting statistical errors. Kalman Filter (KF) state estimation from noisy data is analogous to polynomial LS estimation. A major problem in both LS and KF target tracking is matching estimator order to target dynamics. 2nd order estimators match constant velocity targets; 3rd order estimators match accelerating targets. Filtered error variances from 3rd order estimators are larger than from 2nd order estimators. 2nd order estimators applied to accelerating targets produce increasing biases as more data are filtered, causing their MSEs (variance plus bias-squared) to rapidly exceed 3rd order variances (MSEs). This becomes troublesome when recurrently maneuvering targets make acceleration jumps. A trade-off between 2nd and 3rd order MSEs is needed. The interacting multiple-model (IMM) addresses this problem adaptively by making adjustments between 2nd and 3rd order KFs with model probabilities as functions of likelihoods from KF residuals and transition probabilities of assumed acceleration jumps. The IMM does not address biases, perform variance/bias-squared trade-offs, or minimize MSEs. In this paper linear interpolation is established between the 2nd and 3rd order polynomial estimators creating the LS multiple-model (LSMM), the 2nd order acceleration bias is defined, and the LSMM MSE is minimized in a variance/bias-squared trade-off. A sequence of optimal LSMMs matched to accelerations covering the spectrum of acceleration between zero and assumed maximum are derived and an adaptive algorithm is designed.

Fluorescence calibration and color equivalence for quantitative synthetic biology.

Synthetic Biology, the engineering of biology, is an evolving discipline. The complexity of the gene circuits being designed is increasing. And we are reaching the point where mathematical models are necessary and essential tools for the design of these gene circuits. Models can predict circuit behavior and guide the selection of suitable circuit components and implementations. However, it is necessary to perform a parameter estimation in order to use these models correctly. Measurement calibration, and in particular, fluorescence and absorbance calibrations, is essential for the reproducibility of biological experiments. Moreover, the use of calibrated measurements increases dramatically the usability and interpretability of models and parameters estimated with them. Here, we report a set of protocols and calibration procedures allowing us to obtain measurements of fluorescent E. coli cells in Molecules of Equivalent Fluorescein (MEFL) per cell for GFP constructs and Molecules of Equivalent Fluorophore for other proteins such as YFP, sfGFP and RFP. These simple, low-cost unit calibration protocols can be used to produce units and comparable models, improving dramatically the usability of these models for modular construction of genetic circuits in synthetic biology.

Eating patterns among children aged 13 to 35 months and association with maternal characteristics

This study sought to identify eating patterns among children and to verify their association with maternal characteristics. We studied 1,185 children aged 13 to 35 months. Food consumption was investigated using the 24h dietary recall and the eating patterns were identified using principal components factor analysis, followed by orthogonal varimax rotation. We carried out a hierarchical modeling using poisson regression with robust variance estimates in order to estimate prevalence ratios. We identified four eating patterns: common Brazilian, dairy/porridge, healthy and unhealthy. The variance explained by these factors was of 34.3% and the common Brazilian pattern was the one that most contributed to proportional variance. We highlight the dairy/porridge pattern, in which breast milk had negative factorial loading, suggesting its substitution by cow and modified milk. The data reveal that the characterization of children's eating patterns diverges according to maternal characteristics, such as age, educational level and number of children. Three of the four patterns we found are represented by foods rich in starch, saturated fat and simple sugar and poor in vitamins, minerals and fibers. Multiparity, lower educational levels and maternal age under 20 years were associated with a lower consumption of foods considered to be healthy and important in child development.

Forward Looking Equity Risk Premium: A Normative Long-Term View

We propose a Total Cash Flow present value model to estimate the implied risk premium equity indices typically used in financial models as proxies for the aggregate stock market. Following a bottom-up approach, we use individual companies’ financial information as well as analysts’ earnings estimates in order to reconstruct the index total cash flow and expected future cash flows. Using the prices for these indices, we then extract the implied Equity Risk Premia and analyze their evolution through time. To illustrate our approach, we run our model over a period of 10 years surrounding the 2008 financial crisis on five stock indices, namely the S & P 500, the Euro Stoxx 50, the FTSE 100, the Hang Seng Index and the TOPIX 100. We find that our model is a conceptually robust approach to modeling long-term market Equity Risk Premia and provides a normative view of expected returns for practitioners.

Housing price estimation in order to sustainable housing: Niyavaran area,Tehran, Iran

Housing price estimation in order to sustainable housing: Niyavaran area,Tehran, Iran

Computer Algebra and Algorithms for Unbiased Moment Estimation of Arbitrary Order.

While unbiased central moment estimators of lower orders (such as a sample variance) are easily obtainable and often used in practice, derivation of unbiased estimators of higher orders might be more challenging due to long math and tricky combinatorics. Moreover, higher orders necessitate calculation of estimators of powers and products that also amount to these orders. We develop a software algorithm that allows the user to obtain unbiased estimators of an arbitrary order and provide results up to the 6th order, including powers and products of lower orders. The method also extends to finding pooled estimates of higher central moments of several different populations (e.g. for two-sample tests). We introduce an R package Umoments that calculates one- and two-sample estimates and generates intermediate results used to obtain these estimators.

Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates

Surrogate modeling has become a critical component of scientific computing in situations involving expensive model evaluations. However, training a surrogate model can be remarkably challenging and even computationally prohibitive in the case of intensive simulations and large-dimensional systems. We develop a systematic approach for surrogate model construction in reduced input parameter spaces. A sparse set of model evaluations in the original input space is used to approximate derivative based global sensitivity measures (DGSMs) for individual uncertain inputs of the model. An iterative screening procedure is developed that exploits DGSM estimates in order to identify the unimportant inputs. The screening procedure forms an integral part of an overall framework for adaptive construction of a surrogate in the reduced space. The framework is tested for computational efficiency through an initial implementation in simple test cases such as the classic Borehole function, and a semilinear elliptic PDE with a random source function. The framework is then deployed for a realistic application from chemical kinetics, where we study the ignition delay in an $$\hbox {H}_2{/}\hbox {O}_2$$ reaction mechanism with 19 and 33 uncertain rate-controlling parameters. It is observed that significant computational gains can be attained by constructing accurate low-dimensional surrogates using the proposed framework.

Global weak solutions to a spatio-temporal fractional Landau–Lifshitz–Bloch equation

The present paper deals with global existence of weak solutions of a time-space fractional Landau–Lifshitz–Bloch equation involving the weak Caputo derivative and a fractional Laplacian. We use Faedo–Galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model. The uniqueness is also discussed in a special one dimensional case.

Artificial Neural Networks For Building Projects Cost Estimating

Purpose. To form an idea about the use of neural networks for estimating the cost of construction projects. Artificial neural networks are successfully used in solving numerous complex non-linear problems associated with forecasting, evaluation, decision-making, optimization, systematization, and choice in the fields of construction and its management. Artificial neural networks are particularly effective for solving complex problems, such as cost estimation problems, when the relationship between variables cannot be expressed by simple mathematical relationships. The technique. The parametric estimation method is a method in which the statistical evaluation between historical data and other variables is used for valuation. Using this method, you can get a more accurate estimate of the cost, due to the fact that this approach requires a lower level of detail compared to other methodologies. The level of accuracy of the assessment depends on the complexity, the amount of resources allocated for such work and the cost data embedded in the model. Results. Cost estimation is one of the most important factors in the management of construction projects. Any feasibility study for a project requires an accurate cost estimate in order to make the right decision about the future fate of the project. Scientific novelty. Improving cost estimation methods contributes to more efficient control of time and expenses in construction. Practical value. The use of artificial neural networks can potentially eliminate some of the main disadvantages of traditional evaluation methods. This gives great prospects for improving the reliability and validity of the method of parametric valuation.

Semi-active nonlinear vibration control of a functionally graded material rotating beam with uncertainties, using a frequency estimator

A novel semi-active controller with adaptable parameters is developed to suppress the forced-vibration of a functionally graded material Timoshenko rotating beam with unknown parameters. The control algorithm is provided with a frequency estimator in order to identify the unknown frequency of the external excitations. The simplicity of the adaptive algorithm and efficient performance through a wide range of frequencies, are the advantages of the presented controller. Consecutive calculations allow the control parameters to be adjusted when the excitation frequency changes abruptly. The effects of hub radius, transverse shear deformation, and rotary inertia and tip masses are taken into account and the finite element method is utilized to discretize the dynamic model. The results demonstrate that the control algorithm is able to reduce the nonlinear vibration of the rotating beam at different nodes along its length when the frequency of the excitations changes. The controller is also effective when the rotational speed of the hub changes gradually over time.