Underlying Model Parameters Research Articles

Discretely Observed Brownian Motion Governed by Telegraph Process: Estimation

A Brownian motion whose infinitesimal variance alternates according to a telegraph process is considered. This stochastic process can be employed to model a variety of real-word situations, such as animal movement in ecology and stochastic volatility in mathematical finance. The main goal is to develop an estimation procedure for the underlying model parameters when the process is observed at discrete, possibly irregularly spaced time points. The sequence of observations is not Markov, but the sequence of the state of the telegraph process, if observed, is Markov. The observed sequence is therefore from a hidden Markov model. Likelihood inference is developed via dynamic programming, and is demonstrated to have much higher efficiency than the composite likelihood approach that was applied in an earlier work. The model is applied to model the movement of a mountain lion.

Probabilistic reactor design in the framework of elementary process functions

Computational process models in combination with innovative design methodologies provide a powerful reactor design platform. Yet, model-based design is mostly done in a pure deterministic way. Possible uncertainties of the underlying model parameters, prediction errors due to simplifying assumptions regarding the reactor behavior and suboptimal realizations of the design along the reaction coordinate are in general not considered. Here we propose a systematic design approach to directly account for the impact of such variabilities during the design procedure. The three level design approach of Peschel et al. (2010) based on the concept of elementary process functions (EPF) serves as basis. The dynamic optimizations on each level are extended within a probabilistic framework to account for different sources of randomness. The impact of these sources on the performance prediction of a design is quantified and used to robustify the reactor design aiming at a more reliable performance and thus design prediction. The uncertainties of model parameters, non-idealities of the reactor behavior and inaccuracies in the design are included via statistical moments. By means of the sigma point method (Julier and Uhlmann, 1996) random variables are mapped to the design objective space via the nonlinear process model. Importantly, this work introduces a full probabilistic orthogonal collocation approach, i.e. random and stochastic variables can be described. Whereas the former one relates to randomness independent on the reaction time (e.g. kinetic model parameters or initial conditions), the latter one describes stochasticity along the reaction time (e.g. fluctuating pressure or temperature control). As an example process the hydroformylation of 1-dodecene in a thermomorphic solvent system consisting of n-decane and N,N-dimethylformamide is considered. Our probabilistic EPF approach allows designing robust optimal reactors, which operate within an estimated confidence at their expected optimum considering almost any kind of randomness arising in the design procedure. An additional value is that with increased predictive power of the reactor performance its embedding in an overall process is strongly simplified.

Optimal asset allocation with fixed-term securities

We investigate the optimal asset allocation of an investor who can invest in a fixed-term security that is only traded at time 0. Using a generalized martingale approach, we solve the investor׳s optimal portfolio problem, determine the optimal allocation to fixed-term securities, and provide a representation of trading strategies in terms of a liquidity-related derivative. We apply our approach to two benchmark scenarios: fixed-term fixed-rate bank deposits, and unspanned closed-end securities that can only be traded at time 0. We show that both can be key parts of the investor׳s optimal asset mix, and we investigate the dependence of optimal allocations to fixed-term investments, implied liquidity premia and other characteristics on the underlying model parameters.

High-dimensional classification via nonparametric empirical Bayes and maximum likelihood inference

We propose new nonparametric empirical Bayes methods for high-dimensional classification. Our classifiers are designed to approximate the Bayes classifier in a hypothesized hierarchical model, where the prior distributions for the model parameters are estimated nonparametrically from the training data. As is common with nonparametric empirical Bayes, the proposed classifiers are effective in high-dimensional settings even when the underlying model parameters are in fact nonrandom. We use nonparametric maximum likelihood estimates of the prior distributions, following the elegant approach studied by Kiefer & Wolfowitz in the 1950s. However, our implementation is based on a recent convex optimization framework for approximating these estimates that is well-suited for large-scale problems. We derive new theoretical results on the accuracy of the approximate estimator, which help control the misclassification rate of one of our classifiers. We show that our methods outperform several existing methods in simulations and perform well when gene expression microarray data is used to classify cancer patients.

Hypotheses testing for generalized order statistics with simple order restrictions on model parameters under the alternative

In applications of generalized order statistics as, for instance, reliability analysis of engineering systems, prior knowledge about the order of the underlying model parameters is often available and may therefore be incorporated in inferential procedures. Taking this information into account, we establish the likelihood ratio test, Rao's score test, and Wald's test for test problems arising from the question of appropriate model selection for ordered data, where simple order restrictions are put on the parameters under the alternative hypothesis. For simple and composite null hypothesis, explicit representations of the corresponding test statistics are obtained along with some properties and their asymptotic distributions. A simulation study is carried out to compare the order restricted tests in terms of their power. In the set-up considered, the adapted tests significantly improve the power of the associated omnibus versions for small sample sizes, especially when testing a composite null hypothesis.

Minimizing the Probability of Lifetime Ruin When Shocks Might Occur: Perturbation Analysis

We determine the optimal investment strategy to minimize the probability of an individual’s lifetime ruin when the underlying model parameters are subject to a shock. Specifically, we consider two possibilities: (1) changes in the individual’s net consumption and mortality rate and (2) changes in the parameters of the financial market. We assume that these rates might change once at a random time. Changes in an individual’s net consumption and mortality rate occur when the individual experiences an accident or other unexpected life event, while changes in the financial market occur due to shifts in the economy or in the political climate. We apply perturbation analysis to approximate the probability of lifetime ruin and the corresponding optimal investment strategy for small changes in the model parameters and observe numerically that these approximations are reasonable ones, even when the changes are not small.

Sequential Monte-Carlo sampling based on a committee of artificial neural networks for posterior state estimation and residual lifetime prediction

The application of Bayesian methods to the problem of fatigue crack growth prediction has been growing in recent years. In particular, sequential Monte-Carlo sampling is often presented as an efficient model-based technique to filter the sequential measures of the damage evolution provided as an input to the algorithm. However, a lot of measures are required to reliably identify the system state condition and the underlying model parameters. Many studies rely on the availability of a relatively dense sequence of crack length measures during damage evolution, made in most cases impractical by the consequent maintenance costs. Thus, real-time damage diagnosis is a requirement to enable prognostic health management.This work focuses on the application of sequential Monte-Carlo sampling to estimate the probabilistic residual life of a structural component subjected to fatigue crack propagation, while real-time estimation of crack length is provided through a committee of artificial neural networks, trained with finite element simulated strain patterns. Multiple crack length observations are available at each discrete time and are provided as the input to the prognostic system, based on a sequential importance resampling algorithm. Each time a new set of measures is available, the algorithm evaluates the posterior distribution of the augmented state vector, including the crack length and a material parameter governing damage evolution. This filtered information is used to numerically update the probability density functions of the residual life of the component. The methodology is applied first to a simulated crack and then to a metallic stiffened panel specimen subject to fatigue crack growth.

Universal acoustic modelling framework for electrical drives

The interdisciplinary task of assessing the acoustic characteristics of electrical drive-systems gains importance in traction, industrial and consumer applications. This study presents a universal acoustic modelling framework for efficient, high-quality acoustic modelling of electrical drives. The objective is to make drive acoustic modelling and assessment of an integral part of drive-system design. The approach integrates directly into the general drive-system design process and can be applied to all types of machines (synchronous, induction, switched reluctance and direct current). Inverter-operation-related switching frequencies and spatial machine harmonics are routinely taken into account. The process is applicable to machines with rotor or stator skew as well as to outer-rotor and transversal-flux machines. It combines the two fast and user-interactive steps system simulation and vibration synthesis. The underlying model parameters are obtained via automated offline finite-element simulations based on generic input parameters. This allows using complex electromagnetic and structural models without computation time becoming prohibitive. Application examples are given for permanent magnet synchronous machine traction drives for (hybrid) electric vehicles as well as a for a switched-reluctance auxiliary drive. Simulated run-up spectrograms for structure-borne sound are validated against measurements and operational deflections are presented.

Change-point detection for recursive Bayesian geoacoustic inversions.

In order to carry out geoacoustic inversion in low signal-to-noise ratio (SNR) conditions, extended duration observations coupled with source and/or receiver motion may be necessary. As a result, change in the underlying model parameters due to time or space is anticipated. In this paper, an inversion method is proposed for cases when the model parameters change abruptly or slowly. A model parameter change-point detection method is developed to detect the change in the model parameters using the importance samples and corresponding weights that are already available from the recursive Bayesian inversion. If the model parameters change abruptly, a change-point will be detected and the inversion will restart with the pulse measurement after the change-point. If the model parameters change gradually, the inversion (based on constant model parameters) may proceed until the accumulated model parameter mismatch is significant and triggers the detection of a change-point. These change-point detections form the heuristics for controlling the coherent integration time in recursive Bayesian inversion. The method is demonstrated in simulation with parameters corresponding to the low SNR, 100-900 Hz linear frequency modulation pulses observed in the Shallow Water 2006 experiment [Tan, Gerstoft, Yardim, and Hodgkiss, J. Acoust. Soc. Am. 136, 1187-1198 (2014)].

Uncertainty quantification for a climatology of the frequency and spatial distribution of North Atlantic tropical cyclone landfalls

AbstractA spatially resolved climatology for the annual frequency of tropical cyclone (TC) landfalls along the Atlantic coast of North America is developed, and its uncertainty deriving from multiple sources is quantified. Historical landfall counts in piecewise‐linear segments approximating the coastline are modeled using Poisson regression with spatial random effects. Predictors include index representations of the mean hurricane‐season phases of the Southern Oscillation, the Atlantic Multidecadal Oscillation, and the North Atlantic Oscillation, with the effect of the latter also modeled spatially. This spatial generalized linear model for landfall frequency is used in conjunction with a data level accounting explicitly for the time‐dependent uncertainty in the recorded landfall positions. The model performs skillfully in cross‐validation exercises. The inferred effects of the climatic predictors are also consistent with current scientific understanding of the mechanisms through which related large‐scale climatic variability affects the development and motion of Atlantic tropical cyclones. Sampling variability in the data over the short length of the observational record and observational error in the historical data are found to contribute substantially to the overall climatological uncertainty. The contribution from uncertainty in the underlying model parameters is negligible compared to these other sources. The model presented here could be used for applications in insurance and risk management, and adaptations could also be used to investigate changes in TC landfall climatology under an uncertain and changing climate.

Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation

The proliferation of panel studies which has been greatly motivated by the availability of data and greater capacity for modeling the complexity of human behavior than a single cross-section or time series data has led to the rise of challenging methodologies for estimating the data sets. Much controversy on these methodologies is the under-estimation of the standard errors leading to wrong conclusions of the involved hypothesis test as well as making inappropriate inference to the underlying model parameters. This is due to the heteroscedasticity and autocorrelation nature of the disturbance term in the classical linear regression model. This study sought to estimate linear-panel model parameters using conventional regression techniques which have the capacity to address the correlation and heteroscedasticity problem. By relaxing the homogeneity and non-correlation properties of the disturbance term in the classical linear regression model, we employed the generalized least squares method to estimate the model parameters. Using the available White Heteroscedasticity Consistent estimators i.e. HC0, HC1, HC2, HC3 and HC4, we also obtained estimates for the generalized ordinary least squares covariance matrix.

Estimating Sensitivities of Portfolio Credit Risk Using Monte Carlo

Estimating the sensitivities of portfolio credit risk with respect to the underlying model parameters is an important problem for credit risk management. In this paper, we consider performance measures that may be expressed as an expectation of a performance function of the portfolio credit loss and derive closed-form expressions of its sensitivities to the underlying parameters. Our results are applicable to both idiosyncratic and macroeconomic parameters and to performance functions that may or may not be continuous. Based on the closed-form expressions, we first develop an estimator for sensitivities, in a general framework, that relies on the kernel method for estimation. The unified estimator allows us to further derive two general forms of the estimators by using conditioning techniques on either idiosyncratic or macroeconomic factors. We then specialize our results to develop faster estimators for three popular classes of models used for portfolio credit risk: latent variable models, Bernoulli mixture models, and doubly stochastic models.

Optimal Investment with Illiquid Assets

We investigate the optimal asset allocation of an investor who can invest in a fixed-term security that is only traded at time 0. Using a generalized martingale approach, we solve the investor's optimal portfolio problem, determine the optimal allocation to fixed-term securities, and provide a representation of trading strategies in terms of a liquidity-related derivative. We apply our approach to two benchmark scenarios: fixed-term fixed-rate bank deposits, and unspanned closed-end security that can only be traded at time 0. We show that both can be key parts of the investor's optimal asset mix, and we investigate the dependence of optimal allocations to fixed-term investments, implied liquidity premia and other characteristics on the underlying model parameters.

Voluntary disclosure and the cost of capital

We investigate the association between voluntary disclosure and the risk-related discount investors apply to price. First, we study the association between (endogenous) disclosure choice and the discount in price induced by changes in the underlying model parameters: this informs empirical research that ignores endogeneity of disclosure by, for example, omitting the exogenous determinants of disclosure and the discount in price from the regressions employed. Second, we investigate the incremental effect of disclosure on the discount in price: this informs empirical research that controls for the direct effect of exogenous factors on the discount in price by, for example, including the exogenous variables in regression models employed. Finally, we examine the incremental effect of disclosure on the discount in price when changes in disclosure are not induced by changes in underlying exogenous parameters: this further informs empirical research that controls for the effect of exogenous factors on both the discount in price and disclosure, and focuses on the association between ‘unexplained disclosure’ and the discount.

Media mix modeling – A Monte Carlo simulation study

An algorithm to model both time and revenue response to spend for media mix modeling is proposed in this article. A Monte Carlo simulation study is conducted to investigate the possibility of extracting time and revenue response simultaneously from both revenue- and channel-spend data. The quality and reliability of the underlying model parameter reconstruction from various sizes of data are also inspected. The outcome of re-allocating channel spend optimally based on extracted revenue response is evaluated. Simulation results show that nearly a 60 per cent increase in revenue can be achieved by channel-spend optimization, relative to arbitrary channel-spend assignment. The algorithm presented here is very general and can be applied to any budget allocation optimization at various levels.

The Posterior Probability of Passing a Compendial Standard, Part 1: Uniformity of Dosage Units

A compendial standard is a function of data generated by one or more quality testing procedures. Since the data are sampled from an underlying distribution, the probability of passing a compendial test (Pa) can be expressed as a function of the distribution's model parameters. Applying Bayesian methodology to such a function, we show how to compute the posterior distribution of Pa and other quantities of interest. We apply this methodology to the USP<905> compendial standard and illustrate the importance of considering interbatch variance. We show that the operating characteristics of this Bayesian approach depend on the underlying model parameters almost exclusively through the population Pa and use this to develop a simple univariate procedure to determine the number of batches needed for a process qualification. We note some advantages of this Bayesian approach compared to current approaches. To show the simplicity of the approach and encourage its use, example R and WinBUGS code are provided.

Constant Stress Accelerated Life Test on a Multiple-Component Series System under Weibull Lifetime Distributions

We will discuss the reliability analysis of the constant stress accelerated life test on a series system connected with multiple components under independent Weibull lifetime distributions whose scale parameters are log-linear in the level of the stress variable. The system lifetimes are collected under Type I censoring but the components that cause the systems to fail may or may not be observed. The data are so called masked for the latter case. Maximum likelihood approach and the Bayesian method are considered when the data are masked. Statistical inference on the estimation of the underlying model parameters as well as the mean time to failure and the reliability function will be addressed. Simulation study for a three-component case shows that Bayesian analysis outperforms the maximum likelihood approach especially when the data are highly masked.

R-matrix analysis and prediction of low-energy neutron-induced fission cross sections for a range of Pu isotopes

Neutron-induced fission cross sections for the plutonium isotopes from 236 to 244 are computed for neutrons of a few keV up to 5.5 MeV incident energy, using the Hauser-Feshbach statistical theory of nuclear reactions, modified to treat the fission decay channel in the $R$-matrix formalism. The fluctuations of the fission decay widths owing to the presence of intermediate structures in the second well and to the coupling of class I and class II states are simulated by Monte Carlo sampling of the underlying model parameter distributions. The accuracy of this approach is tested relative to the results of well-known analytical formulations for the average fission cross sections. Special attention is paid to the choice and consistency of the model input parameters, in part obtained from microscopic nuclear structure calculations. The predictive capabilities offered by our method are tested against the neutron-induced fission of the very short-lived ${}^{243}$Pu (${\ensuremath{\tau}}_{1/2}=4.95$ h) for which no measurement exist. Our calculations, consistent over all the Pu isotope series, demonstrate that ${}^{243}$Pu is fissile, in contrast to what is reported in the standard ENDF/B-VII.1 and JEFF-3.1.2 evaluated libraries. No recommendations are made in the JENDL-4.0 data library for this isotope.

A Simulation Optimization Approach to Epidemic Forecasting.

Reliable forecasts of influenza can aid in the control of both seasonal and pandemic outbreaks. We introduce a simulation optimization (SIMOP) approach for forecasting the influenza epidemic curve. This study represents the final step of a project aimed at using a combination of simulation, classification, statistical and optimization techniques to forecast the epidemic curve and infer underlying model parameters during an influenza outbreak. The SIMOP procedure combines an individual-based model and the Nelder-Mead simplex optimization method. The method is used to forecast epidemics simulated over synthetic social networks representing Montgomery County in Virginia, Miami, Seattle and surrounding metropolitan regions. The results are presented for the first four weeks. Depending on the synthetic network, the peak time could be predicted within a 95% CI as early as seven weeks before the actual peak. The peak infected and total infected were also accurately forecasted for Montgomery County in Virginia within the forecasting period. Forecasting of the epidemic curve for both seasonal and pandemic influenza outbreaks is a complex problem, however this is a preliminary step and the results suggest that more can be achieved in this area.

Voluntary Disclosure and the Cost of Capital

We investigate the association between voluntary disclosure and the risk-related discount investors apply to price. First, we study the association between (endogenous) disclosure choice and the discount in price induced by changes in the underlying model parameters: this is akin to an empirical study that overlooks the role of endogenity. Second, we investigate the incremental effect of disclosure on the discount in price: this is akin to an empirical study that controls for the direct effect of exogenous factors on the discount in price. Finally, we examine the incremental effect of disclosure on the discount in price when changes in disclosure are not induced by changes in underlying exogenous parameters: this is akin to an empirical study that controls for the effect of exogenous factors on both the discount in price and disclosure, and focuses on the association between “unexplained disclosure” and the discount.