Reasonable Guess Research Articles

Eliminating the Outside Good Bias in Logit Models of Demand with Aggregate Data

AbstractThe logit model is the most popular tool in estimating demand for differentiated products. In this model, the outside good plays a crucial role because it allows consumers to stop buying the differentiated good altogether if all brands simultaneously become less attractive (e.g. if a simultaneous price increase occurs). But practitioners lack data on the outside good when only aggregate data are available. The currently accepted procedure is to assume a “market potential” that implicitly defines the size of the outside good (i.e. the number of consumers who considered the product but did not purchase); in practice, this means that an endogenous quantity is approximated by a reasonable guess thereby introducing the possibility of an additional source of error and, most importantly, bias. We provide two contributions in this paper. First, we show that structural parameters can be substantially biased when the assumed market potential does not approximate the outside option correctly. Second, we show how to use panel data techniques to produce unbiased structural estimates by treating the market potential as an unobservable in both the simple and the random coefficients logit demand model. We explore three possible solutions: (a) controlling for the unobservable with market fixed effects, (b) specifying the unobservable to be a linear function of product characteristics, and (c) using a “demeaned regression” approach. Solution (a) is feasible (and preferable) when the number of goods is large relative to the number of markets, whereas (b) and (c) are attractive when the number of markets is too large (as in most applications in Marketing). Importantly, we find that all three solutions are nearly as effective in removing the bias. We demonstrate our two contributions in the simple and random coefficients versions of the logit model via Monte Carlo experiments and with data from the automobile and breakfast cereals markets.

Rapid design and optimization of low-thrust rendezvous/interception trajectory for asteroid deflection missions

Asteroid deflection techniques are essential in order to protect the Earth from catastrophic impacts by hazardous asteroids. Rapid design and optimization of low-thrust rendezvous/interception trajectories is considered as one of the key technologies to successfully deflect potentially hazardous asteroids. In this paper, we address a general framework for the rapid design and optimization of low-thrust rendezvous/interception trajectories for future asteroid deflection missions. The design and optimization process includes three closely associated steps. Firstly, shape-based approaches and genetic algorithm (GA) are adopted to perform preliminary design, which provides a reasonable initial guess for subsequent accurate optimization. Secondly, Radau pseudospectral method is utilized to transcribe the low-thrust trajectory optimization problem into a discrete nonlinear programming (NLP) problem. Finally, sequential quadratic programming (SQP) is used to efficiently solve the nonlinear programming problem and obtain the optimal low-thrust rendezvous/interception trajectories. The rapid design and optimization algorithms developed in this paper are validated by three simulation cases with different performance indexes and boundary constraints.

Sorting Through the Arguments on Breast Screening

VIEWS ON THE BENEFITS AND HARMS OF BREAST cancer screening are sharply polarized and increasingly vocal. Allegations of harming women are flung in both directions. The antiscreeners claim that benefit is minimal and overdiagnosis is so frequent that women are being subject to unnecessary interventions and treatment. The proscreeners claim that if the critics win the day, women will be deprived of the benefits that screening brings of early diagnosis and reductions in mortality from breast cancer. To those coming fresh to the argument, such disagreement seems surprising. Given the large body of evidence evaluating breast screening, it seems that the evidence would settle the issue. Such naivete does not allow for the fact that people interpret evidence and, indeed, influence its generation. Judgments often reflect more about starting assumptions than they do about the nature of the evidence. Into this somewhat raucous debate came the Independent UK Panel on Breast Screening. Given that views about the benefits and hazards of breast screening are so polarized that one only has to look at the author of an article to make a reasonable guess whether it will be pro or con, members of the breast screening panel were selected only if they had no prior publications on breast screening. It was hoped, therefore, that the only prior experiences shared by panel members were a desire to reach judgments based on sound science and to improve women’s health. Characteristically, the United Kingdom has a more cautious screening program than the United States. Breast cancer screening in the United Kingdom is recommended for women aged 50 through 70 years, every 3 years—the focus of the UK panel— rather than annual screening starting at age 40 years that is usual in the United States. The purpose of screening is to advance the timing of diagnosis and thereby improve prognosis. Even were screening not to alter the natural history of breast cancer, screening would lead to an apparent prolongation of the time between diagnosis and death—lead time. Therefore, the appropriate end point to evaluate the benefits of screening is mortality from breast cancer. In the panel’s judgment, the best evidence for the relative benefit of screening on mortality reduction is based on 11 randomized controlled trials (RCTs) of breast screening. Meta-analysis of these trials with 13 years of follow-up estimated a 20% reduction in breast cancer mortality among women invited for screening. The panel based its metaanalysis on data reported in a Cochrane review. The Cochrane review came to a similar estimate of relative reduction but, because of concerns about quality of some of the trials, reduced that estimate to 15%. The UK panel did not follow this procedure. Some have claimed that being in the screening group of a trial could be harmful. The correct end point, therefore, should be not breast cancer mortality but all-cause mortality. The power of the trials simply does not allow that: a 20% reduction in breast cancer mortality would translate into a 3% reduction in all cancer mortality and a 1.6% reduction in all-cause mortality. There has been a remarkable range in estimates of absolute benefit of screening, varying from 1 breast cancer death avoided for 2000 women invited to screening to 1 breast cancer death avoided for about 100 women screened, about a 20-fold difference. Major determinants of that large variation are the age of women screened and the durations of screening and follow-up. The panel applied the relative mortality reduction of 20% to achieve the observed cumulative absolute risk of breast cancer mortality over the ages of 55 through 79 years for women in the United Kingdom— assuming that women who began screening at 50 years would gain no benefit in the first 5 years but assuming that the mortality reduction would continue for 10 years after screening ended. This yielded the estimate that for every 235 women invited to screening, 1 breast cancer death would be prevented; correspondingly for 180 actually screened, 1 breast cancer death would be prevented. This seems relatively straightforward—randomized controlled trials show benefit. Yet questions have been raised about the internal and external validity of the trials. One argument against relying on the trials is that they were conducted 20 to 30 years ago and are therefore out of date. However, this criticism applies to all trials—their findings apply to the past. It is a judgment call whether conditions in

Unknown Quantity: Regulating Radionuclides in Tap Water

Radioactivity surrounds us; each day we are exposed to a certain amount by virtue of being alive on planet Earth. Some of this exposure comes from radioactive substances (radionuclides) that occur naturally in a wide variety of geologic and soil formations. Occasionally these naturally occurring substances become more concentrated or accessible through human activities such as mining and nuclear energy production, resulting in greater potential for exposure than their original natural occurrence would suggest. Other radionuclides are artificially created. Residents in almost all parts of the United States live on lands that contain minor to substantial concentrations of radionuclides of one type or another.1 These substances often make their way into tap water, leading to exposures by ingestion, inhalation, or dermal pathways during showering or other contact with the water. Although radionuclides are widespread, there are large gaps in our knowledge about sources of these materials, their distribution, associated health risks, and mitigation measures. However, the information we do have suggests that current drinking water standards for radionuclides established by the U.S. Environmental Protection Agency (EPA) may not adequately protect health. The EPA is set to review these standards relatively soon, and the next two years are prime time for filling in numerous information gaps and doing other legwork to make sure the review is as well informed as possible.

The times they are a‐changin’: time to change glaucoma management

The times they are a‐changin’: time to change glaucoma management

1-D INVERSION OF TRIAXIAL INDUCTION LOGGING IN LAYERED ANISOTROPIC FORMATION

In this paper, we present a one-dimensional (1-D) inversion algorithm for triaxial induction logging tools in multi-layered transverse isotropic (TI) formation. A non-linear least-square model based on Gauss-Newton algorithm is used in the inversion. Cholesky factorization is implemented to improve the stability and the reliability of the inversion. Zero-D inversion is conducted at the center of each layer to provide a reasonable initial guess for the best e-ciency of the inversion procedure. Cross components are used to provide su-cient information for determining the boundaries in the initial guess. It will be illustrated that using all the nine components of the conductivity/resistivity yield more reliable inversion results and even faster convergence than using only the diagonal components. The resultant algorithm can be used to obtain various geophysical parameters such as layer boundaries, horizontal and vertical resistivity, dipping angle and rotation angle etc. from triaxial logging data automatically without any priori information. Several synthetic examples are presented to demonstrate the capability and reliability of the inversion algorithm.

Application of exergy analysis in designing helium liquefiers

Exergy has proved to be a useful tool to analyze and optimize the design and operation of many systems. Some studies on helium refrigerators and liquefiers based on exergy are available in literature. In this paper, systematic evaluation of important operating and geometric parameters has been done to determine the exergy destructions in components as well as in the entire cycle of Collins helium liquefiers. Grassmann diagram of exergy flow has been shown to be of immense help in understanding relative importance of different components used in the system. Compressor pressure, expander flow rates, heat exchanger surface area are some of the parameters optimized considering both presence and absence of pressure drop in the heat exchangers. Non-dimensionalization of parameters makes the results applicable to plants of any capacity. Exergy-analysis based on Second Law proves to be far superior to the First Law based energy analysis in designing of the helium plant as the former is holistic in approach and capable of deriving some additional conclusions. Results derived on Collins cycle may be applicable in large-scale helium liquefiers by providing basic understanding of the influence of components on the plant performance and reasonable initial guess values in their design and simulation.

Digital Image Correlation Search Method Based on Particle Swarm Algorithm

Digital image correlation method is an important optical technique for surface displacement and strain measurement. An approach based on Particle Swarm Optimization algorithm for sub-pixel correlation search is described in this paper. The new Algorithm does not involve reasonable guess of displacement and deformation gradient and the calculation of second-order derivatives of the digital images. Benefiting from the abilities of global optimum and parallelism searching, and compared with genetic algorithm, the new approach can complete the sub-pixel correlation search with high accuracy and less computational consumption. Computer-simulated images are then used to verify this method. The experimental results show that the new approach is a practicable sub-pixel searching method.

Central Venous Catheter-Induced Cardiac Tamponade

Editori have read with great interest the review (1)written by Pittiruti et.al. followed by their multicenter study (2) regarding the use of EKG for central venous catheter (CVC) positioning.Late cardiac tamponade is a fatal complication that might arise if the CVC tip is left within the pericardial reflection by continuously eroding the atrial wall over time (3). it is there-fore that i do not understand why the authors in their study (2) aimed to position the CVCs so low. only procedures that require free blood flow (dialysis, hemofiltration, plasmapher-esis, etc.) are indications for a very low CVC position. in the review the authors claim that the EKG assisted CVC positioning technique is superior to fluoroscopy. Since EKG will position the CVC at the cava-atrial junction it will leave its tip within the pericardial reflection. Additional positioning as well as chest x-ray (CXR) is therefore required. Since CXR is needed to preclude other pathologies (such as pneumotho-rax) the use of expensive EKG catheters did not add any safety to the patients.The recommendations by Pittiruti in his review and study will expose patients to the danger of incorrect (deep) CVC position while using unnecessary expensive equipment. it is my recommendation to use the CVC lengths cited by Kim et. al. (4)and verify the position by CXR.

Estimation of Lung's Air Volume and Its Variations Throughout Respiratory CT Image Sequences

A respiratory image-sequence-segmentation technique is introduced based on a novel image-sequence analysis. The proposed technique is capable of segmenting the lung's air and its soft tissues followed by estimating the lung's air volume and its variations throughout the image sequence. Accurate estimation of these two parameters is very important in many applications related to lung disease diagnosis and treatment systems (e.g., brachytherapy), where the parameters are either the variables of interest themselves or are dependent/independent variables. The concept of the proposed technique involves using the image sequence's combined histogram to obtain a reasonable initial guess for the lung's air segmentation thresholds. This is followed by an optimization process to find the optimum threshold values that best satisfy the lung's air mass conservation and tissue incompressibility principles. These threshold values are consequently applied to estimate the lung's air volume and its variations throughout respiratory Computed Tomography (CT) image sequences. Ex vivo experiments were conducted on porcine left lungs in order to demonstrate the performance of the proposed technique. The proposed method was initially validated using a breath-hold CT image sequence with known air volumes inside the lung, where results show that the proposed technique outperforms single-histogram-based methods. This was followed by demonstrating the proposed technique's application in a 4-D-CT respiratory sequence, where the air volume inside the lung was unknown. Consistency of the obtained results in the latter experiment with tissue near incompressibility principle was validated. The results indicate a very good ability of the proposed method for estimating the lung's air volume and its variations in a respiratory image sequence.

Eliminating the Outside Good Bias in Logit Models of Demand with Aggregate Data

The logit model is the most popular tool in estimating demand for differentiated products. In this model, the outside good plays a crucial role because it allows consumers to stop buying the differentiated good altogether if all brands simultaneously become less attractive (for example if a simultaneous price increase occurs). But practitioners lack data on the outside good when only aggregate data is available. The currently accepted procedure is to assume a “market potential” that implicitly defines the size of the outside good (i.e. the number of consumers who considered the product but did not purchase); in practice, this means that an endogenous quantity is approximated by a reasonable guess thereby introducing the possibility of an additional source of error and, most importantly, bias. We provide two contributions in this paper. First, we show that structural parameters can be substantially biased when the assumed market potential does not approximate the outside option correctly. Second, we show how to use panel data techniques to produce unbiased structural estimates by treating the market potential as a fixed effect (known as a “correlated random effect” in the non-linear panel data literature). We explore three possible solutions: a) controlling for the unobservable with market fixed effects, b) specifying the unobservable to be a linear function of the (average) product characteristics, and c) a “demeaned” regression approach. Solution a) is feasible (and preferable) when the number of goods is large relative to the number of markets, whereas b) and c) are attractive when the number of markets is too large. Importantly, we find that all three solutions are nearly as effective in removing the bias. We demonstrate our two contributions in the simple and random coefficients versions of logit via Monte Carlo experiments and with data from the automobile and breakfast cereals markets.

On the bounding of limit multipliers for combined loading

In the framework of classical plasticity, even when limit multipliers and collapse mechanisms associated with different loads independently acting on a solid or structure are known, not much can be inferred on the limit multiplier of the combined loading. Frame structures under the action of dead loads and seismic forces, soil–foundation interaction problems, tunnels under a variety of loads, deepwater pipelines subject to bending and pressure constitute only a few selected examples for which some sort of superposition rule, as well as bounding techniques, would be extremely useful. The present paper introduces a set of theorems for bounding limit multipliers for combined loads. In particular, ranging from a minimum knowledge about the critical state under a particular loading to a reasonable guess of the kinematics of the problem under combined loads, more and more refined bounds for the overall limit multiplier are derived. The results, to the best of the authors’ knowledge, are novel and a few examples showing their practical value are presented and discussed.

Advanced fitting algorithms for analysing positron annihilation lifetime spectra

The most common way to analyse PALS spectra involves fitting a parameter-dependent model to the experimental data. Traditionally, this fit involves local non-linear optimisation routines that depend on a reasonable initial guess for the searched parameters. This, together with the fact that very different sets of parameters may yield indistinguishably good fits for a given experimental spectrum, gives rise to ambiguities in the data analysis in most but the simplest cases. In order to alleviate these difficulties, a computer program named PAScual was developed that incorporates 2 advanced algorithms to provide a robust fitting tool: on the one hand, it incorporates a global non-linear optimisation routine based on the Simulated Annealing algorithm and, on the other hand, it yields information on the reliability of the results by means of a Markov Chain Monte-Carlo Bayesian Inference method. In this work the methods used in PAScual are described and tested against both simulated and experimental spectra, comparing the results with those from the well-established program LTv9. The examples focus on the type of complex data that results from the study of self-assembled amphiphile materials containing co-existing aqueous and hydrocarbon regions.

Student Thinking about Static Equilibrium: Insights from Written Explanations to a Concept Question

AbstractStudents' thinking during an assessment task was monitored by analyzing their explanations of answers to a multiple‐choice question about the equilibrium of bodies under given loads. Based on coding by independent raters, we found that nearly all students explained answers by appealing to force and/or moment summation; they differed principally on whether they applied both force and moment equilibrium and did so consistently. Correlations between answer selection and explanation as found from coding suggested that a reasonable guess as to a student's thinking can be made based on the answer choice alone. By the final exam, some students improved in their ability to consistently apply both principles or at least to apply them when needed. Many other students apparently learned to apply one of the principles consistently, although they came to ignore the other principle, even if they had acknowledged it at the start of the course.

Time-to-depth conversion and seismic velocity estimation using time-migration velocity

The objective was to build an efficient algorithm (1) to estimate seismic velocity from time-migration velocity, and (2) to convert time-migrated images to depth. We established theoretical relations between the time-migration velocity and seismic velocity in two and three dimensions using paraxial ray-tracing theory. The relation in two dimensions implies that the conventional Dix velocity is the ratio of the interval seismic velocity and the geometric spreading of image rays. We formulated an inverse problem of finding seismic velocity from the Dix velocity and developed a numerical procedure for solving it. The procedure consists of two steps: (1) computation of the geometric spreading of image rays and the true seismic velocity in time-domain coordinates from the Dix velocity; (2) conversion of the true seismic velocity from the time domain to the depth domain and computation of the transition matrices from time-domain coordinates todepth. For step 1, we derived a partial differential equation (PDE) in two and three dimensions relating the Dix velocity and the geometric spreading of image rays to be found. This is a nonlinear elliptic PDE. The physical setting allows us to pose a Cauchy problem for it. This problem is ill posed, but we can solve it numerically in two ways on the required interval of time, if it is sufficiently short. One way is a finite-difference scheme inspired by the Lax-Friedrichs method. The second way is a spectral Chebyshev method. For step 2, we developed an efficient Dijkstra-like solver motivated by Sethian’s fast marching method. We tested numerical procedures on a synthetic data example and applied them to a field data example. We demonstrated that the algorithms produce a significantly more accurate estimate of seismic velocity than the conventional Dix inversion. This velocity estimate can be used as a reasonable first guess in building velocity models for depth imaging.

Reservoir description using a binary level set model

We consider the inverse problem of permeability estimation for two-phase flow in porous media. In the parameter estimation process we utilize both data from the wells (production data) and spatially distributed data (from time-lapse seismic data). The problem is solved by approximating the permeability field by a piecewise constant function, where we allow the discontinuity curves to have arbitrary shape with some forced regularity. To achieve this, we have utilized level set functions to represent the permeability field and applied an additional total variation regularization. The optimization problem is solved by a variational augmented Lagrangian approach. A binary level set formulation is used to determine both the curves of discontinuities and the constant values for each region. We do not need any initial guess for the geometries of the discontinuities, only a reasonable guess of the constant levels is required.

Improved algorithm for calculation of binary liquid-liquid equilibrium compositions with NRTL model based on equal area rule

Typical methods for calculation of binary liquid-liquid equilibrium compositions such as surfactant systems need proper initial guesses and/or checking the sign of the second derivative of molar Gibbs energy change of mixing, ΔG. Eubank and Hall [1] have shown the equal area rule (EAR) applies to the composition derivative of the Gibbs energy of a binary system at fixed pressure and temperature. Methods based on EAR do not need to check the sign of the second derivative of ΔG because EAR is a necessary and sufficient condition for phase equilibrium. However, the algorithm proposed by Eubank and Hall needs a reasonable initial guess. Furthermore, it is not easy to apply the algorithm to activity coefficient models such as Non-Random Two Liquid (NRTL) because the first and second derivatives of ΔG as a function of composition have various shapes for some sets of NRTL parameters. In this work, we have developed an improved algorithm for calculation of binary liquid-liquid equilibrium compositions based on EAR considering the various shapes of NRTL model. This algorithm needs neither any initial guess nor checking the sign of the second derivative of ΔG.

Microcanonical multifractal formalism: Application to the estimation of ocean surface velocities

In this paper we investigate the validity of the multifractal formalism to study sea surface temperature (SST). It is shown that SST patterns observed in moderate resolution SST images have anomalous scaling properties characteristic of a multifractal structure. The most probable origin of the observed structures is the turbulent character of the oceanic flow as they evolve slowly and are very persistent in times compatible with ocean mesoscale dynamics (several days). The spectrum of singularity exponents indicates that the dynamics of the processes leading to the geometrical arrangement of the SST patterns is quite general over the available range of scales. As a consequence, multifractal techniques can be used to extract properties of the underlying flow. In particular, the geometry of the SST multifractal components is closely linked with the ocean flow, which allows to build a reasonable guess of the streamfunction (defined as the maximum singular streamfunction (MSS)) from a single SST image. Thus the ocean surface velocity field can be easily inferred, with some limitations. As multifractal analysis is in essence a geometrical approach, the method is able to retrieve a high resolution velocity field, well localized in space, but with some indetermination on the modulus and sense of velocity vectors. To solve this, a general framework for the integration of extra information is proposed, what is illustrated with an example merging MSS with altimetric data.

A level-set corrector to an adaptive multiscale permeability prediction

We consider the inverse problem of permeability estimation for two-phase porous-media flow. The novel approach is based on regularization by zonation, where the geometry and size of the regions are chosen adaptively during the optimization procedure. To achieve this, we have utilized level-set functions to represent the permeability. The available data are sparsely distributed in space; hence, it is reasonable to confine the estimation to coarse-scale structures. The level-set approach is able to alter the boundaries between regions of different permeability without strict restrictions on their shape; however, when the data are sparse, a reasonable initial guess for the permeability is required. For this task, we use adaptive multiscale permeability estimation, which has the potential of identifying main permeability variations. These are described by a piecewise constant function, where the constant values are attained on rectangular zones. In the current work, we develop a level-set corrector strategy, assuming adaptive multiscale permeability estimation as a predictor.

Stranger and symbolon at Sophocles, ot 216–23

The meaning of σύµβολον (221) is “point of connection,” as Lloyd-Jones and Wilson have argued: “I would not be tracking it over a great distance unless I had some connection.” Hence in the following sentence Oedipus emphasizes his connection to the Thebans. But as transmitted, the immediately preceding sentence denies any connection between Oedipus and the matter at hand. Sense suggests that the second ξϵ́νος is corrupt and the meaning of the uncorrupted passage was “I will speak these words as one who, though a stranger to the report, is yet involved in the deed.” The lost word is unrecoverable, but ξυνϵὼν is a reasonable guess.