Ulrich Menzefricke

ON THE EVALUATION OF CONTROL CHART LIMITS BASED ON PREDICTIVE DISTRIBUTIONS

ABSTRACT We propose a Bayesian approach to obtaining control charts when there is parameter uncertainty. Our approach consists of two stages, (i) construction of the control chart where we use a predictive distribution based on a Bayesian approach to derive the rejection region, and (ii) evaluation of the control chart where we use a sampling theory approach to examine the performance of the control chart under various hypothetical specifications for the data generation model.

Capturing Flexible Heterogeneous Utility Curves: A Bayesian Spline Approach

Empirical evidence suggests that decision makers often weight successive additional units of a valued attribute or monetary endowment unequally, so that their utility functions are intrinsically nonlinear or irregularly shaped. Although the analyst may impose various functional specifications exogenously, this approach is ad hoc, tedious, and reliant on various metrics to decide which specification is “best.” In this paper, we develop a method that yields individual-level, flexibly shaped utility functions for use in choice models. This flexibility at the individual level is accomplished through splines of the truncated power basis type in a general additive regression framework for latent utility. Because the number and location of spline knots are unknown, we use the birth-death process of Denison et al. (1998) and Greens (1995) reversible jump method. We further show how exogenous constraints suggested by theory, such as monotonicity of price response, can be accommodated. Our formulation is particularly suited to estimating reaction to pricing, where individual-level monotonicity is justified theoretically and empirically, but linearity is typically not. The method is illustrated in a conjoint application in which all covariates are splined simultaneously and in three panel data sets, each of which has a single price spline. Empirical results indicate that piecewise linear splines with a modest number of knots fit these data well, substantially better than heterogeneous linear and log-linear a priori specifications. In terms of price response specifically, we find that although aggregate market-level curves can be nearly linear or log-linear, individuals often deviate widely from either. Using splines, hold-out prediction improvement over the standard heterogeneous probit model ranges from 6% to 14% in the scanner applications and exceeds 20% in the conjoint study. Moreover, “optimal” profiles in conjoint and aggregate price response curves in the scanner applications can differ markedly under the standard and the spline-based models.

Challenges to Evidence-Based Prescribing in Clinical Practice

Although there appears to be widespread support of evidence-based medicine as a basis for rational prescribing, the challenges to it are signilicant and often justified. A multitude of factors other than evidence drive clinical decision-making, including patient preferences and social circumstances, presence of diseasedrug and drug-drug interactions, clinical experience, competing demands from more pressing clinical conditions, marketing and promotional activity, and systemlevel drug policies.

Control Charts for the Generalized Variance Based on Its Predictive Distribution

This article develops a control chart for the generalized variance. A Bayesian approach is used to incorporate parameter uncertainty. Our approach has two stages, (i) construction of the control chart where we use a predictive distribution based on a Bayesian approach to derive the rejection region, and (ii) evaluation of the control chart where we use a sampling theory approach to examine the performance of the control chart under various hypothetical specifications for the data generation model.

Control Charts for the Variance and Coefficient of Variation Based on Their Predictive Distribution

This article develops a control chart for the variance of a normal distribution and, equivalently, the coefficient of variation of a log-normal distribution. A Bayesian approach is used to incorporate parameter uncertainty, and the control limits are obtained from the predictive distribution for the variance. We evaluate this control chart by examining its performance for various values of the process variance.

Modeling Parametric Evolution in a Random Utility Framework

Random utility models have become standard econometric tools, allowing parameter inference for individual-level categorical choice data. Such models typically presume that changes in observed choices over time can be attributed to changes in either covariates or unobservables. We study how choice dynamics can be captured more faithfully by also directly modeling temporal changes in parameters, using a vector autoregressive process and Bayesian estimation. This approach offers a number of advantages for theorists and practitioners, including improved forecasts, prediction of long-run parameter levels, and correction for potential aggregation biases. We illustrate the method using choices for a common supermarket good, where we find strong support for parameter dynamics.

Prediction Of Warranty Costs During A Given Period Of Time

AbstractThis paper considers simple warranty policies where a one-time expense, possibly depending on the product’s age, is incurred at product failure. Interest focuses on the mean and variance of total warranty expense for a given future period. Product purchases are assumed to have a nonhomogeneous Poisson process, and so the actual number of products sold is not known at the time of the forecast. The special case is discussed where the distribution of product failure times is exponential, as is the case when average product failure time is unknown and must be estimated.

A decision-theoretic approach to some screening problems

SummarySuppose an item is acceptable if its measurement on the variable of interestY isY≦u. It may be expensive (or impossible) to measureY, and a correlated variableX exists which is relatively inexpensive to measure and is used to screen items, i.e., to declare them acceptable ifX≦w. We examine two situations in both of whichl acceptable items are needed. (i) Before use of the item,Y is measured directly to ensure acceptability: ShouldX be used for screening purposes before theY measurement or not? (ii)Y cannot be measured directly before use, but screening is possible to determine the items that are to be used. We assume thatX andY have a bivariate normal distribution for which the parameters are known. Some comments are made about the case when the parameters are not known.

Bayesian prediction in growth-curve models with correlated errors

We treat the Bayesian prediction problem in growth-curve models with correlated errors when the underlying model is hierarchical. We assume there to be data on several individuals randomly drawn from the same population. For each individual, several responses are available that arise from a lincar model with autocorrelated errors. The regression parameters for the individuals are modeled to arise from a multivariate normal distribution. We investigate two prediction problems, (a) where another individual is randomly drawn from the same population and we want to predict several responses for this individual, and (b) where we want to predict additional responses for one of the individuals in our sample. A detailed numerical example is given; calibration is discussed in the context of this example.

Counting by Weighing: An Approach Using Renewal Theory

Abstract Renewal theory and Bayesian decision theory are used to solve a problem related to counting a large number of items by weighing them. Specifically, a batch is to be obtained containing a given number of items by adding items until their total weight reaches a critical value that can depend on the results of a preliminary sample. Furthermore, the optimal sample size for this preliminary sample is to be determined. The distribution of individual weights is assumed to be normal.