A bayesian approach to bioassay. technical report m498

We describe the design and analysis for a simulation experiment to compare the mean-squared errors (MSE's) of two quantile estimators defined for random walk designs. The dependence of the easily computed MSE of the first estimator on the levels of five factors is examined via multiple regression. This information is used to plan a simulation to compute the MSE of the second estimator using a fraction of a 3³5²factorial allowing uncorrelated estimates for all main effects and the two-factor interactions of a specified factor. Efficient estimation of the MSE of the second estimator is attempted through antithetic and control variate techniques of variance reduction, with modest success.     

Understanding the Kalman Filter

This is an expository article. Here we show how the successfully used Kalman filter, popular with control engineers and other scientists, can be easily understood by statisticians if we use a Bayesian formulation and some well-known results in multivariate statistics. We also give a simple example illustrating the use of the Kalman filter for quality control work.     

Default Estimation and Expert Information

Default is a rare event, even in segments in the midrange of a bank’s portfolio. Inference about default rates is essential for risk management and for compliance with the requirements of Basel II. Most commercial loans are in the middle-risk categories and are to unrated companies. Expert information is crucial in inference about defaults. A Bayesian approach is proposed and illustrated using a prior distribution assessed from an industry expert. The binomial model, most common in applications, is extended to allow correlated defaults. A check of robustness is illustrated with an ε-mixture of priors.     

A Simple Variance Estimator for Unequal Probability Sampling without Replacement

Survey sampling textbooks often refer to the Sen–Yates–Grundy variance estimator for use with without-replacement unequal probability designs. This estimator is rarely implemented because of the complexity of determining joint inclusion probabilities. In practice, the variance is usually estimated by simpler variance estimators such as the Hansen–Hurwitz with replacement variance estimator; which often leads to overestimation of the variance for large sampling fractions that are common in business surveys. We will consider an alternative estimator: the Hájek (1964 Hájek J 1981 Sampling from a Finite Population New York: Marcel Dekker  [Google Scholar]) variance estimator that depends on the first-order inclusion probabilities only and is usually more accurate than the Hansen–Hurwitz estimator. We review this estimator and show its practical value. We propose a simple alternative expression; which is as simple as the Hansen–Hurwitz estimator. We also show how the Hájek estimator can be easily implemented with standard statistical packages.     

Reliability Estimation Based on System Data with an Unknown Load Share Rule

We consider a multicomponent load-sharing system in which the failure rate of a given component depends on the set of working components at any given time. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example. A load-share rule dictates how stress or load is redistributed to the surviving components after a component fails within the system. In this paper, we assume the load share rule is unknown and derive methods for statistical inference on load-share parameters based on maximum likelihood. Components with (individual) constant failure rates are observed in two environments: (1) the system load is distributed evenly among the working components, and (2) we assume only the load for each working component increases when other components in the system fail. Tests for these special load-share models are investigated.     

Interpolation models with multiple hyperparameters

A traditional interpolation model is characterized by the choice of regularizer applied to the interpolant, and the choice of noise model. Typically, the regularizer has a single regularization constant , and the noise model has a single parameter . The ratio / alone is responsible for determining globally all these attributes of the interpolant: its complexity, flexibility, smoothness, characteristic scale length, and characteristic amplitude. We suggest that interpolation models should be able to capture more than just one flavour of simplicity and complexity. We describe Bayesian models in which the interpolant has a smoothness that varies spatially. We emphasize the importance, in practical implementation, of the concept of conditional convexity when designing models with many hyperparameters. We apply the new models to the interpolation of neuronal spike data and demonstrate a substantial improvement in generalization error.     

Analysis of the human sex ratio by using overdispersion models

For study of the human sex ratio, one of the most important data sets was collected in Saxony in the 19th century by Geissler. The data contain the sizes of families, with the sex of all children, at the time of registration of the birth of a child. These data are reanalysed to determine how the probability for each sex changes with family size. Three models for overdispersion are fitted: the beta–binomial model of Skellam, the 'multiplicative' binomial model of Altham and the double-binomial model of Efron. For each distribution, both the probability and the dispersion parameters are allowed to vary simultaneously with family size according to two separate regression equations. A finite mixture model is also fitted. The models are fitted using non-linear Poisson regression. They are compared using direct likelihood methods based on the Akaike information criterion. The multiplicative and beta–binomial models provide similar fits, substantially better than that of the double-binomial model. All models show that both the probability that the child is a boy and the dispersion are greater in larger families. There is also some indication that a point probability mass is needed for families containing children uniquely of one sex.     

Central Limit Theorems for the Non‐Parametric Estimation of Time‐Changed Lévy Models

Abstract. Let {Z_t}_{t 0} be a Lévy process with Lévy measure ν and let be a random clock, where g is a non‐negative function and is an ergodic diffusion independent of Z. Time‐changed Lévy models of the form are known to incorporate several important stylized features of asset prices, such as leptokurtic distributions and volatility clustering. In this article, we prove central limit theorems for a type of estimators of the integral parameter β(?):=∫?(x)ν(dx), valid when both the sampling frequency and the observation time‐horizon of the process get larger. Our results combine the long‐run ergodic properties of the diffusion process with the short‐term ergodic properties of the Lévy process Z via central limit theorems for martingale differences. The performance of the estimators are illustrated numerically for Normal Inverse Gaussian process Z and a Cox–Ingersoll–Ross process .     

Approximate Bayesian Inference for Survival Models

Abstract. Bayesian analysis of time‐to‐event data, usually called survival analysis, has received increasing attention in the last years. In Cox‐type models it allows to use information from the full likelihood instead of from a partial likelihood, so that the baseline hazard function and the model parameters can be jointly estimated. In general, Bayesian methods permit a full and exact posterior inference for any parameter or predictive quantity of interest. On the other side, Bayesian inference often relies on Markov chain Monte Carlo (MCMC) techniques which, from the user point of view, may appear slow at delivering answers. In this article, we show how a new inferential tool named integrated nested Laplace approximations can be adapted and applied to many survival models making Bayesian analysis both fast and accurate without having to rely on MCMC‐based inference.     

论刘劭《人物志》中的逻辑思想

刘劭的《人物志》一直以来被当成是一部人材学著作,而该书中所渗透的逻辑思想却不太受重视。笔者将谈谈《人物志》中隐含的“名实观”、“论辩思想”、“推论方法和分类形式”等逻辑学思想。