Abstract. This chapter provides a survey of the main methods in non-uniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorithms, before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods.

Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0, 1) random variables (i.e., continuous random variables distributed uniformly over the interval

. A standard method for handling Bayesian models is to use Markov chain Monte Carlo methods to draw samples from the posterior. We demonstrate this method on two core problems in computer vision---structure from motion and colour constancy. These examples illustrate a samplers producing useful representations for very large problems. We demonstrate that the sampled representations are trustworthy, using consistency checks in the experimental design. The sampling solution to structure from motion is strictly better than the factorisation approach, because: it reports uncertainty on structure and position measurements in a direct way; it can identify tracking errors; and its estimates of covariance in marginal point position are reliable. Our colour constancy solution is strictly better than competing approaches, because: it reports uncertainty on surface colour and illuminant measurements in a direct way; it incorporates all available constraints on surface reflectance and on illumination in a direct way; and it integrates a spatial model of reflectance and illumination distribution with a rendering model in a natural way. One advantage of a sampled representation is that it can be resampled to take into account other information. We demonstrate the effect of knowing that, in our colour constancy example, a surface viewed in two different images is in fact the same object. We conclude with a general discussion of the strengths and weaknesses of the sampling paradigm as a tool for computer vision. Keywords: Markov chain Monte Carlo, colour constancy, structure from motion 1.

The method of control variates is one of the most widely used variance reduction techniques associated with Monte Carlo simulation. This paper studies the method of control variates from several di#erent viewpoints, and establishes new connections between the method of control variates and: conditional Monte Carlo, antithetics, rotation sampling, stratification, and nonparametric maximum likelihood. We also develop limit theory for the method of control variates under weak assumptions on the estimator of the optimal control coe#cient.

Abstract—Friction and nonlinearities result in large residual errors and deteriorate the performance of head positioning of hard disk drive (HDD) servo systems and other mechanical servo systems. Thus, it is highly desirable to characterize the behaviors of nonlinearities and friction in the servo systems. This paper presents a fairly comprehensive modeling and compensation of friction and nonlinearities of a typical voice-coil-motor (VCM) actuator used in commercial HDDs, and the design of an HDD servo system using an enhanced nonlinear control technique. Our contributions are two-fold: We will first obtain a complete model of the VCM actuator including friction and nonlinear characteristics through a careful examination of the configuration and structure of the actual system and through a thorough analysis of its physical effects together with its time-domain and frequency-domain responses. We will then proceed to design a servo system for the hard drive using an enhanced composite nonlinear feedback (CNF) control technique with a simple friction and nonlinearity compensation scheme. The enhanced CNF technique has a feature of removing the uncompensated portion of friction and nonlinearities without sacrificing the overall tracking performance. Simulation and experimental results for both the modeling and the servo design show that our approach is very effective and successful. In particular, our experimental results show that the enhanced CNF control has outperformed the conventional proportional-integral-derivative (PID) control in settling time by 76%. We believe that this approach can be adopted to solve other servomechanism problems. Index Terms—Actuators, friction, hard disks, identification, modeling, motion control, nonlinearities, servo systems. I.

Abstract: We consider various properties of Bayesian inferences related to repeated sampling interpretations, when we have a proper prior. While these can be seen as particularly relevant when the prior is diffuse, we argue that it is generally reasonable to consider such properties as part of our assessment of Bayesian inferences. We discuss the logical implications for how repeated sampling properties should be assessed when we have a proper prior. We develop optimal Bayesian repeated sampling inferences using a generalized idea of what it means for a credible region to contain a false value and discuss the practical use of this idea for error assessment and experimental design. We present results that connect Bayes factors with optimal inferences and develop a generalized concept of unbiasedness for credible regions. Further, we consider the effect of reparameterizations on hpd-like credible regions and argue that one reparameterization is most relevant, when repeated sampling properties and the prior are taken into account. Key words and phrases: repeated sampling properties, relative surprise inferences, prior-data conflict, Bayes factors, relative belief ratios. 1

This paper reviews current quadrature methods for approximate calculation of integrals within S-Plus or R. Starting with the general framework, Gaussian quadrature will be discussed first, followed by adaptive rules and Monte Carlo methods. Finally, a comparison of the methods presented is given. The aim of this survey paper is to help readers, not expert in computing, to apply numerical integration methods and to realize that numerical analysis is an art, not a science

Abstract — Reliable state estimation is an important enabler for robot operation in human environments. Uncertainty and unpredictability of these environments requires global uncertainty problems to be solved for dependable operation. Relative sensors — such as vision, laser and tactile — are common in these applications leading to challenging perceptual problems, for which modern inference methods fail to guarantee accurate estimates. Further, as we show, the reliability of these estimates degrades quickly as initial uncertainty increases. In this paper, our aim is to maximize the amount of information extracted from sensory data, allowing the robot to make the most of its sensors. We present an inference algorithm, which guarantees that all optimal solutions will be found and provides provable error bounds on the approximation of the underlying probability distribution. The approach is based on insight into the sensor model, which is used to guide the refinement process in an adaptive grid algorithm. The approach is applicable to a variety of pose estimation problems with relative sensors. We demonstrate the generality of the approach on the examples of indoor robot localization and tactile manipulation, where it dramatically outperforms state-of-the-art. Empirically, our method increased safety of decision making to 100%. The proposed algorithm also demonstrated logarithmic dependence on desired precision, allowing for efficient highaccuracy estimation. In indoor localization experiments, the approach led to 1mm accuracy of pose estimation based on the commonly used laser range finders. This high accuracy is useful for accurate maneuvering in tight spaces and is sufficient for reliable manipulation of stationary objects of interest within the environment (e.g. door handles, elevator buttons, etc.) It also opens up new potential applications during building construction, inspection and maintenance. In the tactile manipulation setting, the method results in efficient, accurate and reliable 6DOF object pose estimation from tactile data, allowing for reliable manipulation. I.

regression structure may be the primary focus. The marginalized latent variable models allow a exible choice between modelling the marginal means or the conditional means. The marginalized transition models separate the dependence on the exposure variables from the dependence on previous response values. Orthogonality properties between the mean and the dependence parameters in a marginalized model secure robustness for the marginal means. Marginalized models further allow for simple procedures to determine a suitable dependence model for the data. Chapter 12 on time-dependent covariates is also new. The temporal order between key exposure and response events is emphasized and exogenous and endogenous covariates are formally de ned. When covariates are endogenous, then meaningful targets for inference need to be formulated as well as valid methods of estimation. A longitudinal study on maternal stress, child illness and maternal employment illustrates concepts. The scienti c questions include (i) Is there an association between maternal employment and stress? (ii) Is there an association between maternal employment and child illness? (iii) Do the data provide evidence that maternal stress causes child illness? Since stress may be in the causal pathway that leads from employment to illness no adjustment is made for the daily stress indicators when evaluating the dependence of illness on employment. Similarly no adjustment is made for illness in the analysis of employment and stress. Question (iii) raises issues such as ‘does illness at day t depend on prior stress measured at day (t − k) ’ and ‘does illness on day (t − k) predict stress on day t’. A covariate which is both a predictor for the response and is predicted by earlier responses is endogenous. No standard regression methods are available to obtain causal statements when dealing with endogenous covariates. Targets for inference are discussed in terms of counterfactual outcomes. Causal e ects refer to interventions in the entire population rather than among possibly select, observed subgroups. Focus

The naive Bayes classifier (NB) has exhibited its “mysterious ” but outstanding classification ability in practice, in spite of its often unrealistic conditional inde-pendence assumption. This simple assumption implies the adoption of a diagonal structure for the underlying class-specific precision matrices. However, the NB leaves covariates interrelationships unrevealed. In this dissertation, we will ex-tend the NB from the perspectives of covariance modeling and classification. Due to the positive definiteness constraint and the rapidly-growing number of parameters with dimensions, covariance estimation in a multivariate normal population has been a classic but challenging statistical problem. Sparse shrinkage covariance/precision matrix estimation has been obeyed as an important principle in covariance/precision matrix modeling. However, many existing models can only shrink the covariance/precision matrix toward a predefined diagonal structure. We model a precision matrix via its Cholesky decomposition in terms of compositional regression coefficient matrix and error precisions. Our approach aims at estimating