Calibrated multivariate distributions for improved conditional prediction

The specification of multivariate prediction regions, having coverage probability closed to the target nominal value, is a challenging problem both from the theoretical and the practical point of view. In this paper we define a well-calibrated multivariate predictive distribution giving suitable conditional prediction intervals with the desired overall coverage accuracy. This distribution is the extension in the multivariate setting of a calibrated predictive distribution defined for the univariate case and it is found on the idea of calibrating prediction regions for improving the coverage probability. This solution is asymptotically equivalent to that one based on asymptotic calculations and, whenever its explicit computation is not feasible, an approximation based on a simple bootstrap simulation procedure is readily available. Moreover, we state a simple, simulation-based, procedure for computing the associated improved conditional prediction limits

A note on predictive densities based on composite likelihood methods

Whenever the computation of data distribution is unfeasible or inconvenient, the classical predictive procedures prove not to be useful. These rely, after all, on the conditional distribution of the future random variable, which is also unavailable. This paper considers a notion of composite likelihood for specifying composite predictive distributions, viewed as surrogates for true unknown predictive distribution. In particular, the focus is on the pairwise likelihood obtained as a weighted product of likelihood factors related to bivariate events associated with both the sample data and future observation. The specification of the weights, andmore generally the evaluation of the frequentist properties of alternative pairwise predictive distributions, is performed by considering the mean square prediction error of the associated predictors and the expected Kullback\u2013Liebler loss of the related predictive densities. Finally, simple examples concerning autoregressive models are presented

Improved multivariate prediction regions for Markov process models

This paper concerns the specification of multivariate prediction regions which may be useful in time series applications whenever we aim at considering not just one single forecast but a group of consecutive forecasts. We review a general result on improved multivariate prediction and we use it in order to calculate conditional prediction intervals for Markov process models so that the associated coverage probability turns out to be close to the target value. This improved solution is asymptotically superior to the estimative one, which is simpler but it may lead to unreliable predictive conclusions. An application to general autoregressive models is presented, focusing in particular on AR and ARCH models

Finding the largest triangle in a graph in expected quadratic time

Finding the largest triangle in an n-nodes edge-weighted graph belongs to a set of problems all equivalent under subcubic reductions. Namely, a truly subcubic algorithm for any one of them would imply that they are all subcubic. A recent strong conjecture states that none of them can be solved in less than \u398(n3) time, but this negative result does not rule out the possibility of algorithms with average, rather than worst-case, subcubic running time. Indeed, in this work we describe the first truly-subcubic average complexity procedure for this problem for graphs whose edge lengths are uniformly distributed in [0,1]. Our procedure finds the largest triangle in average quadratic time, which is the best possible complexity of any algorithm for this problem. We also give empirical evidence that the quadratic average complexity holds for many other random distributions of the edge lengths. A notable exception is when the lengths are distances between random points in Euclidean space, for which the algorithm takes average cubic time

Confidence distributions for predictive tail probabilities

In this short paper we propose the use of a calibration procedure in order to obtain predictive probabilities for a future random variable of interest. The new calibration method gives rise to a confidence distribution function which probabilities are close to the nominal ones to a high order of approximation. Moreover, the proposed predictive distribution can be easily obtained by means of a bootstrap simulation procedure. A simulation study is presented in order to assess the good properties of our proposal. The calibrated procedure is also applied to a series of real data related to sport records, with the aim of closely estimate the probability of future records

The temporalized Massey's method

We propose and throughly investigate a temporalized version of the popular Massey's technique for rating actors in sport competitions. The method can be described as a dynamic temporal process in which team ratings are updated at every match according to their performance during the match and the strength of the opponent team. Using the Italian soccer dataset, we empirically show that the method has a good foresight prediction accuracy

A note on simultaneous calibrated prediction intervals for time series

This paper deals with simultaneous prediction for time series models. In particular, it presents a simple procedure which gives well-calibrated simultaneous prediction intervals with coverage probability close to the target nominal value. Although the exact computation of the proposed intervals is usually not feasible, an approximation can be easily attained by means of a suitable bootstrap simulation procedure. This new predictive solution is much simpler to compute than those ones already proposed in the literature, based on asymptotic calculations. Applications of the bootstrap calibrated procedure to AR, MA and ARCH models are presented

Probabilistic prediction: aims and solutions

The goodness of a predictive distribution depends on the aim of the prediction. This presentation intends to shed light on properties of predictive distributions in use nowadays. We also propose a new predictive distribution that may be useful to obtain calibrated predictions for the probabilities of a future random variable of interest. This predictive distribution can be easily computed by a simple bootstrap procedure. In order to compare the different predictive distributions, some simulation studies are also presented

Modeling the vibration of spatial flexible mechanisms through an equivalent rigid-link system/component mode synthesis approach

In this paper, a novel formulation for modeling the vibration of spatial flexible mechanisms and robots is introduced. The formulation is based on the concepts of equivalent rigid-link system (ERLS) that allows kinematic equations of motion for the ERLS decoupled from the compatibility equations of the displacement at the joint to be written. With respect to the available literature, in which the ERLS concept has been proposed together with a finite element method (FEM) approach (ERLS-FEM), the formulation is extended in this paper through a modal approach and, in particular, a component mode synthesis technique which allows a reduced-order system of dynamic equations to be maintained even when a fine discretization is needed. The model is validated numerically by comparing it with the results obtained from the Adams-Flex\u2122 software, which implements the well-known floating frame of reference approach for a benchmark L-shaped mechanism. A good agreement between the two models is shown