A Bayesian method of estimating an unknown regression curve by a polynomial of random order is proposed. A joint distribution is assigned over both the set of possible orders of the polynomial and the polynomial coeecients. 1995) are used to compute required posteriors. The methodology is extended to polynomials of random order with discontinuties and to piecewise poly-nomials of random order. ...

We introduce a nonparametric approach for estimating drift functions in systems of stochastic differential equations from sparse observations of the state vector. Using a Gaussian process prior over the drift as a function of the state vector, we develop an approximate EM algorithm to deal with the unobserved, latent dynamics between observations. The posterior over states is approximated by a ...

Capacity control is a very important problem in civil infrastructure operation, but no general model exists for it. In this project we • Formulate the real-time capacity control problem of a single facility • Perform dynamic programming to search for the optimal solution • Implement piecewise linear regression to update the objective function, and SCP to update the policy • Extend the model to ...

This paper concerns a method of selecting a subset of features for a logistic regression model. Information criteria, such as the Akaike information criterion and Bayesian information criterion, are employed as a goodness-offit measure. The feature subset selection problem is formulated as a mixed integer linear optimization problem, which can be solved with standard mathematical optimization s...

This article introduces a method to determine the threshold of unimodal image histograms in a robust manner. It is based on a piecewise linear regression that finds the two segments that fit the descending slope of the histogram. The algorithm gives a good estimation of the threshold, and is practically insensitive to the noise distribution, to the quantity of objects to segment, and to random ...

Abstract. We present a Bayesian analysis for recurrent events data using a nonhomogeneous mixed Poisson point process with a dynamic subject-specific frailty function and a dynamic baseline intensity func- tion. The dynamic subject-specific frailty employs a dynamic piecewise constant function with a known pre-specified grid and the baseline in- tensity uses an unknown grid for the piecewise ...

We estimate a linear and a piecewise linear Phillips curve model with regional labor market data for West German and Neue Länder. Employing regional observations allows us to country difference the data. This eliminates, under the assumption of homogeneous Länder, supply shocks and changes in the formation of expectations as possible identification failures. With seemingly unrelated regressions...

A non-parametric estimator of a non-increasing density is found in a class of piecewise linear functions when the data consist only of counts. An EM-Algorithm for computing the estimator is developed, and the iterates in the algorithm are shown to converge to the maximum likelihood estimator. Potential applications to distance sampling models are described and illustrated with a numerical examp...

We study the fixed design segmented regression problem – a classical statistical inference task that encompasses several natural problems as a special case. Given noisy samples from a piecewise linear function f , we want to recover f up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on dynamic programming (DP) and, while sample efficient, have r...