Smoothing and filtering with a class of outer measures

Filtering and smoothing with a generalised representation of uncertainty is considered. Here, uncertainty is represented using a class of outer measures. It is shown how this representation of uncertainty can be propagated using outer-measure-type versions of Markov kernels and generalised Bayesian-like update equations. This leads to a system of generalised smoothing and filtering equations where integrals are replaced by supremums and probability density functions are replaced by positive functions with supremum equal to one. Interestingly, these equations retain most of the structure found in the classical Bayesian filtering framework. It is additionally shown that the Kalman filter recursion can be recovered from weaker assumptions on the available information on the corresponding hidden Markov model

Towards a quantum theory of de Sitter space

We describe progress towards constructing a quantum theory of de Sitter space in four dimensions. In particular we indicate how both particle states and Schwarzschild de Sitter black holes can arise as excitations in a theory of a finite number of fermionic oscillators. The results about particle states depend on a conjecture about algebras of Grassmann variables, which we state, but do not prove.Comment: JHEP3 LaTex - 19 page

Enrichment Procedures for Soft Clusters: A Statistical Test and its Applications

Clusters, typically mined by modeling locality of attribute spaces, are often evaluated for their ability to demonstrate ‘enrichment’ of categorical features. A cluster enrichment procedure evaluates the membership of a cluster for significant representation in pre-defined categories of interest. While classical enrichment procedures assume a hard clustering definition, in this paper we introduce a new statistical test that computes enrichments for soft clusters. We demonstrate an application of this test in refining and evaluating soft clusters for classification of remotely sensed images

Latent class analysis for segmenting preferences of investment bonds

Market segmentation is a key component of conjoint analysis which addresses consumer preference heterogeneity. Members in a segment are assumed to be homogenous in their views and preferences when worthing an item but distinctly heterogenous to members of other segments. Latent class methodology is one of the several conjoint segmentation procedures that overcome the limitations of aggregate analysis and a-priori segmentation. The main benefit of Latent class models is that market segment membership and regression parameters of each derived segment are estimated simultaneously. The Latent class model presented in this paper uses mixtures of multivariate conditional normal distributions to analyze rating data, where the likelihood is maximized using the EM algorithm. The application focuses on customer preferences for investment bonds described by four attributes; currency, coupon rate, redemption term and price. A number of demographic variables are used to generate segments that are accessible and actionable.peer-reviewe