We investigate existence and properties of discrete mixture representations $P_{\theta }=\sum _{i\in E}w_{\theta }(i)\,Q_{i}$ for a given family }$, $\theta \in \Theta $, probability measures. The noncentral chi-squared distributions provide classical example. obtain results about geometric statistical aspects the problem, latter including loss Fisher information, Rao-Blackwellization, asymptot...

This paper focuses on sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use Rao-Blackwellization: particle approximation is used to sample sequences of hidden regimes while the Gaussian states are explicitly integrated conditional on the sequence of reg...

let be a random sample from a normal distribution with unknown mean and known variance the usual estimator of the mean, i.e., sample mean is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. in many practical situations, is known in advance to lie in an interval, say for some in this case, the maximum likelihood estimator changes and d...

The braking rate and train arresting operation is important in the train braking performance. It is difficult to obtain the states of the train on time because of the measurement noise and a long calculation time. A type of Group Stochastic M-algorithm (GSMA) based on Rao-Blackwellization Particle Filter (RBPF) algorithm and Stochastic M-algorithm (SMA) is proposed in this paper. Compared with ...

Multipath is one of the dominant sources of error in highprecision GNSS applications. A tracking algorithm is presented that explicitely accounts for direct signal and multipath replicas in the model, in order to mitigate the contributions of the latter. A Bayesian approach has been taken, to infer some information from the time evolution model of the parameters. Due to the nonlinearity of the ...

Rao–Blackwellization is an approximation technique for probabilistic inference that flexibly combines exact inference with sampling. It is useful in models where conditioning on some of the variables leaves a simpler inference problem that can be solved tractably. This paper presents Sample Propagation, an efficient implementation of Rao–Blackwellized approximate inference for a large class of ...

This paper proposes methods to improve Monte Carlo estimates when the Independent MetropolisHastings Algorithm (IMHA) is used. Our rst approach uses a control variate based on the sample generated by the proposal distribution. We derive the variance of our estimator for a xed sample size n and show that, as n tends to in nity, this variance is asymptotically smaller than the one obtained with t...

We present a method for efficiently tracking objects represented as constellations of parts by integrating out the shape of the model. Parts-based models have been successfully applied to object recognition and tracking. However, the high dimensionality of such models present an obstacle to traditional particle filtering approaches. We can efficiently use parts-based models in a particle filter...

Sampling from high-dimensional systems often suffers from the curse of dimensionality. In this paper, we explored the use of sequential structures in sampling from high-dimensional systems with an aim at eliminating the curse of dimensionality, and proposed an algorithm, so-called sequential parallel tempering as an extension of parallel tempering. The algorithm was tested with the witch's hat ...

Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods provide computational tools for systematic inference and learning in complex dynamical systems, such as nonlinear and non-Gaussian state-space models. This thesis builds upon several methodological advances within these classes of Monte Carlo methods. Particular emphasis is placed on the combination of SMC and MCMC in so c...