In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and nested sampling from a unified perspective.

This paper presents a probabilistic representation for 3D objects, and details the mechanism of inferring the pose of real-world objects from vision. Our object model has the form of a hierarchy of increasingly expressive 3D features, and probabilistically represents 3D relations between these. Features at the bottom of the hierarchy are bound to local perceptions; while we currently only use v...

Default loss distribution of corporate portfolios plays a crucial role in CDO tranche pricing, tracking error calculation and profit/loss assessment of corporation systems. This work gives an efficient algorithm to calculate the default loss distribution based on Hull-White probability bucketing approach and importance sampling method. The Gaussian copula model is assumed to calculate the condi...

We consider an unbiased simulation method for multidimensional diffusions based on the parametrix method for solving partial differential equations with H’́older continuous coefficients. This Monte Carlo method which is based on an Euler scheme with random time steps, can be considered as an infinite dimensional extension of the Multilevel Monte Carlo method for solutions of stochastic different...

In this paper an optimal importance sampling (IS) method is derived for a transient markov system. Several propositions are presented. It is showned that the optimal IS method is unique, and it must converge to the standard Monte Carlo (MC) simulation method when the sample path length approaches infinity. Therefore, it is not the size of the state space of the Markov system, but the sample pat...

To estimate the value functions of policies from exploratory data, most model-free offpolicy algorithms rely on importance sampling, where the use of importance sampling ratios often leads to estimates with severe variance. It is thus desirable to learn off-policy without using the ratios. However, such an algorithm does not exist for multi-step learning with function approximation. In this pap...

In a previous paper we introduced a new variance-reduction technique for regenerative simulations based on permuting regeneration cycles. In this paper we apply this idea to new classes of estimators. In particular, we derive permuted versions of likelihood-ratio derivative estimators for steady-state performance measures, importance-sampling estimators of the mean cumulative reward until hitti...

The researcher faced with a computationally intensive simulation will either seek powerful processing capabilities or turn to variance reduction techniques. In many situations, a combination of both approaches is required to achieve the desired accuracy. In the study of rare events, importance sampling (IS) is the only variance reduction technique which has been shown to offer the potential for...

Recently, a state-dependent change of measure for simulating overflows in the two-node tandem queue was proposed by Dupuis et al. (Ann. Appl. Probab. 17(4):1306– 1346, 2007), together with a proof of its asymptotic optimality. In the present paper, we present an alternative, shorter and simpler proof. As a side result, we obtain interpretations for several of the quantities involved in the chan...

In this paper we consider a slotted queueing model with nite buuers and correlated input. Arrivals are generated by diierent sources and ooered in batches at the end of each slot. The batch sizes depend on the states of the sources which change their states according to Markov schemes. In case that the buuer reaches its limits, the excess of the buuer is lost. At the end of a slot a random batc...