105,488 research outputs found
Variance Analysis for Monte Carlo Integration: A Representation-Theoretic Perspective
In this report, we revisit the work of Pilleboue et al. [2015], providing a
representation-theoretic derivation of the closed-form expression for the
expected value and variance in homogeneous Monte Carlo integration. We show
that the results obtained for the variance estimation of Monte Carlo
integration on the torus, the sphere, and Euclidean space can be formulated as
specific instances of a more general theory. We review the related
representation theory and show how it can be used to derive a closed-form
solution
Monte Carlo Complexity of Parametric Integration
The Monte Carlo complexity of computing integrals depending on a parameter is analyzed for smooth integrands. An optimal algorithm is developed on the basis of a multigrid variance reduction technique. The complexity analysis implies that our algorithm attains a higher convergence rate than any deterministic algorithm. Moreover, because of savings due to computation on multiple grids, this rate is also higher than that of previously developed Monte Carlo algorithms for parametric integration
Pareto Smoothed Importance Sampling
Importance weighting is a general way to adjust Monte Carlo integration to
account for draws from the wrong distribution, but the resulting estimate can
be noisy when the importance ratios have a heavy right tail. This routinely
occurs when there are aspects of the target distribution that are not well
captured by the approximating distribution, in which case more stable estimates
can be obtained by modifying extreme importance ratios. We present a new method
for stabilizing importance weights using a generalized Pareto distribution fit
to the upper tail of the distribution of the simulated importance ratios. The
method, which empirically performs better than existing methods for stabilizing
importance sampling estimates, includes stabilized effective sample size
estimates, Monte Carlo error estimates and convergence diagnostics.Comment: Major revision: 1) proofs for consistency, finite variance, and
asymptotic normality, 2) justification of k<0.7 with theoretical
computational complexity analysis, 3) major rewrit
The marginal likelihood of Structural Time Series Models, with application to the euroareaa nd US NAIRU
We propose a simple procedure for evaluating the marginal likelihood in univariate Structural Time Series (STS) models. For this we exploit the statistical properties of STS models and the results in Dickey (1968) to obtain the likelihood function marginally to the variance parameters. This strategy applies under normal-inverted gamma-2 prior distributions for the structural shocks and associated variances. For trend plus noise models such as the local level and the local linear trend, it yields the marginal likelihood by simple or double integration over the (0,1)-support. For trend plus cycle models, we show that marginalizing out the variance parameters greatly improves the accuracy of the Laplace method. We apply this ethodology to the analysis of US and euro area NAIRU.Marginal likelihood, Markov Chain Monte Carlo, unobserved components,
bridge sampling, Laplace method, NAIRU
Long Memory Modelling of Inflation with Stochastic Variance and Structural Breaks
We investigate changes in the time series characteristics of postwar U.S. inflation. In a model-based analysis the conditional mean of inflation is specified by a long memory autoregressive fractionally integrated moving average process and the conditional variance is modelled by a stochastic volatility process. We develop a Monte Carlo maximum likelihood method to obtain efficient estimates of the parameters using a monthly data-set of core inflation for which we consider different subsamples of varying size. Based on the new modelling framework and the associated estimation technique, we find remarkable changes in the variance, in the order of integration, in the short memory characteristics and in the volatility of volatility
Heteroskedastic Factor Vector Autoregressive Estimation of Persistent and Non Persistent Processes Subject to Structural Breaks
In the paper the fractionally integrated heteroskedastic factor vec- tor autoregressive (FI-HF-VAR) model is introduced. The proposed approach is characterized by minimal pretesting requirements and sim- plicity of implementation also in very large systems, performing well independently of integration properties and sources of persistence, i.e. deterministic or stochastic, accounting for common features of di¤erent kinds, i.e. common integrated (of the fractional or inte- ger type) or non integrated stochastic factors, also featuring condi- tional heteroskedasticity, and common deterministic break processes. The proposed approach allows for accurate investigation of economic time series, from persistence and copersistence analysis to impulse responses and forecast error variance decomposition. Monte Carlo results strongly support the proposed methodology. Key words: long and short memory, structural breaks, fractionally integrated heteroskedastic factor vector autoregressive model.
- …