9,630 research outputs found
Bayesian Conditional Density Filtering
We propose a Conditional Density Filtering (C-DF) algorithm for efficient
online Bayesian inference. C-DF adapts MCMC sampling to the online setting,
sampling from approximations to conditional posterior distributions obtained by
propagating surrogate conditional sufficient statistics (a function of data and
parameter estimates) as new data arrive. These quantities eliminate the need to
store or process the entire dataset simultaneously and offer a number of
desirable features. Often, these include a reduction in memory requirements and
runtime and improved mixing, along with state-of-the-art parameter inference
and prediction. These improvements are demonstrated through several
illustrative examples including an application to high dimensional compressed
regression. Finally, we show that C-DF samples converge to the target posterior
distribution asymptotically as sampling proceeds and more data arrives.Comment: 41 pages, 7 figures, 12 table
Bayesian Estimation of Mixed Multinomial Logit Models: Advances and Simulation-Based Evaluations
Variational Bayes (VB) methods have emerged as a fast and
computationally-efficient alternative to Markov chain Monte Carlo (MCMC)
methods for scalable Bayesian estimation of mixed multinomial logit (MMNL)
models. It has been established that VB is substantially faster than MCMC at
practically no compromises in predictive accuracy. In this paper, we address
two critical gaps concerning the usage and understanding of VB for MMNL. First,
extant VB methods are limited to utility specifications involving only
individual-specific taste parameters. Second, the finite-sample properties of
VB estimators and the relative performance of VB, MCMC and maximum simulated
likelihood estimation (MSLE) are not known. To address the former, this study
extends several VB methods for MMNL to admit utility specifications including
both fixed and random utility parameters. To address the latter, we conduct an
extensive simulation-based evaluation to benchmark the extended VB methods
against MCMC and MSLE in terms of estimation times, parameter recovery and
predictive accuracy. The results suggest that all VB variants with the
exception of the ones relying on an alternative variational lower bound
constructed with the help of the modified Jensen's inequality perform as well
as MCMC and MSLE at prediction and parameter recovery. In particular, VB with
nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta)
is up to 16 times faster than MCMC and MSLE. Thus, VB-NCVMP-Delta can be an
attractive alternative to MCMC and MSLE for fast, scalable and accurate
estimation of MMNL models
Modeling operational risk data reported above a time-varying threshold
Typically, operational risk losses are reported above a threshold. Fitting
data reported above a constant threshold is a well known and studied problem.
However, in practice, the losses are scaled for business and other factors
before the fitting and thus the threshold is varying across the scaled data
sample. A reporting level may also change when a bank changes its reporting
policy. We present both the maximum likelihood and Bayesian Markov chain Monte
Carlo approaches to fitting the frequency and severity loss distributions using
data in the case of a time varying threshold. Estimation of the annual loss
distribution accounting for parameter uncertainty is also presented
Bayesian inference and prediction for the GI/M/1 queueing system
This article undertake Bayesian inference and prediction for GI/M/1 queueing systems. A semiparametric model based on mixtures of Erlang distributions is considered to model the general interarrival time distribution. Given arrival and service data, a Bayesian procedure based on birth-death Markov Chain Monte Carlo methods is proposed. An estimation of the system parameters and predictive distributions of measures such as the stationary system size and waiting time is give
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