768 research outputs found
Neural network approximations to posterior densities: an analytical approach
Get PDFIn Hoogerheide, Kaashoek and Van Dijk (2002) the class of neural networksampling methods is introduced to sample from a target (posterior)distribution that may be multi-modal or skew, or exhibit strong correlationamong the parameters. In these methods the neural network is used as animportance function in IS or as a candidate density in MH. In this note wesuggest an analytical approach to estimate the moments of a certain (target)distribution, where `analytical' refers to the fact that no samplingalgorithm like MH or IS is needed.We show an example in which our analyticalapproach is feasible, even in a case where a `standard' Gibbs approach wouldfail or be extremely slow.Markov chain Monte Carlo;Bayesian inference;importance sampling;neural networks
Bayesian analysis of latent variable models in finance
Get PDFLucas, A. [Promotor]Koopman, S.J. [Promotor]Hoogerheide, L.F. [Copromotor
The Econometrics of Financial Comovement
Get PDFLucas, A. [Promotor]Hoogerheide, L.F. [Copromotor]Blasques Albergaria Amaral, F. [Copromotor
Joint Bayesian Analysis of Parameters and States in Nonlinear, Non-Gaussian State Space Models
Get PDFWe propose a new methodology for designing flexible proposal densities for the joint posterior density of parameters and states in a nonlinear non-Gaussian state space model. We show that a highly efficient Bayesian procedure emerges when these proposal densities are used in an independent Metropolis-Hastings algorithm. A particular feature of our approach is that smoothed estimates of the states and the marginal likelihood are obtained directly as an output of the algorithm. Our method provides a computationally efficient alternative to several recently proposed algorithms. We present extensive simulation evidence for stochastic volatility and stochastic intensity models. For our empirical study, we analyse the performance of our method for stock returns and corporate default panel data. (This paper is an updated version of the paper that appeared earlier as Barra, I., Hoogerheide, L.F., Koopman, S.J., and Lucas, A. (2013) "Joint Independent Metropolis-Hastings Methods for Nonlinear Non-Gaussian State Space Models". TI Discussion Paper 13-050/III. Amsterdam: Tinbergen Institute.
AdMit: adaptive mixtures of student-t distributions
Get PDFThis note presents the package AdMit (Ardia et al.,
2008, 2009), an R implementation of the adaptive
mixture of Student-t distributions (AdMit) procedure
developed by Hoogerheide (2006); see also
Hoogerheide et al. (2007); Hoogerheide and van Dijk
(2008). The AdMit strategy consists of the construction
of a mixture of Student-t distributions which
approximates a target distribution of interest. The
fitting procedure relies only on a kernel of the target
density, so that the normalizing constant is not
required. In a second step, this approximation is
used as an importance function in importance sampling
or as a candidate density in the independence
chain Metropolis-Hastings (M-H) algorithm to estimate
characteristics of the target density. The estimation
procedure is fully automatic and thus avoids
the difficult task, especially for non-experts, of tuning
a sampling algorithm. Typically, the target is a
posterior distribution in a Bayesian analysis, where
we indee
Essays on Neural Network Sampling Methods and Instrumental Variables
Get PDFDe laatste decennia zijn voor allerlei economische processen complexe modellen afgeleid, zoals voor de groei van het Bruto Binnenlands Product (BBP). In deze modellen zijn in sommige gevallen geavanceerde methoden nodig om kansen te berekenen, bijvoorbeeld de kans op een naderende recessie. In zijn proefschrift Essays on Neural Network Sampling Methods and Instrumental Variables vergelijkt Lennart Hoogerheide een nieuwe, op neurale netwerken gebaseerde, methode met verschillende bekende methoden. De nieuwe methode blijkt betrouwbaar en snel te zijn.
Tevens bekritiseert Hoogerheide een beroemd artikel van Angrist en Krueger uit 1991. Zij concludeerden dat in de Verenigde Staten ieder extra jaar onderwijs - gemiddeld genomen - later leidt tot een inkomensstijging van ongeveer 10 procent. Dit resultaat werd echter volledig bepaald door data van maar drie zuidelijke staten, en is dus niet representatief voor de gehele Verenigde Staten. Het meten van het effect van het genoten onderwijs van mensen op hun verdiende inkomen is van belang voor het vaststellen van onderwijsbeleid. Om dit effect te meten wordt een model met zogenaamde instrumentele variabelen gebruikt.This thesis consists of two parts. In the first part a class of sampling methods, which can be used in Bayesian analysis to get insight into the posterior density of model parameters, is introduced and explored. These sampling methods, which make use of neural network approximations to posterior densities, can quickly simulate draws from posterior distributions in many models. In the second part of this thesis new results are given for instrumental variables (IV) regression models. Particular attention is paid to a well-known IV model of Angrist and Krueger (1991, Quarterly Journal of Economics), who use quarter of birth to form instrumental variables in order to estimate the monetary returns to education. Measuring the effect of education on income is relevant for many decision processes; for example, for government agencies responsible for compulsory schooling laws. It should be noted that there is a connection between the two parts of this thesis: the ex!
posed neural network sampling methods can be especially useful if one desires to get insight into irregularly shaped posterior distributions, and such posteriors may occur in IV regression models
On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: an application of flexible sampling methods using neural networks
Get PDFLikelihoods and posteriors of instrumental variable regression models with strongendogeneity and/or weak instruments may exhibit rather non-elliptical contours inthe parameter space. This may seriously affect inference based on Bayesian crediblesets. When approximating such contours using Monte Carlo integration methods likeimportance sampling or Markov chain Monte Carlo procedures the speed of the algorithmand the quality of the results greatly depend on the choice of the importance orcandidate density. Such a density has to be `close' to the target density in order toyield accurate results with numerically efficient sampling. For this purpose we introduce neural networks which seem to be natural importance or candidate densities, as they have a universal approximation property and are easy to sample from.A key step in the proposed class of methods is the construction of a neural network that approximates the target density accurately. The methods are tested on a set ofillustrative models. The results indicate the feasibility of the neural networkapproach.Markov chain Monte Carlo;Bayesian inference;credible sets;importance sampling;instrumental variables;neural networks;reduced rank
Note on neural network sampling for Bayesian inference of mixture processes
Get PDFIn this paper we show some further experiments with neural network sampling,a class of sampling methods that make use of neural network approximationsto (posterior) densities, introduced by Hoogerheide et al. (2007). We considera method where a mixture of Student's t densities, which can be interpreted asa neural network function, is used as a candidate density in importance samplingor the Metropolis-Hastings algorithm. It is applied to an illustrative2-regime mixture model for the US real GNP growth rate. We explain thenon-elliptical shapes of the posterior distribution, and show that the proposedmethod outperforms Gibbs sampling with data augmentation and the griddy Gibbs sampler.
The AdMit Package
Get PDFThis short note presents the R package AdMit which provides flexible functions to approximate a certain target distribution and it provides an efficient sample of random draws from it, given only a kernel of the target density function. The estimation procedure is fully automatic and thus avoids the time-consuming anddifficult task of tuning a sampling algorithm. To illustrate the use of the package, we apply the AdMit methodology to a bivariate bimodal distribution. We describe the use of the functions provided by the package and document the ability and relevance of the methodology to reproduce the shape of non-elliptical distributions.importance sampling;R software;Bayesian;adaptive mixture;student-t distribution;independence chain Metropolis-Hasting algorithm
Note on neural network sampling for Bayesian inference of mixture processes
Get PDFIn this paper we show some further experiments with neural network sampling,
a class of sampling methods that make use of neural network approximations
to (posterior) densities, introduced by Hoogerheide et al. (2007). We consider
a method where a mixture of Student's t densities, which can be interpreted as
a neural network function, is used as a candidate density in importance sampling
or the Metropolis-Hastings algorithm. It is applied to an illustrative
2-regime mixture model for the US real GNP growth rate. We explain the
non-elliptical shapes of the posterior distribution, and show that the proposed
method outperforms Gibbs sampling with data augmentation and the griddy Gibbs sampler
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