610 research outputs found
Control Variates for Reversible MCMC Samplers
A general methodology is introduced for the construction and effective
application of control variates to estimation problems involving data from
reversible MCMC samplers. We propose the use of a specific class of functions
as control variates, and we introduce a new, consistent estimator for the
values of the coefficients of the optimal linear combination of these
functions. The form and proposed construction of the control variates is
derived from our solution of the Poisson equation associated with a specific
MCMC scenario. The new estimator, which can be applied to the same MCMC sample,
is derived from a novel, finite-dimensional, explicit representation for the
optimal coefficients. The resulting variance-reduction methodology is primarily
applicable when the simulated data are generated by a conjugate random-scan
Gibbs sampler. MCMC examples of Bayesian inference problems demonstrate that
the corresponding reduction in the estimation variance is significant, and that
in some cases it can be quite dramatic. Extensions of this methodology in
several directions are given, including certain families of Metropolis-Hastings
samplers and hybrid Metropolis-within-Gibbs algorithms. Corresponding
simulation examples are presented illustrating the utility of the proposed
methods. All methodological and asymptotic arguments are rigorously justified
under easily verifiable and essentially minimal conditions.Comment: 44 pages; 6 figures; 5 table
Arbitrage-free prediction of the implied volatility smile
This paper gives an arbitrage-free prediction for future prices of an
arbitrary co-terminal set of options with a given maturity, based on the
observed time series of these option prices. The statistical analysis of such a
multi-dimensional time series of option prices corresponding to strikes
(with large, e.g. ) and the same maturity, is a difficult task
due to the fact that option prices at any moment in time satisfy non-linear and
non-explicit no-arbitrage restrictions. Hence any -dimensional time series
model also has to satisfy these implicit restrictions at each time step, a
condition that is impossible to meet since the model innovations can take
arbitrary values. We solve this problem for any n\in\NN in the context of
Foreign Exchange (FX) by first encoding the option prices at each time step in
terms of the parameters of the corresponding risk-neutral measure and then
performing the time series analysis in the parameter space. The option price
predictions are obtained from the predicted risk-neutral measure by effectively
integrating it against the corresponding option payoffs. The non-linear
transformation between option prices and the risk-neutral parameters applied
here is \textit{not} arbitrary: it is the standard mapping used by market
makers in the FX option markets (the SABR parameterisation) and is given
explicitly in closed form. Our method is not restricted to the FX asset class
nor does it depend on the type of parameterisation used. Statistical analysis
of FX market data illustrates that our arbitrage-free predictions outperform
the naive random walk forecasts, suggesting a potential for building management
strategies for portfolios of derivative products, akin to the ones widely used
in the underlying equity and futures markets.Comment: 18 pages, 2 figures; a shorter version of this paper has appeared as
a Technical Paper in Risk (30 April 2014) under the title "Smile
transformation for price prediction
Copula-like Variational Inference
This paper considers a new family of variational distributions motivated by
Sklar's theorem. This family is based on new copula-like densities on the
hypercube with non-uniform marginals which can be sampled efficiently, i.e.
with a complexity linear in the dimension of state space. Then, the proposed
variational densities that we suggest can be seen as arising from these
copula-like densities used as base distributions on the hypercube with Gaussian
quantile functions and sparse rotation matrices as normalizing flows. The
latter correspond to a rotation of the marginals with complexity . We provide some empirical evidence that such a variational family can
also approximate non-Gaussian posteriors and can be beneficial compared to
Gaussian approximations. Our method performs largely comparably to
state-of-the-art variational approximations on standard regression and
classification benchmarks for Bayesian Neural Networks.Comment: 33rd Conference on Neural Information Processing Systems (NeurIPS
2019), Vancouver, Canad
IMBEDDED INTEGRATION RULES AND THEIR APPLICATIONS IN BAYESIAN ANALYSIS
This thesis deals with the development and application of numerical
integration techniques for use in Bayesian Statistics. In particular,
it describes how imbedded sequences of positive interpolatory
integration rules (PIIR's) obtained from Gauss-Hermite product rules
can extend the applicability and efficiency of currently available
numerical methods.
The numerical strategy suggested by Naylor and Smith (1982) is
reviewed, criticised and applied to some examples with real and
artificial data. The performance of this strategy is assessed from
the viewpoint of 3 criteria: reliability, efficiency and accuracy.
The imbedded sequences of PIIR’s are introduced as an alternative and
an extension to the above strategy for two major reasons. Firstly,
they provide a rich class of spatially ditributed rules which are
particularly useful in high dimensions. Secondly, they provide a way
of producing more efficient integration strategies by enabling
approximations to be updated sequentially through the addition of new
nodes at each step rather than through changing to a completely new
set of nodes.
Finally, the Improvement in the reliability and efficiency achieved by
the adaption of an integration strategy based on PIIR's is
demonstrated with various illustrative examples. Moreover, it is
directly compared with the Gibbs sampling approach introduced recently
by Gelfand and Smith (1988).University of Sheffiel
The effect of the work environment on accounting students\u27 moral reasoning and development
Puxty et al. (1994) claim that professional accountants are induced to act ethically through two aspects of their socialisation, the education process, and the influence of work experience and role models who show what it means to be ethical. The education of accountants is not simply a matter of becoming technically competent, it is also a process of internalising accepted norms of professional conduct. Student accountants learn acceptable behaviour by learning the principles of good conduct in their education, and receiving advice and observing what significant others do in the workplace. The purpose of this paper is to explore the effect of the work environment on accounting students moral reasoning and development by comparing the DIT P-scores of accounting students pre and post cooperative education. Cooperative eduction is an industry placement program where students are required to work in commerce and industry for one year. Findings indicate that DIT P-scores decrease during cooperative education suggesting that accounting students, whilst in the work environment, do not reason according to their capability as measured by their pre-test scores.<br /
Likelihood-based inference for correlated diffusions
We address the problem of likelihood based inference for correlated diffusion
processes using Markov chain Monte Carlo (MCMC) techniques. Such a task
presents two interesting problems. First, the construction of the MCMC scheme
should ensure that the correlation coefficients are updated subject to the
positive definite constraints of the diffusion matrix. Second, a diffusion may
only be observed at a finite set of points and the marginal likelihood for the
parameters based on these observations is generally not available. We overcome
the first issue by using the Cholesky factorisation on the diffusion matrix. To
deal with the likelihood unavailability, we generalise the data augmentation
framework of Roberts and Stramer (2001 Biometrika 88(3):603-621) to
d-dimensional correlated diffusions including multivariate stochastic
volatility models. Our methodology is illustrated through simulation based
experiments and with daily EUR /USD, GBP/USD rates together with their implied
volatilities
Inference for stochastic volatility model using time change transformations
We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which overcomes the inherent difficulties of time change transformations is also presented. The algorithm is fast to implement and applies to models with stochastic volatility. The methodology is tested through simulation based experiments and illustrated on data consisting of US treasury bill rates.Imputation, Markov chain Monte Carlo, Stochastic volatility
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