1,842 research outputs found
Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration
Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a thermodynamic integration scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods
Inference for reaction networks using the Linear Noise Approximation
We consider inference for the reaction rates in discretely observed networks
such as those found in models for systems biology, population ecology and
epidemics. Most such networks are neither slow enough nor small enough for
inference via the true state-dependent Markov jump process to be feasible.
Typically, inference is conducted by approximating the dynamics through an
ordinary differential equation (ODE), or a stochastic differential equation
(SDE). The former ignores the stochasticity in the true model, and can lead to
inaccurate inferences. The latter is more accurate but is harder to implement
as the transition density of the SDE model is generally unknown. The Linear
Noise Approximation (LNA) is a first order Taylor expansion of the
approximating SDE about a deterministic solution and can be viewed as a
compromise between the ODE and SDE models. It is a stochastic model, but
discrete time transition probabilities for the LNA are available through the
solution of a series of ordinary differential equations. We describe how a
restarting LNA can be efficiently used to perform inference for a general class
of reaction networks; evaluate the accuracy of such an approach; and show how
and when this approach is either statistically or computationally more
efficient than ODE or SDE methods. We apply the LNA to analyse Google Flu
Trends data from the North and South Islands of New Zealand, and are able to
obtain more accurate short-term forecasts of new flu cases than another
recently proposed method, although at a greater computational cost
Universal Codes from Switching Strategies
We discuss algorithms for combining sequential prediction strategies, a task
which can be viewed as a natural generalisation of the concept of universal
coding. We describe a graphical language based on Hidden Markov Models for
defining prediction strategies, and we provide both existing and new models as
examples. The models include efficient, parameterless models for switching
between the input strategies over time, including a model for the case where
switches tend to occur in clusters, and finally a new model for the scenario
where the prediction strategies have a known relationship, and where jumps are
typically between strongly related ones. This last model is relevant for coding
time series data where parameter drift is expected. As theoretical ontributions
we introduce an interpolation construction that is useful in the development
and analysis of new algorithms, and we establish a new sophisticated lemma for
analysing the individual sequence regret of parameterised models
ON THE SMALL SAMPLE PROPERTIES OF DICKEY FULLER AND MAXIMUM LIKELIHOOD UNIT ROOT TESTS ON DISCRETE-SAMPLED SHORT-TERM INTEREST RATES
Testing for unit roots in short-term interest rates plays a key role in the empirical modelling of these series. It is widely assumed that the volatility of interest rates follows some time-varying function which is dependent of the level of the series. This may cause distortions in the performance of conventional tests for unit root nonstationarity since these are typically derived under the assumption of homoskedasticity. Given the relative unfamiliarity on the issue, we conducted an extensive Monte Carlo investigation in order to assess the performance of the DF unit root tests, and examined the effects on the limiting distributions of test procedures (t- and likelihood ratio tests) based on maximum likelihood estimation of models for short-term rates with a linear drift.Unit root, interest rates, CKLS model.
A Variational Autoencoder for Heterogeneous Temporal and Longitudinal Data
The variational autoencoder (VAE) is a popular deep latent variable model
used to analyse high-dimensional datasets by learning a low-dimensional latent
representation of the data. It simultaneously learns a generative model and an
inference network to perform approximate posterior inference. Recently proposed
extensions to VAEs that can handle temporal and longitudinal data have
applications in healthcare, behavioural modelling, and predictive maintenance.
However, these extensions do not account for heterogeneous data (i.e., data
comprising of continuous and discrete attributes), which is common in many
real-life applications. In this work, we propose the heterogeneous longitudinal
VAE (HL-VAE) that extends the existing temporal and longitudinal VAEs to
heterogeneous data. HL-VAE provides efficient inference for high-dimensional
datasets and includes likelihood models for continuous, count, categorical, and
ordinal data while accounting for missing observations. We demonstrate our
model's efficacy through simulated as well as clinical datasets, and show that
our proposed model achieves competitive performance in missing value imputation
and predictive accuracy.Comment: Preprin
On the Small Sample Properties of Dickey Fuller and Maximum Likelihood Unit Root Tests on Discrete-Sampled Short-Term Interest Rates
Testing for unit roots in short-term interest rates plays a key role in the empirical modelling of these series. It is widely assumed that the volatility of interest rates follows some time-varying function which is dependent of the level of the series. This may cause distortions in the performance of conventional tests for unit root nonstationarity since these are typically derived under the assumption of homoskedasticity. Given the relative unfamiliarity on the issue, we conducted an extensive Monte Carlo investigation in order to assess the performance of the DF unit root tests, and examined the effects on the limiting distributions of test procedures (t- and likelihood ratio tests) based on maximum likelihood estimation of models for short-term rates with a linear drift.Unit root, interest rates, CKLS model.
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