18,831 research outputs found
Sequential Bayesian inference for static parameters in dynamic state space models
A method for sequential Bayesian inference of the static parameters of a
dynamic state space model is proposed. The method is based on the observation
that many dynamic state space models have a relatively small number of static
parameters (or hyper-parameters), so that in principle the posterior can be
computed and stored on a discrete grid of practical size which can be tracked
dynamically. Further to this, this approach is able to use any existing
methodology which computes the filtering and prediction distributions of the
state process. Kalman filter and its extensions to non-linear/non-Gaussian
situations have been used in this paper. This is illustrated using several
applications: linear Gaussian model, Binomial model, stochastic volatility
model and the extremely non-linear univariate non-stationary growth model.
Performance has been compared to both existing on-line method and off-line
methods
A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market
We propose a dynamic network model where two mechanisms control the
probability of a link between two nodes: (i) the existence or absence of this
link in the past, and (ii) node-specific latent variables (dynamic fitnesses)
describing the propensity of each node to create links. Assuming a Markov
dynamics for both mechanisms, we propose an Expectation-Maximization algorithm
for model estimation and inference of the latent variables. The estimated
parameters and fitnesses can be used to forecast the presence of a link in the
future. We apply our methodology to the e-MID interbank network for which the
two linkage mechanisms are associated with two different trading behaviors in
the process of network formation, namely preferential trading and trading
driven by node-specific characteristics. The empirical results allow to
recognise preferential lending in the interbank market and indicate how a
method that does not account for time-varying network topologies tends to
overestimate preferential linkage.Comment: 19 pages, 6 figure
Modeling heterogeneity in random graphs through latent space models: a selective review
We present a selective review on probabilistic modeling of heterogeneity in
random graphs. We focus on latent space models and more particularly on
stochastic block models and their extensions that have undergone major
developments in the last five years
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