84,683 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 partially linearized sigma point filter for latent state estimation in nonlinear time series models
A new technique for the latent state estimation of a wide class of nonlinear time
series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment matching algorithm and then a linear programming-based procedure is used in the update step of the state estimation. The effectiveness of the new ¯ltering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process
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A new algorithm for latent state estimation in nonlinear time series models
We consider the problem of optimal state estimation for a wide class of nonlinear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in
engineering where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing
the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples
Deep Recurrent Survival Analysis
Survival analysis is a hotspot in statistical research for modeling
time-to-event information with data censorship handling, which has been widely
used in many applications such as clinical research, information system and
other fields with survivorship bias. Many works have been proposed for survival
analysis ranging from traditional statistic methods to machine learning models.
However, the existing methodologies either utilize counting-based statistics on
the segmented data, or have a pre-assumption on the event probability
distribution w.r.t. time. Moreover, few works consider sequential patterns
within the feature space. In this paper, we propose a Deep Recurrent Survival
Analysis model which combines deep learning for conditional probability
prediction at fine-grained level of the data, and survival analysis for
tackling the censorship. By capturing the time dependency through modeling the
conditional probability of the event for each sample, our method predicts the
likelihood of the true event occurrence and estimates the survival rate over
time, i.e., the probability of the non-occurrence of the event, for the
censored data. Meanwhile, without assuming any specific form of the event
probability distribution, our model shows great advantages over the previous
works on fitting various sophisticated data distributions. In the experiments
on the three real-world tasks from different fields, our model significantly
outperforms the state-of-the-art solutions under various metrics.Comment: AAAI 2019. Supplemental material, slides, code:
https://github.com/rk2900/drs
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