3,296 research outputs found
Efficient Inference of Gaussian Process Modulated Renewal Processes with Application to Medical Event Data
The episodic, irregular and asynchronous nature of medical data render them
difficult substrates for standard machine learning algorithms. We would like to
abstract away this difficulty for the class of time-stamped categorical
variables (or events) by modeling them as a renewal process and inferring a
probability density over continuous, longitudinal, nonparametric intensity
functions modulating that process. Several methods exist for inferring such a
density over intensity functions, but either their constraints and assumptions
prevent their use with our potentially bursty event streams, or their time
complexity renders their use intractable on our long-duration observations of
high-resolution events, or both. In this paper we present a new and efficient
method for inferring a distribution over intensity functions that uses direct
numeric integration and smooth interpolation over Gaussian processes. We
demonstrate that our direct method is up to twice as accurate and two orders of
magnitude more efficient than the best existing method (thinning). Importantly,
the direct method can infer intensity functions over the full range of bursty
to memoryless to regular events, which thinning and many other methods cannot.
Finally, we apply the method to clinical event data and demonstrate the
face-validity of the abstraction, which is now amenable to standard learning
algorithms.Comment: 8 pages, 4 figure
A Semi-Markov Modulated Interest Rate Model
In this paper we propose a semi-Markov modulated model of interest rates. We
assume that the switching process is a semi-Markov process with finite state
space E and the modulated process is a diffusive process. We derive recursive
equations for the higher order moments of the discount factor and we describe a
Monte Carlo al- gorithm to execute simulations. The results are specialized to
classical models as those by Vasicek, Hull and White and CIR with a semi-Markov
modulation
A Method for the Combination of Stochastic Time Varying Load Effects
The problem of evaluating the probability that a structure becomes unsafe under a
combination of loads, over a given time period, is addressed. The loads and load effects
are modeled as either pulse (static problem) processes with random occurrence time, intensity and a specified shape or intermittent continuous (dynamic problem) processes which
are zero mean Gaussian processes superimposed 'on a pulse process. The load coincidence
method is extended to problems with both nonlinear limit states and dynamic responses,
including the case of correlated dynamic responses. The technique of linearization of a
nonlinear limit state commonly used in a time-invariant problem is investigated for timevarying
combination problems, with emphasis on selecting the linearization point. Results
are compared with other methods, namely the method based on upcrossing rate, simpler
combination rules such as Square Root of Sum of Squares and Turkstra's rule. Correlated
effects among dynamic loads are examined to see how results differ from correlated static
loads and to demonstrate which types of load dependencies are most important, i.e., affect'
the exceedance probabilities the most.
Application of the load coincidence method to code development is briefly discussed.National Science Foundation Grants CME 79-18053 and CEE 82-0759
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