75,787 research outputs found
Estimating Discrete Markov Models From Various Incomplete Data Schemes
The parameters of a discrete stationary Markov model are transition
probabilities between states. Traditionally, data consist in sequences of
observed states for a given number of individuals over the whole observation
period. In such a case, the estimation of transition probabilities is
straightforwardly made by counting one-step moves from a given state to
another. In many real-life problems, however, the inference is much more
difficult as state sequences are not fully observed, namely the state of each
individual is known only for some given values of the time variable. A review
of the problem is given, focusing on Monte Carlo Markov Chain (MCMC) algorithms
to perform Bayesian inference and evaluate posterior distributions of the
transition probabilities in this missing-data framework. Leaning on the
dependence between the rows of the transition matrix, an adaptive MCMC
mechanism accelerating the classical Metropolis-Hastings algorithm is then
proposed and empirically studied.Comment: 26 pages - preprint accepted in 20th February 2012 for publication in
Computational Statistics and Data Analysis (please cite the journal's paper
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Quantum Model Averaging
Standard tomographic analyses ignore model uncertainty. It is assumed that a
given model generated the data and the task is to estimate the quantum state,
or a subset of parameters within that model. Here we apply a model averaging
technique to mitigate the risk of overconfident estimates of model parameters
in two examples: (1) selecting the rank of the state in tomography and (2)
selecting the model for the fidelity decay curve in randomized benchmarking.Comment: For a summary, see http://i.imgur.com/nMJxANo.pn
Fitting stochastic predator-prey models using both population density and kill rate data
Most mechanistic predator-prey modelling has involved either parameterization
from process rate data or inverse modelling. Here, we take a median road: we
aim at identifying the potential benefits of combining datasets, when both
population growth and predation processes are viewed as stochastic. We fit a
discrete-time, stochastic predator-prey model of the Leslie type to simulated
time series of densities and kill rate data. Our model has both environmental
stochasticity in the growth rates and interaction stochasticity, i.e., a
stochastic functional response. We examine what the kill rate data brings to
the quality of the estimates, and whether estimation is possible (for various
time series lengths) solely with time series of population counts or biomass
data. Both Bayesian and frequentist estimation are performed, providing
multiple ways to check model identifiability. The Fisher Information Matrix
suggests that models with and without kill rate data are all identifiable,
although correlations remain between parameters that belong to the same
functional form. However, our results show that if the attractor is a fixed
point in the absence of stochasticity, identifying parameters in practice
requires kill rate data as a complement to the time series of population
densities, due to the relatively flat likelihood. Only noisy limit cycle
attractors can be identified directly from population count data (as in inverse
modelling), although even in this case, adding kill rate data - including in
small amounts - can make the estimates much more precise. Overall, we show that
under process stochasticity in interaction rates, interaction data might be
essential to obtain identifiable dynamical models for multiple species. These
results may extend to other biotic interactions than predation, for which
similar models combining interaction rates and population counts could be
developed
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