scholarly journals Fitting deterministic population models to stochastic data: from trajectory matching to state-space models

2021 ◽  
Author(s):  
Benjamin Rosenbaum ◽  
Emanuel A. Fronhofer
Keyword(s):  
State Space ◽  
Empirical Data ◽  
Community Dynamics ◽  
Simulated Data ◽  
Single Species ◽  
State Space Models ◽  
Model Parameters ◽  
Observation Error ◽  
Ode Models ◽  
Stochastic Data

Population and community ecology traditionally has a very strong theoretical foundation with well-known models, such as the logistic and its many variations, and many modification of the classical Lotka-Volterra predator-prey and interspecific competition models. More and more, these classical models are confronted to data via fitting to empirical time-series, from the field or from the laboratory, for purposes of projections or for estimating model parameters of interest. However, the interface between mathematical population or community models and data, provided by a statistical model, is far from trivial. In order to help empiricists make informed decisions, we here ask which error structure one should use when fitting classical deterministic ODE models to empirical data, from single species to community dynamics and trophic interactions. We use both realistically simulated data and empirical data from microcosms to answer this question in a Bayesian framework. We find that pure observation error models mostly perform adequately overall. However, state-space models clearly outperform simpler approaches when observation errors are sufficiently large or biological models sufficiently complex. Finally, we provide a comprehensive tutorial for fitting these models in R.

Evaluating evidence for alternative natural mortality and process error assumptions using a state-space, age-structured assessment model

2018 ◽  
Vol 75 (5) ◽  
pp. 691-703 ◽  
Author(s):  
Timothy J. Miller ◽  
Saang-Yoon Hyun
Keyword(s):  
State Space ◽  
Gulf Of Maine ◽  
Model Performance ◽  
Simulated Data ◽  
State Space Models ◽  
Assessment Model ◽  
Biomass Estimation ◽  
Natural Mortality ◽  
Space Age ◽  
Age Structured

State-space models explicitly separate uncertainty associated with unobserved, time-varying parameters from that which arises from sampling the population. The statistical aspects of formal state-space models are appealing and these models are becoming more widely used for assessments. However, treating natural mortality as known and constant across ages continues to be common practice. We developed a state-space, age-structured assessment model that allowed different assumptions for natural mortality and the degree of temporal stochasticity in abundance. We fit a suite of models where natural mortality was either age-invariant or an allometric function of mass and interannual transitions of abundance were deterministic or stochastic to observations on Gulf of Maine – Georges Bank Acadian redfish (Sebastes fasciatus). We found that allowing stochasticity in the interannual transition in abundance was important and estimating age-invariant natural mortality was sufficient. A simulation study showed low bias in annual biomass estimation when the estimation and simulation model matched and the Akaike imformation criterion accurately measured relative model performance, but it was important to allow simulated data sets to include the stochasticity in interannual transitions of abundance-at-age.

scholarly journals A review of Bayesian state-space modelling of capture–recapture–recovery data

2012 ◽  
Vol 2 (2) ◽  
pp. 190-204 ◽  
Author(s):  
Ruth King
Keyword(s):  
State Space ◽  
State Space Model ◽  
Model Fitting ◽  
The State ◽  
State Space Models ◽  
Observation Error ◽  
Space Model ◽  
System Process ◽  
Observation Process ◽  
Capture Recapture

Traditionally, state-space models are fitted to data where there is uncertainty in the observation or measurement of the system. State-space models are partitioned into an underlying system process describing the transitions of the true states of the system over time and the observation process linking the observations of the system to the true states. Open population capture–recapture–recovery data can be modelled in this framework by regarding the system process as the state of each individual observed within the study in terms of being alive or dead, and the observation process the recapture and/or recovery process. The traditional observation error of a state-space model is incorporated via the recapture/recovery probabilities being less than unity. The models can be fitted using a Bayesian data augmentation approach and in standard BUGS packages. Applying this state-space framework to such data permits additional complexities including individual heterogeneity to be fitted to the data at very little additional programming effort. We consider the efficiency of the state-space model fitting approach by considering a random effects model for capture–recapture data relating to dippers and compare different Bayesian model-fitting algorithms within WinBUGS.

Time Series Decomposition into Oscillation Components and Phase Estimation

2017 ◽  
Vol 29 (2) ◽  
pp. 332-367 ◽  
Author(s):  
Takeru Matsuda ◽  
Fumiyasu Komaki
Keyword(s):  
Time Series ◽  
State Space ◽  
Empirical Bayes ◽  
Real Data ◽  
Information Criterion ◽  
State Space Models ◽  
Model Parameters ◽  
Seasonal Adjustment ◽  
Phase Dynamics ◽  
Time Series Decomposition

Many time series are naturally considered as a superposition of several oscillation components. For example, electroencephalogram (EEG) time series include oscillation components such as alpha, beta, and gamma. We propose a method for decomposing time series into such oscillation components using state-space models. Based on the concept of random frequency modulation, gaussian linear state-space models for oscillation components are developed. In this model, the frequency of an oscillator fluctuates by noise. Time series decomposition is accomplished by this model like the Bayesian seasonal adjustment method. Since the model parameters are estimated from data by the empirical Bayes’ method, the amplitudes and the frequencies of oscillation components are determined in a data-driven manner. Also, the appropriate number of oscillation components is determined with the Akaike information criterion (AIC). In this way, the proposed method provides a natural decomposition of the given time series into oscillation components. In neuroscience, the phase of neural time series plays an important role in neural information processing. The proposed method can be used to estimate the phase of each oscillation component and has several advantages over a conventional method based on the Hilbert transform. Thus, the proposed method enables an investigation of the phase dynamics of time series. Numerical results show that the proposed method succeeds in extracting intermittent oscillations like ripples and detecting the phase reset phenomena. We apply the proposed method to real data from various fields such as astronomy, ecology, tidology, and neuroscience.

scholarly journals Reproducible parallel inference and simulation of stochastic state space models using odin, dust, and mcstate

2020 ◽  
Vol 5 ◽  
pp. 288
Author(s):  
Edward S. Knock ◽  
Lilith K. Whittles ◽  
Pablo N. Perez-Guzman ◽  
Sangeeta Bhatia ◽  
Fernando Guntoro ◽  
...  
Keyword(s):  
Infectious Disease ◽  
State Space ◽  
High Performance ◽  
Sequential Monte Carlo ◽  
Time Series Data ◽  
Random Number Generator ◽  
State Space Models ◽  
Series Data ◽  
Model Parameters ◽  
Efficient Manner

State space models, including compartmental models, are used to model physical, biological and social phenomena in a broad range of scientific fields. A common way of representing the underlying processes in these models is as a system of stochastic processes which can be simulated forwards in time. Inference of model parameters based on observed time-series data can then be performed using sequential Monte Carlo techniques. However, using these methods for routine inference problems can be made difficult due to various engineering considerations: allowing model design to change in response to new data and ideas, writing model code which is highly performant, and incorporating all of this with up-to-date statistical techniques. Here, we describe a suite of packages in the R programming language designed to streamline the design and deployment of state space models, targeted at infectious disease modellers but suitable for other domains. Users describe their model in a familiar domain-specific language, which is converted into parallelised C++ code. A fast, parallel, reproducible random number generator is then used to run large numbers of model simulations in an efficient manner. We also provide standard inference and prediction routines, though the model simulator can be used directly if these do not meet the user’s needs. These packages provide guarantees on reproducibility and performance, allowing the user to focus on the model itself, rather than the underlying computation. The ability to automatically generate high-performance code that would be tedious and time-consuming to write and verify manually, particularly when adding further structure to compartments, is crucial for infectious disease modellers. Our packages have been critical to the development cycle of our ongoing real-time modelling efforts in the COVID-19 pandemic, and have the potential to do the same for models used in a number of different domains.

scholarly journals Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state-space models

2021 ◽  
Vol 31 (5) ◽  
Author(s):  
Jacob Vorstrup Goldman ◽  
Sumeetpal S. Singh
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Simulated Data ◽  
State Space Models ◽  
High Dimensional ◽  
Effective Sample Size ◽  
Stat Assoc ◽  
Dimensional State Space ◽  
State Inference ◽  
New Algorithms

AbstractWe propose a novel blocked version of the continuous-time bouncy particle sampler of Bouchard-Côté et al. (J Am Stat Assoc 113(522):855–867, 2018) which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state-space models (Singh et al. in Biometrika 104(4):953–969, 2017) and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the resulting algorithm. The new algorithms are particularly efficient for latent state inference in high-dimensional state-space models, where blocking in both space and time is necessary to avoid degeneracy of MCMC. The efficiency of our blocked bouncy particle sampler, in comparison with both the standard implementation of the bouncy particle sampler and the particle Gibbs algorithm of Andrieu et al. (J R Stat Soc Ser B Stat Methodol 72(3):269–342, 2010), is illustrated numerically for both simulated data and a challenging real-world financial dataset.

scholarly journals On Sequential Learning for Parameter Estimation in Particle Algorithms for State-Space Models

2016 ◽  
Vol 6 (1) ◽  
pp. 13
Author(s):  
Chunlin Ji
Keyword(s):  
State Space ◽  
Blind Deconvolution ◽  
State Space Model ◽  
The State ◽  
State Space Models ◽  
Sequential Learning ◽  
Model Parameters ◽  
Learning Method ◽  
Space Model ◽  
Deconvolution Problem

Particle methods, also known as Sequential Monte Carlo, have been ubiquitous for Bayesian inference for state-space models, particulary when dealing with nonlinear non-Gaussian scenarios. However, in many practical situations, the state-space model contains unknown model parameters that need to be estimated simultaneously with the state. In this paper, We discuss a sequential analysis for combined parameter and state estimation. An online learning method is proposed to approach the distribution of the model parameter by tuning a flexible proposal mixture distribution to minimize their Kullback-Leibler divergence. We derive the sequential learning method by using a truncated Dirichlet processes normal mixture and present a general algorithm under a framework of the auxiliary particle filtering. The proposed algorithm is verified in a blind deconvolution problem, which is a typical state-space model with unknown model parameters. Furthermore, in a more challenging application that we call meta-modulation, which is a more complex blind deconvolution problem with sophisticated system evolution equations, the proposed method performs satisfactorily and achieves an exciting result for high efficiency communication.

scholarly journals Maximum approximate likelihood estimation of general continuous-time state-space models

2022 ◽  
pp. 1471082X2110657
Author(s):  
Sina Mews ◽  
Roland Langrock ◽  
Marius Ötting ◽  
Houda Yaqine ◽  
Jost Reinecke
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Likelihood Estimation ◽  
The State ◽  
State Space Models ◽  
State Transitions ◽  
Model Parameters ◽  
State Process ◽  
Approximate Likelihood ◽  
Non Gaussian

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretization of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean.

scholarly journals Reproducible parallel inference and simulation of stochastic state space models using odin, dust, and mcstate

2021 ◽  
Vol 5 ◽  
pp. 288
Author(s):  
Richard G. FitzJohn ◽  
Edward S. Knock ◽  
Lilith K. Whittles ◽  
Pablo N. Perez-Guzman ◽  
Sangeeta Bhatia ◽  
...  
Keyword(s):  
Infectious Disease ◽  
State Space ◽  
High Performance ◽  
Sequential Monte Carlo ◽  
Time Series Data ◽  
Random Number Generator ◽  
State Space Models ◽  
Series Data ◽  
Model Parameters ◽  
Efficient Manner

State space models, including compartmental models, are used to model physical, biological and social phenomena in a broad range of scientific fields. A common way of representing the underlying processes in these models is as a system of stochastic processes which can be simulated forwards in time. Inference of model parameters based on observed time-series data can then be performed using sequential Monte Carlo techniques. However, using these methods for routine inference problems can be made difficult due to various engineering considerations: allowing model design to change in response to new data and ideas, writing model code which is highly performant, and incorporating all of this with up-to-date statistical techniques. Here, we describe a suite of packages in the R programming language designed to streamline the design and deployment of state space models, targeted at infectious disease modellers but suitable for other domains. Users describe their model in a familiar domain-specific language, which is converted into parallelised C++ code. A fast, parallel, reproducible random number generator is then used to run large numbers of model simulations in an efficient manner. We also provide standard inference and prediction routines, though the model simulator can be used directly if these do not meet the user’s needs. These packages provide guarantees on reproducibility and performance, allowing the user to focus on the model itself, rather than the underlying computation. The ability to automatically generate high-performance code that would be tedious and time-consuming to write and verify manually, particularly when adding further structure to compartments, is crucial for infectious disease modellers. Our packages have been critical to the development cycle of our ongoing real-time modelling efforts in the COVID-19 pandemic, and have the potential to do the same for models used in a number of different domains.

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