scholarly journals Characterization of tumor heterogeneity by latent haplotypes: a sequential Monte Carlo approach

PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e4838 ◽  
Author(s):  
Oyetunji E. Ogundijo ◽  
Xiaodong Wang
Keyword(s):  
Monte Carlo ◽  
State Space ◽  
Tumor Heterogeneity ◽  
Sequential Monte Carlo ◽  
State Space Model ◽  
Sequential Algorithm ◽  
Model Parameters ◽  
Single Nucleotide Variants ◽  
Time Step ◽  
Allocation Model

Tumor samples obtained from a single cancer patient spatially or temporally often consist of varying cell populations, each harboring distinct mutations that uniquely characterize its genome. Thus, in any given samples of a tumor having more than two haplotypes, defined as a scaffold of single nucleotide variants (SNVs) on the same homologous genome, is evidence of heterogeneity because humans are diploid and we would therefore only observe up to two haplotypes if all cells in a tumor sample were genetically homogeneous. We characterize tumor heterogeneity by latent haplotypes and present state-space formulation of the feature allocation model for estimating the haplotypes and their proportions in the tumor samples. We develop an efficient sequential Monte Carlo (SMC) algorithm that estimates the states and the parameters of our proposed state-space model, which are equivalently the haplotypes and their proportions in the tumor samples. The sequential algorithm produces more accurate estimates of the model parameters when compared with existing methods. Also, because our algorithm processes the variant allele frequency (VAF) of a locus as the observation at a single time-step, VAF from newly sequenced candidate SNVs from next-generation sequencing (NGS) can be analyzed to improve existing estimates without re-analyzing the previous datasets, a feature that existing solutions do not possess.

scholarly journals Uniform convergence over time of a nested particle filtering scheme for recursive parameter estimation in state-space Markov models

2017 ◽  
Vol 49 (4) ◽  
pp. 1170-1200 ◽  
Author(s):  
Dan Crisan ◽  
Joaquín Míguez
Keyword(s):  
Monte Carlo ◽  
Uniform Convergence ◽  
State Space ◽  
Particle Filtering ◽  
Sequential Monte Carlo ◽  
Markov Models ◽  
Empirical Distribution ◽  
Model Parameters ◽  
Posterior Probability Distribution ◽  
Over Time

Abstract We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete-time state-space Markov model. The algorithm employs two layers of particle filters to approximate the posterior probability distribution of the model parameters. In particular, the first layer yields an empirical distribution of samples on the parameter space, while the filters in the second layer are auxiliary devices to approximate the (analytically intractable) likelihood of the parameters. This approach relates the novel algorithm to the recent sequential Monte Carlo square method, which provides a nonrecursive solution to the same problem. In this paper we investigate the approximation of integrals of real bounded functions with respect to the posterior distribution of the system parameters. Under assumptions related to the compactness of the parameter support and the stability and continuity of the sequence of posterior distributions for the state-space model, we prove that the Lp norms of the approximation errors vanish asymptotically (as the number of Monte Carlo samples generated by the algorithm increases) and uniformly over time. We also prove that, under the same assumptions, the proposed scheme can asymptotically identify the parameter values for a class of models. We conclude the paper with a numerical example that illustrates the uniform convergence results by exploring the accuracy and stability of the proposed algorithm operating with long sequences of observations.

Motion Response Control of the DWSC Spar Based on State-Space Model

2012 ◽  
Author(s):  
Xiaochuan Yu ◽  
Jeffrey Falzarano
Keyword(s):  
State Space ◽  
Transfer Functions ◽  
State Space Model ◽  
Development Program ◽  
Naval Research ◽  
Hydrodynamic Coefficients ◽  
Time Step ◽  
Response Control ◽  
Motion Response ◽  
Space Model

In 2007, the Office of Naval Research (ONR) started a technology development program called STLVAST (Small to Large Vessel At-Sea Transfer), in order to develop ‘enabling capabilities’ in the realm of logistic transfer (i.e. stores, equipment, vehicles) between a large transport vessel and a smaller T-craft ship, using a Deep Water Stable Crane (DWSC) spar between them. In this paper, the equation of motions of the single DWSC spar is initially expressed as the standard state-space model. Then the ODE solver of Matlab is directly employed to obtain the motion responses at each time step. Two levels of approximation of hydrodynamic coefficients are considered in this study. One is the Constant Coefficient Method (CCM), and the other one is the Impulse Response Function (IRF) method, with fluid memory effects considered. WAMIT software is used to calculate the hydrodynamic coefficients, including the added mass, radiation damping, IRF, the first order and second order waves loads transfer functions, etc. The motion response control is achieved by assuming the thrusters can provide the optimal feedback force derived from Linear Quadratic Regulator (LQR) method.

scholarly journals Bayesian Analysis of Interleaved Learning and Response Bias in Behavioral Experiments

2007 ◽  
Vol 97 (3) ◽  
pp. 2516-2524 ◽  
Author(s):  
Anne C. Smith ◽  
Sylvia Wirth ◽  
Wendy A. Suzuki ◽  
Emery N. Brown
Keyword(s):  
Bayesian Analysis ◽  
State Space ◽  
State Space Model ◽  
Estimation Procedure ◽  
Ideal Observer ◽  
Model Parameters ◽  
Behavioral Experiments ◽  
Actual Object ◽  
Space Model ◽  
Multiple Tasks

Accurate characterizations of behavior during learning experiments are essential for understanding the neural bases of learning. Whereas learning experiments often give subjects multiple tasks to learn simultaneously, most analyze subject performance separately on each individual task. This analysis strategy ignores the true interleaved presentation order of the tasks and cannot distinguish learning behavior from response preferences that may represent a subject's biases or strategies. We present a Bayesian analysis of a state-space model for characterizing simultaneous learning of multiple tasks and for assessing behavioral biases in learning experiments with interleaved task presentations. Under the Bayesian analysis the posterior probability densities of the model parameters and the learning state are computed using Monte Carlo Markov Chain methods. Measures of learning, including the learning curve, the ideal observer curve, and the learning trial translate directly from our previous likelihood-based state-space model analyses. We compare the Bayesian and current likelihood–based approaches in the analysis of a simulated conditioned T-maze task and of an actual object–place association task. Modeling the interleaved learning feature of the experiments along with the animal's response sequences allows us to disambiguate actual learning from response biases. The implementation of the Bayesian analysis using the WinBUGS software provides an efficient way to test different models without developing a new algorithm for each model. The new state-space model and the Bayesian estimation procedure suggest an improved, computationally efficient approach for accurately characterizing learning in behavioral experiments.

scholarly journals Adaptive Model Predictive Vibration Control of a Cantilever Beam with Real-Time Parameter Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Gergely Takács ◽  
Tomáš Polóni ◽  
Boris Rohal’-Ilkiv
Keyword(s):  
Control System ◽  
Vibration Control ◽  
State Space ◽  
Real Time ◽  
Cantilever Beam ◽  
State Space Model ◽  
Model Parameters ◽  
Extended Kalman Filtering ◽  
Space Model ◽  
Continuous State

This paper presents an adaptive-predictive vibration control system using extended Kalman filtering for the joint estimation of system states and model parameters. A fixed-free cantilever beam equipped with piezoceramic actuators serves as a test platform to validate the proposed control strategy. Deflection readings taken at the end of the beam have been used to reconstruct the position and velocity information for a second-order state-space model. In addition to the states, the dynamic system has been augmented by the unknown model parameters: stiffness, damping constant, and a voltage/force conversion constant, characterizing the actuating effect of the piezoceramic transducers. The states and parameters of this augmented system have been estimated in real time, using the hybrid extended Kalman filter. The estimated model parameters have been applied to define the continuous state-space model of the vibrating system, which in turn is discretized for the predictive controller. The model predictive control algorithm generates state predictions and dual-mode quadratic cost prediction matrices based on the updated discrete state-space models. The resulting cost function is then minimized using quadratic programming to find the sequence of optimal but constrained control inputs. The proposed active vibration control system is implemented and evaluated experimentally to investigate the viability of the control method.

A Nonlinear State-Space Model of a Resonating Single Fiber Scanner for Tracking Control: Theory and Experiment

2004 ◽  
Vol 126 (1) ◽  
pp. 88-101 ◽  
Author(s):  
Quinn Y. J. Smithwick ◽  
Per G. Reinhall ◽  
Juris Vagners ◽  
Eric J. Seibel
Keyword(s):  
State Space ◽  
State Space Model ◽  
Single Fiber ◽  
Model Parameters ◽  
Experimental Frequency ◽  
Centripetal Acceleration ◽  
Frequency Responses ◽  
Continuum Dynamics ◽  
Nonlinear Continuum ◽  
Nonlinear State

A nonlinear state-space dynamic model of a resonating single fiber scanner is developed to understand scan distortion—jump, whirl, amplitude dependent amplitude and phase shifts—and as the basis for controllers to remove those distortions. The non-planar nonlinear continuum dynamics of a resonating base excited cantilever are reduced to a set of state-space coupled Duffing equations with centripetal acceleration. Methods for experimentally determining the model parameters are developed. The analytic frequency responses for raster, spiral and propeller scans are derived, and match experimental frequency responses for all three scan patterns, for various amplitudes, and using the same model parameters.

scholarly journals Bayesian Parameter Estimation for Nonlinear Dynamics Using Sensitivity Analysis

2019 ◽  
Author(s):  
Yi Chou ◽  
Sriram Sankaranarayanan
Keyword(s):  
Monte Carlo ◽  
Parameter Space ◽  
Sequential Monte Carlo ◽  
Measurement Data ◽  
Reachability Analysis ◽  
Model Parameters ◽  
Reference Trajectory ◽  
Nonlinear Odes ◽  
Ode Models ◽  
Inference Techniques

We investigate approximate Bayesian inference techniques for nonlinear systems described by ordinary differential equation (ODE) models. In particular, the approximations will be based on set-valued reachability analysis approaches, yielding approximate models for the posterior distribution. Nonlinear ODEs are widely used to mathematically describe physical and biological models. However, these models are often described by parameters that are not directly measurable and have an impact on the system behaviors. Often, noisy measurement data combined with physical/biological intuition serve as the means for finding appropriate values of these parameters. Our approach operates under a Bayesian framework, given prior distribution over the parameter space and noisy observations under a known sampling distribution. We explore subsets of the space of model parameters, computing bounds on the likelihood for each subset. This is performed using nonlinear set-valued reachability analysis that is made faster by means of linearization around a reference trajectory. The tiling of the parameter space can be adaptively refined to make bounds on the likelihood tighter. We evaluate our approach on a variety of nonlinear benchmarks and compare our results with Markov Chain Monte Carlo and Sequential Monte Carlo approaches.

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