Joint Model Selection and Parameter Estimation of GTD Model using RJ-MCMC Algorithm

In this paper, we present and evaluate dynamic dictionary-based estimation methods for joint model order and parameter estimation. In dictionary-based estimation, a continuous parameter space is discretized, and vector-valued dictionary elements are formed for specific parameter values. A linear combination of a subset of dictionary elements is used to represent the model, where the number of elements used is the estimated model order, and the parameters corresponding to the selected elements are the parameter estimates. In static-based methods, the dictionary is fixed; while in the dynamic methods proposed here, the parameter sampling, and hence the dictionary, adapt to the data. We propose two dynamic dictionary-based estimation algorithms in which the dictionary elements are dynamically adjusted to improve parameter estimation performance. We examine the performance of both static and dynamic algorithms in terms of probability of correct model order selection and the root mean-squared error of parameter estimates. We show that dynamic dictionary methods overcome the problem of estimation bias induced by quantization effects in static dictionary-based estimation, and we demonstrate that dictionary-based estimation methods are capable of parameter estimation performance comparable to the Cramér-Rao lower bound and to traditional ML-based model estimation over a wide range of signal-to-noise ratios.

The purpose of this simulation study is to explore the limitation of the population PK/PD analysis using data from a clinical study and to help to construct an appropriate PK/PD design that enable precise and unbiased estimation of both fixed and random PD parameters in PK/PD analysis under different doses and Hill coefficients. Seven escalating doses of virtual drugs with equal potency and efficacy but with five different Hill coefficients were used in simulations of single and multiple dose scenarios with dense sampling design. A total of 70 scenarios with 100 subjects were simulated and estimated 100 times applying 1-compartment PK model and sigmoid Emax model. The bias and precision of the parameter estimates in each scenario were assessed using relative bias and relative root mean square error. For the single dose scenarios, most PD parameters of sigmoid Emax model were accurately and precisely estimated when the Cmax was more than 85% of EC50, except for typical value and inter-individual variability of EC50 which were poorly estimated at low Hill coefficients. For the multiple dose studies, the parameter estimation performance was not good. This simulation study demonstrated the effect of the relative range of sampled concentrations to EC50 and sigmoidicity on the parameter estimation performance using dense sampling design.

Undirected graphical models such as Markov random fields or Boltzmann machines prove useful in many signal processing and machine learning tasks. However, parameter estimation in these models is difficult due to the intractable normalising constant in their probability density functions. One powerful technique for parameter estimation in such models is score matching. This technique makes use of an objective function which is independent of the normalising constant and constitutes locally consistent estimators for the parameters of such models. However, score matching is only applicable to fully-observed models. In this paper, we extend the applicability of score matching to models with latent variables. Our estimators are unbiased, based on Monte Carlo integration. Unbiased gradient estimators open the way to optimisation through stochastic approximation. We demonstrate the performance of our methodology on two synthetic problems.

The demographic history of most species is complex, with multiple evolutionary processes combining to shape the observed patterns of genetic diversity. To infer this history, the discipline of phylogeography has (to date) used models that simplify the historical demography of the focal organism, for example by assuming or ignoring ongoing gene flow between populations or by requiring a priori specification of divergence history. Since no single model incorporates every possible evolutionary process, researchers rely on intuition to choose the models that they use to analyze their data. Here, we describe an approximate likelihood approach that reduces this reliance on intuition. PHRAPL allows users to calculate the probability of a large number of complex demographic histories given a set of gene trees, enabling them to identify the most likely underlying model and estimate parameters for a given system. Available model parameters include coalescence time among populations or species, gene flow, and population size. We describe the method and test its performance in model selection and parameter estimation using simulated data. We also compare model probabilities estimated using our approximate likelihood method to those obtained using standard analytical likelihood. The method performs well under a wide range of scenarios, although this is sometimes contingent on sampling many loci. In most scenarios, as long as there are enough loci and if divergence among populations is sufficiently deep, PHRAPL can return the true model in nearly all simulated replicates. Parameter estimates from the method are also generally accurate in most cases. PHRAPL is a valuable new method for phylogeographic model selection and will be particularly useful as a tool to more extensively explore demographic model space than is typically done or to estimate parameters for complex models that are not readily implemented using current methods. Estimating relevant parameters using the most appropriate demographic model can help to sharpen our understanding of the evolutionary processes giving rise to phylogeographic patterns. [AIC; grid search; isolation-with-migration; migration rate; multispecies coalescent; parameter optimization; population genetics; tree topologies.].

Abstract. Parameters in sea ice-ocean coupled models greatly affect the simulated evolution of the ocean and sea ice, and are typically tuned to bring the model state close to observations. Using an adjoint method, spatiotemporally varying parameters of an Arctic sea ice-ocean coupled model are optimized simultaneously with the initial conditions and atmospheric forcing by assimilating satellite and in-situ observations. The assimilation results show that the joint state and parameter estimation (SPE) substantially improves the sea ice concentration simulations. Particularly in October, when the ocean surface starts to refreeze, SPE reduces the lead closing parameter Ho (which determines the minimum ice thickness formed in the open water), thereby increasing the sea ice growth and facilitating the seasonal rapid sea ice recovery in the Arctic's Pacific sector. Comparisons with sea ice thickness observations from the moored upward-looking sonars and Ice Mass Balance buoys demonstrate that incorporating optimized model parameters into the coupled model also leads to better sea ice thickness estimation. Given that the optimal set of sea ice parameters may evolve alongside the thinning of Arctic sea ice, the adjoint-based SPE scheme has the potential to more accurately reconstruct the histical Arctic ocean and sea ice changes covering the satellite era, supporting research on Arctic sea ice and ocean variability.

A methodology is proposed to aid parameter estimation in fundamental models of pharmaceutical processes. This methodology addresses situations with insufficient data to reliably estimate all parameters, when the estimation is complicated by uncertain independent variables. The proposed method uses an augmented sensitivity matrix to rank the combined set of parameters and uncertain inputs from most estimable to least estimable. An updated mean‐squared‐error criterion is then used to determine the appropriate parameters and inputs that should be estimated, based on the ranked list. A model for one step in a batch pharmaceutical production process with an uncertain initial reactant concentration is used to illustrate the method, revealing that the initial reactant concentration in each batch should be estimated along with three out of six model parameters. Non‐estimable parameters are fixed at their initial values to prevent overfitting. The method will aid error‐in‐variables parameter estimation in many situations involving limited data.

A degree-corrected stochastic block model for community discovery in signed networks with heterogeneous degree distributions

Model selection is an important part of any statistical analysis. Many tools are suggested for selecting the best model including frequentist and Bayesian perspectives. There is often a considerable uncertainty in the selection of a particular model to be the best approximating model. Model selection uncertainty arises when the data are used for both model selection and parameter estimation. Bias in estimators of model parameters often arise when data based selection has been done. Therefore, model averaging of the parameter estimators will be done to alleviate the bias in model selection in a set of candidate models, by combining the information from a set of candidate models. This paper is two-fold, new criteria of model selection are proposed based on different averages of AIC, BIC, AICc, and HQC. Also, model averaging is introduced to compare the parameter estimators in model averaging with the ones in model selection. Two Simulation studies are considered, the first is for model selection and showed that the new proposed criteria are lies between some of the known criteria such as AIC, BIC, AICc, and HQC, and so they can be used as new criteria of model selection. The second simulation study is for model averaging and showed that the parameter estimators have less bias and less predicted mean square error (PMSE) compared with the parameter estimators in model selection.

The problem of identifying single degree-of-freedom (SDOF) nonlinear mechanical oscillators with piecewise-linear (PWL) restoring forces is considered. PWL nonlinear systems are a class of models that specify or approximate nonlinear systems via a set of locally-linear maps, each defined over different operating regions. They are useful in modelling hybrid phenomena common in practical situations, such as, systems with different modes of operation, or systems whose dynamics change because of physical limits or thresholds. However, identifying PWL models can be a challenging task when the number of operating regions and their partitions are unknown. This paper formulates the identification of oscillators with PWL restoring forces as a task of concurrent model selection and parameter estimation, where the selection of the number of linear regions is treated as a model selection task and identifying the associated system parameters as a task of parameter estimation. In this study, PWL maps in restoring forces with up to four regions are considered, and the task of model selection and parameter estimation task is addressed in a Bayesian framework. A likelihood-free Approximate Bayesian Computation (ABC) scheme is followed, which is easy to implement and provides a simplified way of doing model selection. The proposed approach has been demonstrated using two numerical examples and an experimental study, where ABC has been used to select models and identify parameters from among four SDOF PWL systems with different number of PWL regions. The results demonstrate the flexibility of using the proposed Bayesian approach for identifying the correct model and parameters of PWL systems, in addition to furnishing uncertainty estimates of the identified parameters.

A stable estimation of the THz model parameters for low SNR configurations is essential to achieve acquisition times required for applications in, e.g., quality control. The deep optimization prior approach was introduced with application to the estimation of material-related model parameters from THz data, which is acquired by a FMCW THz scanning system. Conceptually, this approach estimates the desired THz model parameters by optimizing for the weights of a 3D spatially coupled deep neural network. This approach was verified numerically on various THz parameter estimation problems for synthetic and real data. In this paper, we propose to combine the deep optimization prior approach to the modern 2D blind deblurring method for the FMCW THz image resolution enhancement. The experimental results show that this approach improves the lateral resolution enhancement robustly under low SNR noise condition in comparison to the per-pixel curve fitting method.

Data assimilation is predominantly used for state estimation, combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts, we need good estimates of both the current system state and the model parameters. This article presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three‐dimensional variational (3D‐Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from synthetic aperture radar (SAR) satellite imagery and a ship‐borne survey is shown to significantly improve the predictive capability of the model over a 2‐year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this article considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D‐Var data assimilation algorithm for joint state‐parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation‐based state‐parameter estimation in coastal morphodynamic modelling. Copyright © 2012 Royal Meteorological Society

Cancer is one of the most fatal diseases in the world. Governments and researchers from various areas have continuously concentrated efforts to better understand the disease and propose diagnostic and treatment techniques. The use of mathematical models of tumor growth is of great importance for the development of such techniques. Due to the variety of models nowadays available in the literature, the problems of model selection and parameter estimation come into picture, aiming at suitably predicting the patient’s status of the disease. As the available data on dependent variables of existing models might not justify the use of common likelihood functions, approximate Bayesian computation (ABC) becomes a very attractive tool for model selection and model calibration (parameter estimation) in tumor growth models. In the present study, a Monte Carlo approximate Bayesian computation (ABC) algorithm is applied to select among competing models of tumor growth, with and without chemotherapy treatment. Simulated measurements are used in this work. The results obtained show that the algorithm correctly selects the model and estimates the parameters used to generate the simulated measurements.

It is attractive for wideband Radar system that sampling rate can be reduced by compressed sensing method. The GTD model can simulate wideband scattering with high accuracy. A compressed sensing method for parameter estimation of GTD model is proposed, and is applied in tomographic SAR imaging. By this method, complex scatter intensity can be estimated accurately.

In order to solve the problem of parameter estimation of nonlinear model in chemical engineering, a novel heuristic optimization approach is presented. The proposed approach develops and employs particle swarm optimization (PSO) technique to search for optimal solution of the parameter estimation. Firstly, the proposed approach converts the problem of parameter estimation of nonlinear model into an equation solving problem that is prone to be optimized. Secondly, two extrema of PSO are used as the target, and all the particles synchronously move through the solution space roundly and efficiently to find the optimum parameter estimation. The feasibility of the proposed method is demonstrated by the parameter estimation example of the pyrolysis model for fir.

Model selection is a topic of special relevance in molecular phylogenetics that affects many, if not all, stages of phylogenetic inference. Here we discuss some fundamental concepts and techniques of model selection in the context of phylogenetics. We start by reviewing different aspects of the selection of substitution models in phylogenetics from a theoretical, philosophical and practical point of view, and summarize this comparison in table format. We argue that the most commonly implemented model selection approach, the hierarchical likelihood ratio test, is not the optimal strategy for model selection in phylogenetics, and that approaches like the Akaike Information Criterion (AIC) and Bayesian methods offer important advantages. In particular, the latter two methods are able to simultaneously compare multiple nested or nonnested models, assess model selection uncertainty, and allow for the estimation of phylogenies and model parameters using all available models (model-averaged inference or multimodel inference). We also describe how the relative importance of the different parameters included in substitution models can be depicted. To illustrate some of these points, we have applied AIC-based model averaging to 37 mitochondrial DNA sequences from the subgenus Ohomopterus(genus Carabus) ground beetles described by Sota and Vogler (2001).