Stochastic Approximation Expectation Maximization Research Articles

Parameter Estimation of Heavy-Tailed AR Model With Missing Data Via Stochastic EM

The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data, are non-Gaussian, therefore, the AR model with more general heavy-tailed innovations is preferred. Another issue that frequently occurs in time series is missing values, due to system data record failure or unexpected data loss. Although there are numerous works about Gaussian AR time series with missing values, as far as we know, there does not exist any work addressing the issue of missing data for the heavy-tailed AR model. In this paper, we consider this issue for the first time, and propose an efficient framework for parameter estimation from incomplete heavy-tailed time series based on a stochastic approximation expectation maximization (SAEM) coupled with a Markov Chain Monte Carlo (MCMC) procedure. The proposed algorithm is computationally cheap and easy to implement. The convergence of the proposed algorithm to a stationary point of the observed data likelihood is rigorously proved. Extensive simulations and real datasets analyses demonstrate the efficacy of the proposed framework.

A Simple and Flexible Computational Framework for Inferring Sources of Heterogeneity from Single-Cell Dynamics.

Single-cell time-lapse data provide the means for disentangling sources of cell-to-cell and intra-cellular variability, a key step for understanding heterogeneity in cell populations. However, single-cell analysis with dynamic models is a challenging open problem: current inference methods address only single-gene expression or neglect parameter correlations. We report on a simple, flexible, and scalable method for estimating cell-specific and population-average parameters of non-linear mixed-effects models of cellular networks, demonstrating its accuracy with a published model and dataset. We also propose sensitivity analysis for identifying which biological sub-processes quantitatively and dynamically contribute to cell-to-cell variability. Our application to endocytosis in yeast demonstrates that dynamic models of realistic size can be developed for the analysis of single-cell data and that shifting the focus from single reactions or parameters to nuanced and time-dependent contributions of sub-processes helps biological interpretation. Generality and simplicity of the approach will facilitate customized extensions for analyzing single-cell dynamics.

Pharmacokinetic Parameters of Quinine in Healthy Subjects and in Patients with Uncomplicated Malaria in Nigeria: Analysis of Data using a Population Approach

The varied disposition of the antimalarial quinine partly explains its poor tolerance and toxicity in humans. Using a population approach, the disposition of quinine in healthy subjects and patients with acute uncomplicated symptomatic malaria from Nigeria was re-examined with a view to providing population-specific attributes. Concentration versus time profiles of quinine over 48 hours in healthy individuals, and over 7 days in malaria-infected patients, were stratified to reflect: concentration versus time data during the first 48 hours of quinine administration for healthy subjects and infected patients, concentration versus time data after 48 hours in infected patients, and all concentration versus time data available for healthy subjects and infected patients. Pharmacokinetic parameters were then estimated with a stochastic approximation expectation maximization algorithm. All datasets were fitted by a 1-compartment model with covariate contributions from body weight and infection status. The absorption rate constant, and volume of distribution and clearance were 1.72 h-1, 86.8 to 157.4 L, and 6.6 to 9.6 L/h, respectively. Infected patients experienced a 38% decrease in volume of distribution and a 31% decrease in clearance in the first 48 hours relative to healthy individuals. The contraction in volume of distribution and clearance diminished significantly after 48 hours of chronic quinine dosing in infected patients. The study findings suggest that clinical interventions aimed at enhancing the safety and tolerance of quinine might be achieved by a rational decrease in dose size and/or dosing interval, post-48 hours of chronic quinine administration, in malaria-infected patients.

IRT scoring procedures for TIMSS data

In large-scale international assessment programs, results for mathematics proficiency are typically reported for jurisdictions such as provinces or countries. An overall score is provided along with subscores based on content subdomains defined in the test specifications. In this paper, an alternative method for obtaining empirical subscores is described, where the empirical subscores are based on an exploratory item response theory (IRT) factor solution. This alternative scoring is intended to augment rather than to replace traditional scoring procedures. The IRT scoring method is applied to the mathematics achievement data from the Trends in International Mathematics and Science Study (TIMSS). A brief overview of the method is given, and additional material is given for validation of the empirical subscores. The ultimate goal of scoring is to provide diagnostic feedback in the form of naturally occurring item clustering. This provides useful information in addition to traditional subscores based on test specifications. As shown by Camilli and Dossey (2019), the achievement ranks of countries may change depending on which empirical subscore of mathematics is considered. Traditional subscores are highly correlated and tend to provide similar rank orders.•The methods takes advantage of the TIMSS sampling design, specifically pairs of jackknife zones, to aggregate categorical to higher-order sampling units for IRT factor analysis.•Once factor scores are estimated for sampling units and interpreted, they are aggregated to the jurisdiction level (countries, states, provinces) using sampling weights. The procedure for obtaining standard errors of jurisdictional level scores combines cross-sampling-unit variance and Monte Carlo sampling variation.•Full technical details of the IRT factoring procedures are given in Camilli and Fox (2015). Fox (2010) provides additional background for Bayesian item response modeling techniques. The estimation algorithm is based on stochastic approximation expectation-maximization (SAEM).

Hypoelliptic Diffusions: Filtering and Inference from Complete and Partial Observations

SummaryThe statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, because of the noise structure, where the noise components of the different co-ordinates of the multi-dimensional process operate on different timescales, standard inference tools are ill conditioned. We propose to use a higher order scheme to approximate the likelihood, such that the different timescales are appropriately accounted for. We show consistency and asymptotic normality with non-typical convergence rates. When only partial observations are available, we embed the approximation in a filtering algorithm for the unobserved co-ordinates and use this as a building block in a stochastic approximation expectation–maximization algorithm. We illustrate on simulated data from three models: the harmonic oscillator, the FitzHugh–Nagumo model used to model membrane potential evolution in neuroscience and the synaptic inhibition and excitation model used for determination of neuronal synaptic input.

Modelling and genetic evaluation of Markhoz goat growth curve parameters

The objectives of our study were to compare different non-linear mixed effect models (Brody, Von Bertalanffy, Richards, Gompertz and Logistic) for best description the growth patterns of Markhoz kids, evaluate the influence of environmental (fixed) effects on growth curve parameters of the best-fit growth model and finally estimate the genetic parameters for growth curve characteristics. Live weights of 3678 individuals from the historical archives of the Markhoz Goat Performance Testing Station (in Sanandaj), which were collected from birth to 365 days of age during 1992 to 2015, were used in the analysis. Models were fitted according to the stochastic approximation expectation-maximization (SAEM) procedure implemented in R package SAEMIX. All studied mixed models described the growth pattern in Markhoz goat, except Richards model. However, the Brody model best fit the data. The analysis of variance on the growth curve parameters (at the individual level) showed that among the fixed effects (i.e., sex, birth type, age of dam and year of birth) for the Brody model, only age of dam had no effect on any of the growth parameters. Estimates of heritability for growth curve parameters were low, with 0.067 ± 0.011, 0.063 ± 0.010 and 0.044 ± 0.001 for mature weight (a), constant of integration (b) and rate of maturing (k), respectively. Low heritability estimates suggest that the environment is not favorable for expression of genetic potential of Markhoz kids. The negative genetic (−0.866 ± 0.000) and phenotypic (−0.723 ± 0.008) correlations between the parameters a and k indicates that animals with lower growth rates are more likely to reach higher weight values when adults.

Population Pharmacokinetic Analysis of Immediate-Release Oral Tacrolimus Co-administered with Mycophenolate Mofetil in Corticosteroid-Free Adult Kidney Transplant Recipients.

Tacrolimus is the mainstay calcineurin inhibitor frequently administered with mycophenolic acid with or without corticosteroids to prevent graft rejection in adult kidney transplant recipients. The primary objective of this study was to develop and evaluate a population pharmacokinetic model characterizing immediate-release oral tacrolimus co-administered with mycophenolate mofetil (a pro-drug of mycophenolic acid) in adult kidney transplant recipients on corticosteroid-free regimens. The secondary objective was to investigate the effects of clinical covariates on the pharmacokinetics of tacrolimus, emphasizing the interacting effects of mycophenolic acid. Population modeling and evaluation were conducted with Monolix (Suite-2018R1) using the stochastic approximation expectation-maximization algorithm in 49 adult subjects (a total of 320 tacrolimus whole-blood concentrations). Effects of clinical variables on tacrolimus pharmacokinetics were determined by population covariate modeling, regression modeling, and categorical analyses. A two-compartment, first-order absorption with a lag-time, linear elimination, and constant error model best represented the population pharmacokinetics of tacrolimus. The apparent clearance value for tacrolimus was 17.9l/h (6.95% relative standard error) in our model, which is lower compared with similar subjects on corticosteroid-based therapy. The glomerular filtration rate had significant effects on the apparent clearance and central compartment volume of distribution. Conversely, mycophenolic acid did not affect the apparent clearance of tacrolimus. We have developed and internally evaluated a novel population pharmacokinetic model for tacrolimus co-administered with mycophenolate mofetil in corticosteroid-free adult kidney transplant patients. These findings are clinically important and provide further reasons for conducting therapeutic drug monitoring in this specific population.

Model-based curve registration via stochastic approximation EM algorithm

Functional data often exhibit both amplitude and phase variation around a common base shape, with phase variation represented by a so called warping function. The process of removing phase variation by curve alignment and inference of the warping functions is referred to as curve registration. When functional data are observed with substantial noise, model-based methods can be employed for simultaneous smoothing and curve registration. However, the nonlinearity of the model often renders the inference computationally challenging. An alternative method for model-based curve registration is proposed which is computationally more stable and efficient than existing approaches in the literature. The proposed method is applied to the analysis of elephant seal dive profiles. The result shows that more intuitive groupings can be obtained by clustering on phase variations via the predicted warping functions.

Mixed-Effects Estimation in Dynamic Models of Plant Growth for the Assessment of Inter-individual Variability

Modeling inter-individual variability in plant populations is a key issue to understand crop heterogeneity and its variations in response to the environment. Being able to describe the interactions among plants and explain the variability observed in the population could provide useful information on how to control it and improve global plant growth. We propose here a method to model plant variability within a field, by extending the so-called GreenLab functional-structural plant model from the individual to the population scale via nonlinear mixed-effects modeling. Parameter estimation of the population model is achieved using the stochastic approximation expectation maximization algorithm, implemented in the platform for plant growth modeling and analysis PyGMAlion. The method is first applied on a set of simulated data and then on a real dataset from a population of 34 winter oilseed rape plants at the rosette stage. Results show that our method allows for a good characterization of the variability in the population with only a limited number of parameters, which is a key point for plant models. Results on simulated data show that parameters associated with a low sensitivity index are inaccurately estimated by the algorithm when considered as random effects, but a good stability of the results can be obtained by considering them as fixed effects. These results open new ways for the analysis of inter-plant variability within a population and the study of plant–plant competition.Supplementary materials accompanying this paper appear online.

Likelihood-free stochastic approximation EM for inference in complex models

ABSTRACTA maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function of model parameters. While SAEM is best suited for models having a tractable “complete likelihood” function, its application to moderately complex models is a difficult or even impossible task. We show how to construct a likelihood-free version of SAEM by using the “synthetic likelihood” paradigm. Our method is completely plug-and-play, requires almost no tuning and can be applied to both static and dynamic models.

A Particle Stochastic Approximation EM Algorithm to Identify Jump Markov Nonlinear Models

The identification of static parameters in jump Markov nonlinear models (JMNMs) poses a key challenge in explaining nonlinear and abruptly changing behavior of dynamical systems. This paper introduces a stochastic approximation expectation maximization algorithm to facilitate offline maximum likelihood parameter estimation in JMNMs. The method relies on the construction of a particle Gibbs kernel that takes advantage of the inherent structure of the model to increase the efficiency through Rao-Blackwellization. Numerical examples illustrate that the proposed solution outperforms related approaches.

Coupling stochastic EM and approximate Bayesian computation for parameter inference in state-space models

We study the class of state-space models and perform maximum likelihood estimation for the model parameters. We consider a stochastic approximation expectation–maximization (SAEM) algorithm to maximize the likelihood function with the novelty of using approximate Bayesian computation (ABC) within SAEM. The task is to provide each iteration of SAEM with a filtered state of the system, and this is achieved using an ABC sampler for the hidden state, based on sequential Monte Carlo methodology. It is shown that the resulting SAEM-ABC algorithm can be calibrated to return accurate inference, and in some situations it can outperform a version of SAEM incorporating the bootstrap filter. Two simulation studies are presented, first a nonlinear Gaussian state-space model then a state-space model having dynamics expressed by a stochastic differential equation. Comparisons with iterated filtering for maximum likelihood inference, and Gibbs sampling and particle marginal methods for Bayesian inference are presented.

Statistical Characterization of the State-of-Health of Lithium-Ion Batteries with Weibull Distribution Function—A Consideration of Random Effect Model in Charge Capacity Decay Estimation

Effective prognosis of lithium-ion batteries involves the inclusion of the influences of uncertainties that can be incorporated through random effect parameters in a nonlinear mixed effect degradation model framework. This study is geared towards the estimation of the reliability of lithium-ion batteries, using parametric effects determination involving uncertainty, using a multiphase decay patterned sigmoidal model, experimental data and the Weibull distribution function. The random effect model, which uses Maximum Likelihood Estimation (MLE) and Stochastic Approximation Expectation Maximization (SAEM) algorithm to predict the parametric values, was found to estimate the remaining useful life (RUL) to an accuracy of more than 98%. The State-of-Health (SOH) of the batteries was estimated using the Weibull distribution function, which is found to be an appropriate formulation to use.

Quantile regression in linear mixed models: a stochastic approximation EM approach.

This paper develops a likelihood-based approach to analyze quantile regression (QR) models for continuous longitudinal data via the asymmetric Laplace distribution (ALD). Compared to the conventional mean regression approach, QR can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. Exploiting the nice hierarchical representation of the ALD, our classical approach follows a Stochastic Approximation of the EM (SAEM) algorithm in deriving exact maximum likelihood estimates of the fixed-effects and variance components. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the ML estimates through empirical experiments and applications to two real life datasets. Our empirical results clearly indicate that the SAEM estimates outperforms the estimates obtained via the combination of Gaussian quadrature and non-smooth optimization routines of the Geraci and Bottai (2014) approach in terms of standard errors and mean square error. The proposed SAEM algorithm is implemented in the R package qrLMM().

Exploratory Population PK Analysis of Dupilumab, a Fully Human Monoclonal Antibody Against IL-4Rα, in Atopic Dermatitis Patients and Normal Volunteers.

An exploratory population pharmacokinetic model for functional dupilumab was developed. Data from healthy volunteers and patients with atopic dermatitis (AD) receiving intravenous or subcutaneous doses were integrated. The data included 197 participants (2,518 measurements of dupilumab in serum) from six phase I and II studies. The data were analyzed using stochastic approximation expectation‐maximization and importance sampling methods. The best structural model was a two‐compartment model with parallel linear and Michaelis–Menten elimination from the central compartment. Estimated parameters were: central volume 2.74 L, elimination rate 0.0459 d−1, central‐to‐peripheral rate 0.0652 d−1, peripheral‐to‐central rate 0.129 d−1, bioavailability 60.7%, maximal target‐mediated elimination rate 0.968 mg/L/d, and Michaelis–Menten constant 0.01 mg/L. Body weight was a significant covariate of the central volume. No gender effect was observed when controlling for weight. No differences between healthy volunteers and patients with AD were found. The model adequately described dupilumab pharmacokinetics for intravenous and subcutaneous routes of administration.

A Generalized Mixed Effect Kijima Model and Application in Optimal Maintenance Planning

The Kijima model has been widely used in reliability literature to analyze repairable systems with various degrees of repair efficiency including “perfect repair,” “minimal repair,” and situations in between. Most existing studies, however, treat repair efficiency as a fixed value even though repair efficiency can vary among a series of repairs. In this paper, we propose a generalized mixed effect Kijima model to characterize the variation of repair efficiency. In particular, the newly proposed “mixed effect” model incorporates a fixed time-dependent effect and a random effect of repair efficiency, while the term “generalized” refers to the fact that the classic Kijima model is generalized to handle more maintenance situations such as “better than new” and “worse than old” situations after repair. To estimate the model parameters given a series of observed system failure times, we develop a stochastic approximation expectation maximization algorithm which is a type of maximum likelihood estimation method. Further, an optimal periodic maintenance planning is developed based on the proposed reliability model. A simulation study and a real-world case study are conducted to demonstrate the developed methods.

High-Frequency Volatility Modelling: A Markov-Switching Autoregressive Conditional Intensity Model

We develop a Markov-Switching Autoregressive Conditional Intensity (MS-ACI) model by extending the Autoregressive Conditional Intensity model (ACI) (Russell 1999) with a Markov-switching structure. The model provides reliable parametric intraday volatility estimation through the absolute price change point process. We apply the Stochastic Approximation Expectation Maximization (Celeux and Diebolt 1992) algorithm to obtain maximum likelihood estimates of the model. By applying our model to the most recent intraday price duration data for IBM, JPM and KO, and incorporating a regime-switching relationship between volatility, contemporaneous volume and bid-ask spread, we discover two distinct regimes that have distinct diurnal pattern which can be explained by the diurnal information arrival pattern and the heterogeneous volume-volatility relationship as documented in Bessembinder and Seguin (1993), Arago and Nieto (2005), Hussain (2011). We provide a high-frequency measure of the probability of information shock to the market, and a measure of the impact of information on volatility.

Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm

Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm

A SAEM algorithm for fused lasso penalized NonLinear Mixed Effect Models: Application to group comparison in pharmacokinetics

Nonlinear mixed effect models are classical tools to analyze nonlinear longitudinal data in many fields such as population pharmacokinetics. Groups of observations are usually compared by introducing the group affiliations as binary covariates with a reference group that is stated among the groups. This approach is relatively limited as it allows only the comparison of the reference group to the others. The proposed method compares groups using a penalized likelihood approach. Groups are described by the same structural model but with parameters that are group specific. The likelihood is penalized with a fused lasso penalty that induces sparsity in the differences between groups for both fixed effects and variances of random effects. A penalized Stochastic Approximation EM algorithm is proposed that is coupled to Alternating Direction Method Multipliers to solve the maximization step. An extensive simulation study illustrates the performance of this algorithm when comparing more than two groups. Then the approach is applied to real data from two pharmacokinetic drug–drug interaction trials.

An Aggregate IRT Procedure for Exploratory Factor Analysis

An aggregation strategy is proposed to potentially address practical limitation related to computing resources for two-level multidimensional item response theory (MIRT) models with large data sets. The aggregate model is derived by integration of the normal ogive model, and an adaptation of the stochastic approximation expectation maximization algorithm is used for estimation. This methodology is used to conduct an exploratory factor analysis of the 2007 mathematics data from Trends in International Mathematics and Science Study (TIMSS) fourth grade to illustrate potential uses. A comparison to flexMIRT and two brief simulations indicate the aggregate model provides accurate estimates of Level 2 parameters despite loss of information ensuing from key assumption.