Inference for reaction networks using the Linear Noise Approximation

We consider inference for the reaction rates in discretely observed networks such as those found in models for systems biology, population ecology and epidemics. Most such networks are neither slow enough nor small enough for inference via the true state-dependent Markov jump process to be feasible. Typically, inference is conducted by approximating the dynamics through an ordinary differential equation (ODE), or a stochastic differential equation (SDE). The former ignores the stochasticity in the true model, and can lead to inaccurate inferences. The latter is more accurate but is harder to implement as the transition density of the SDE model is generally unknown. The Linear Noise Approximation (LNA) is a first order Taylor expansion of the approximating SDE about a deterministic solution and can be viewed as a compromise between the ODE and SDE models. It is a stochastic model, but discrete time transition probabilities for the LNA are available through the solution of a series of ordinary differential equations. We describe how a restarting LNA can be efficiently used to perform inference for a general class of reaction networks; evaluate the accuracy of such an approach; and show how and when this approach is either statistically or computationally more efficient than ODE or SDE methods. We apply the LNA to analyse Google Flu Trends data from the North and South Islands of New Zealand, and are able to obtain more accurate short-term forecasts of new flu cases than another recently proposed method, although at a greater computational cost

Bayesian inference of biochemical kinetic parameters using the linear noise approximation

Background Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data. Results We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo. Conclusion The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods

Stochastic Functional Data Analysis: A Diffusion Model‐Based Approach

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/89505/1/j.1541-0420.2011.01591.x.pd

Efficacy of Vitamin D Supplementation in Addition to Aerobic Exercise Training in Obese Women with Perceived Myalgia: A Single-Blinded Randomized Controlled Clinical Trial

Obese women were more susceptible to myalgia because of their significantly lower vitamin D concentrations; the present study investigated the efficacy of vitamin D in addition to an aerobic interval training in the management of obese women with myalgia. Forty-five obese women with vitamin D deficiency and myalgia (30 to 40 years old) were assigned randomly into three equal groups. Group A received an aerobic interval training with vitamin D supplementation, Group B received vitamin D supplementation only, and Group C received aerobic interval training only; participants in all groups were on calorie deficient diets. The study outcomes were the Visual Analog Scale (VAS) for Pain Evaluation, serum vitamin D level, and Cooper 12-Minute Walk Test for Functional Capacity Evaluation, while the Short-Form Health Survey (SF) was used for assessment of quality of life. We detected a significant improvement in pain intensity level, serum vitamin D level, and quality of life in all groups with significant difference between Group A and groups B and C. We also detected a significant improvement in functional capacity in groups A and C, with no significant change in Group B. Aerobic interval training with vitamin D supplementation was more effective for the management of obese women with perceived myalgia

Effectiveness of Shock Wave Therapy versus Intra-Articular Corticosteroid Injection in Diabetic Frozen Shoulder Patients’ Management: Randomized Controlled Trial

Frozen shoulder is a major musculoskeletal illness in diabetic patients. This study aimed to compare the effectiveness of shock wave and corticosteroid injection in the management of diabetic frozen shoulder patients. Fifty subjects with diabetic frozen shoulder were divided randomly into group A (the intra-articular corticosteroid injection group) and group B that received 12 sessions of shock wave therapy, while each patient in both groups received the traditional physiotherapy program. The level of pain and disability, the range of motion, as well as the glucose triad were evaluated before patient assignment to each group, during the study and at the end of the study. Compared to the pretreatment evaluations there were significant improvements of shoulder pain and disability and in shoulder flexion and abduction range of motion in both groups (p < 0.05). The shock wave group revealed a more significant improvement the intra-articular corticosteroid injection group, where p was 0.001 for shoulder pain and disability and shoulder flexion and abduction. Regarding the effect of both interventions on the glucose triad, there were significant improvements in glucose control with group B, where p was 0.001. Shock waves provide a more effective and safer treatment modality for diabetic frozen shoulder treatment than corticosteroid intra-articular injection

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods

A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions

www.elsevier.com/locate/jeconom A simple approach to the parametric estimation of potentially nonstationary diffusions

Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models

Ministry of Education, Singapore under its Academic Research Funding Tier