Estimating the Parameters of Fitzhugh–Nagumo Neurons from Neural Spiking Data

A theoretical and computational study on the estimation of the parameters of a single Fitzhugh–Nagumo model is presented. The difference of this work from a conventional system identification is that the measured data only consist of discrete and noisy neural spiking (spike times) data, which contain no amplitude information. The goal can be achieved by applying a maximum likelihood estimation approach where the likelihood function is derived from point process statistics. The firing rate of the neuron was assumed as a nonlinear map (logistic sigmoid) relating it to the membrane potential variable. The stimulus data were generated by a phased cosine Fourier series having fixed amplitude and frequency but a randomly shot phase (shot at each repeated trial). Various values of amplitude, stimulus component size, and sample size were applied to examine the effect of stimulus to the identification process. Results are presented in tabular and graphical forms, which also include statistical analysis (mean and standard deviation of the estimates). We also tested our model using realistic data from a previous research (H1 neurons of blowflies) and found that the estimates have a tendency to converge.

Download Full-text

Explaining the magnetism of gold

10.26434/chemrxiv.5393944.v1 ◽

2017 ◽

Author(s):

Robson de Farias

Keyword(s):

Gas Phase ◽

Computational Study ◽

Formation Enthalpy ◽

Gold Atom ◽

Orbital Energy ◽

Knudsen Effusion ◽

Energy Diagram ◽

Unpaired Electrons ◽

The Difference ◽

Good Agreement

In the present work, a computational study is performed in order to clarify the possible magnetic nature of gold. For such purpose, gas phase Au2 (zero charge) is modelled, in order to calculate its gas phase formation enthalpy. The calculated values were compared with the experimental value obtained by means of Knudsen effusion mass spectrometric studies [5]. Based on the obtained formation enthalpy values for Au2, the compound with two unpaired electrons is the most probable one. The calculated ionization energy of modelled Au2 with two unpaired electrons is 8.94 eV and with zero unpaired electrons, 11.42 eV. The difference (11.42-8.94 = 2.48 eV = 239.29 kJmol-1), is in very good agreement with the experimental value of 226.2 ± 0.5 kJmol-1 to the Au-Au bond7. So, as expected, in the specie with none unpaired electrons, the two 6s1 (one of each gold atom) are paired, forming a chemical bond with bond order 1. On the other hand, in Au2 with two unpaired electrons, the s-d hybridization prevails, because the relativistic contributions. A molecular orbital energy diagram for gas phase Au2 is proposed, explaining its paramagnetism (and, by extension, the paramagnetism of gold clusters and nanoparticles).

Download Full-text

Evaluating the Observed Log-Likelihood Function in Two-Level Structural Equation Modeling with Missing Data: From Formulas to R Code

Psych ◽

10.3390/psych3020017 ◽

2021 ◽

Vol 3 (2) ◽

pp. 197-232

Author(s):

Yves Rosseel

Keyword(s):

Structural Equation ◽

Structural Equation Models ◽

Likelihood Function ◽

Likelihood Estimation ◽

Missing At Random ◽

Equation Modeling ◽

Computationally Efficient ◽

Log Likelihood ◽

Efficient Expression ◽

Special Case

This paper discusses maximum likelihood estimation for two-level structural equation models when data are missing at random at both levels. Building on existing literature, a computationally efficient expression is derived to evaluate the observed log-likelihood. Unlike previous work, the expression is valid for the special case where the model implied variance–covariance matrix at the between level is singular. Next, the log-likelihood function is translated to R code. A sequence of R scripts is presented, starting from a naive implementation and ending at the final implementation as found in the lavaan package. Along the way, various computational tips and tricks are given.

Download Full-text

The feasibility and validity of using a real time location system (RTLS) to measure bedside contact time

Journal of Research in Nursing ◽

10.1177/17449871211016169 ◽

2021 ◽

pp. 174498712110161

Author(s):

Ann-Marie Cannaby ◽

Vanda Carter ◽

Thomas Hoe ◽

Stephenson Strobel ◽

Elena Ashtari Tafti ◽

...

Keyword(s):

Real Time ◽

Contact Time ◽

Measured Data ◽

Complete Agreement ◽

Observation Data ◽

The Real ◽

Measured Time ◽

The Difference ◽

Hospital Wards ◽

Location Systems

Background The association between the nurse-to-patient ratio and patient outcomes has been extensively investigated. Real time location systems have the potential capability of measuring the actual amount of bedside contact patients receive. Aims This study aimed to determine the feasibility and accuracy of real time location systems as a measure of the amount of contact time that nurses spent in the patients’ bed space. Methods An exploratory, observational, feasibility study was designed to compare the accuracy of data collection between manual observation performed by a researcher and real time location systems data capture capability. Four nurses participated in the study, which took place in 2019 on two hospital wards. They were observed by a researcher while carrying out their work activities for a total of 230 minutes. The amount of time the nurses spent in the patients’ bed space was recorded in 10-minute blocks of time and the real time location systems data were extracted for the same nurse at the time of observation. Data were then analysed for the level of agreement between the observed and the real time location systems measured data, descriptively and graphically using a kernel density and a scatter plot. Results The difference (in minutes) between researcher observed and real time location systems measured data for the 23, 10-minute observation blocks ranged from zero (complete agreement) to 5 minutes. The mean difference between the researcher observed and real time location systems time in the patients’ bed space was one minute (10% of the time). On average, real time location systems measured time in the bed space was longer than the researcher observed time. Conclusions There were good levels of agreement between researcher observation and real time location systems data of the time nurses spend at the bedside. This study confirms that it is feasible to use real time location systems as an accurate measure of the amount of time nurses spend at the patients’ bedside.

Download Full-text

On Bayesian procedure for maximum earthquake magnitude estimation

Research in Geophysics ◽

10.4081/rg.2012.e7 ◽

2012 ◽

Vol 2 (1) ◽

pp. 7 ◽

Cited By ~ 5

Author(s):

Andrzej Kijko

Keyword(s):

Maximum Likelihood ◽

Posterior Distribution ◽

Ad Hoc ◽

Likelihood Function ◽

Fundamental Problem ◽

Likelihood Estimation ◽

Earthquake Magnitude ◽

Bayesian Estimator ◽

Bayesian Procedure ◽

Posterior Estimate

This work is focused on the Bayesian procedure for the estimation of the regional maximum possible earthquake magnitude mmax. The paper briefly discusses the currently used Bayesian procedure for mmax, as developed by Cornell, and a statistically justifiable alternative approach is suggested. The fundamental problem in the application of the current Bayesian formalism for mmax estimation is that one of the components of the posterior distribution is the sample likelihood function, for which the range of observations (earthquake magnitudes) depends on the unknown parameter mmax. This dependence violates the property of regularity of the maximum likelihood function. The resulting likelihood function, therefore, reaches its maximum at the maximum observed earthquake magnitude mobsmax and not at the required maximum possible magnitude mmax. Since the sample likelihood function is a key component of the posterior distribution, the posterior estimate of m^max is biased. The degree of the bias and its sign depend on the applied Bayesian estimator, the quantity of information provided by the prior distribution, and the sample likelihood function. It has been shown that if the maximum posterior estimate is used, the bias is negative and the resulting underestimation of mmax can be as big as 0.5 units of magnitude. This study explores only the maximum posterior estimate of mmax, which is conceptionally close to the classic maximum likelihood estimation. However, conclusions regarding the shortfall of the current Bayesian procedure are applicable to all Bayesian estimators, e.g. posterior mean and posterior median. A simple, ad hoc solution of this non-regular maximum likelihood problem is also presented.

Download Full-text

Computational investigation on the role of C-Terminal of human albumin on the dimerization of Aβ1-42 peptide

Biointerface Research in Applied Chemistry ◽

10.33263/briac101.944955 ◽

2020 ◽

Vol 10 (1) ◽

pp. 4944-4955 ◽

Cited By ~ 1

Keyword(s):

Computational Study ◽

Binding Free Energy ◽

Conformational Dynamics ◽

Human Albumin ◽

Potential Of Mean Force ◽

Amber Force Field ◽

Aβ Aggregation ◽

The Difference ◽

Dynamics Simulations

Alzheimer’s disease (AD) is characterized by the presence of Amyloid-beta (Aβ) peptide, which has the propensity to fold into β-sheets under stress forming aggregated amyloid plaques. Nowadays many studies have focused on the development of novel, specific therapeutic strategies to slow down Aβ aggregation or control preformed aggregates. Albumin, the most abundant protein in the cerebrospinal fluid, was reported to bind Aβ impeding its aggregation. Recently, it has been reported that C-terminal (CTerm) of Human Albumin binds with Aβ1-42, impairs Aβ aggregation and promotes disassembly of Aβ aggregates protecting neurons. In this computational study, we have investigated the effect of CTerm on the conformational dynamics and the aggregation propensity of Aβ1-42 peptide. We have performed molecular dynamics simulations on the Aβ1-42-Aβ1-42 homodimer and Aβ1-42-CTerm of albumin heterodimer using the AMBER force field ff99SBildn. From the Potential of mean force (PMF) study and Binding free energy (BFE) analysis, we observed the association of Aβ1-42 peptide monomer with itself in the form of homodimer to be stronger than its association with the CTerm in the heterodimer complex. The difference in the number of residues in the Aβ1-42 peptide monomer (42 AAs) and CTerm (35 AAs) may be probable reason for the difference in association between the monomeric units in corresponding homodimer and heterodimer complexes. But even then CTerm shows a significant effect on the dimerization of Aβ1-42 peptide. Our findings therefore suggest that CTerm can be used for the disassembly of Aβ1-42 peptide monomer.

Download Full-text

ESTIMASI PARAMETER PADA MODEL COX MULTIVARIAT DENGAN METODE MAXIMUM PARTIAL LIKELIHOOD ESTIMATION

Jurnal Ilmiah Matematika dan Pendidikan Matematika ◽

10.20884/1.jmp.2012.4.1.2954 ◽

2012 ◽

Vol 4 (1) ◽

pp. 185

Author(s):

Irfan Wahyudi ◽

Purhadi Purhadi ◽

Sutikno Sutikno ◽

Irhamah Irhamah

Keyword(s):

Parameter Estimation ◽

Likelihood Function ◽

Cox Model ◽

Hessian Matrix ◽

Likelihood Estimation ◽

Partial Likelihood ◽

Estimation Methods ◽

Hazard Functions ◽

Score Vector ◽

Parameter Estimation Methods

Multivariate Cox proportional hazard models have ratio property, that is the ratio of hazard functions for two individuals with covariate vectors z1 and z2 are constant (time independent). In this study we talk about estimation of prameters on multivariate Cox model by using Maximum Partial Likelihood Estimation (MPLE) method. To determine the appropriate estimators that maximize the ln-partial likelihood function, after a score vector and a Hessian matrix are found, numerical iteration methods are applied. In this case, we use a Newton Raphson method. This numerical method is used since the solutions of the equation system of the score vector after setting it equal to zero vector are not closed form. Considering the studies about multivariate Cox model are limited, including the parameter estimation methods, but the methods are urgently needed by some fields of study related such as economics, engineering and medical sciences. For this reasons, the goal of this study is designed to develop parameter estimation methods from univariate to multivariate cases.

Download Full-text

Continuous Autoregressive Moving Average Models

Methodologies and Applications of Computational Statistics for Machine Intelligence - Advances in Systems Analysis, Software Engineering, and High Performance Computing ◽

10.4018/978-1-7998-7701-1.ch007 ◽

2021 ◽

pp. 118-141

Author(s):

Yakup Ari

Keyword(s):

Time Series ◽

Parameter Estimation ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Discrete Time ◽

Moving Average ◽

Likelihood Estimation ◽

Real Data ◽

Autoregressive Moving Average ◽

The Difference

The financial time series have a high frequency and the difference between their observations is not regular. Therefore, continuous models can be used instead of discrete-time series models. The purpose of this chapter is to define Lévy-driven continuous autoregressive moving average (CARMA) models and their applications. The CARMA model is an explicit solution to stochastic differential equations, and also, it is analogue to the discrete ARMA models. In order to form a basis for CARMA processes, the structures of discrete-time processes models are examined. Then stochastic differential equations, Lévy processes, compound Poisson processes, and variance gamma processes are defined. Finally, the parameter estimation of CARMA(2,1) is discussed as an example. The most common method for the parameter estimation of the CARMA process is the pseudo maximum likelihood estimation (PMLE) method by mapping the ARMA coefficients to the corresponding estimates of the CARMA coefficients. Furthermore, a simulation study and a real data application are given as examples.

Download Full-text

Maximum likelihood estimation for symmetric α-stable Ornstein–Uhlenbeck processes

Stochastics and Dynamics ◽

10.1142/s0219493721500180 ◽

2020 ◽

pp. 2150018

Author(s):

Zhifen Chen ◽

Xiaopeng Chen

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Likelihood Function ◽

Likelihood Estimation ◽

Transition Function ◽

Closed Form Expression ◽

Discrete Observations ◽

Form Expression ◽

Probability Density Function Pdf ◽

Accuracy And Stability

In this paper, we consider the maximum likelihood estimation for the symmetric [Formula: see text]-stable Ornstein–Uhlenbeck (S[Formula: see text]S-OU) processes based on discrete observations. Since the closed-form expression of maximum likelihood function is hard to obtain in the Lévy case, we choose a mixture of Cauchy and Gaussian distribution to approximate the probability density function (PDF) of the S[Formula: see text]S distribution. By means of transition function and Laplace transform, we construct an explicit approximate sequence of likelihood function, which converges to the likelihood function of S[Formula: see text]S distribution. Based on the approximation of likelihood function we give an algorithm for computing maximum likelihood estimation. We also numerically simulate some experiments which demonstrate the accuracy and stability of the proposed estimator.

Download Full-text

Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

Mathematical Problems in Engineering ◽

10.1155/2019/6281781 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8 ◽

Cited By ~ 5

Author(s):

Fan Yang ◽

Hu Ren ◽

Zhili Hu

Keyword(s):

Parameter Estimation ◽

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Weibull Distribution ◽

Likelihood Function ◽

Likelihood Estimation ◽

Estimation Procedure ◽

Evolutionary Strategy ◽

Likelihood Method ◽

Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

Download Full-text

Pairwise likelihood estimation of latent autoregressive count models

Statistical Methods in Medical Research ◽

10.1177/0962280220924068 ◽

2020 ◽

Vol 29 (11) ◽

pp. 3278-3293

Author(s):

Xanthi Pedeli ◽

Cristiano Varin

Keyword(s):

Likelihood Function ◽

Likelihood Estimation ◽

Autoregressive Models ◽

Suggested Approach ◽

Pairwise Likelihood ◽

Simulation Based ◽

Likelihood Approach ◽

Computationally Intensive ◽

Methodological Aspects

Latent autoregressive models are useful time series models for the analysis of infectious disease data. Evaluation of the likelihood function of latent autoregressive models is intractable and its approximation through simulation-based methods appears as a standard practice. Although simulation methods may make the inferential problem feasible, they are often computationally intensive and the quality of the numerical approximation may be difficult to assess. We consider instead a weighted pairwise likelihood approach and explore several computational and methodological aspects including estimation of robust standard errors and the role of numerical integration. The suggested approach is illustrated using monthly data on invasive meningococcal disease infection in Greece and Italy.

Download Full-text