Maximum approximate likelihood estimation of general continuous-time state-space models

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretization of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean.

Depressive Symptoms, Alcohol Beliefs and Heavy Episodic Drinking in Adolescents

Adolescents who engage in heavy episodic drinking (HED—i.e., 5+ drinks on a single occasion) increase risks for psychopathology, alcohol dependence, and similar negative consequences in adulthood. We explored associations among depressive symptoms, positive alcohol beliefs, and progression of heavy episodic drinking (HED) in 3021 German adolescents (M(SD) age at baseline = 12.4 (1.0)) followed for 30 months in 4 waves, using a conditional parallel process linear growth model, with full information maximum likelihood estimation. By wave 4, 40.3% of participants had engaged in HED more than once; 16.4% had done so ≥5 times. Depressive symptoms were indirectly related to baseline values of HED (through positive beliefs and wave 1 drinking frequency and quantity) and to the rate of growth in HED (through positive beliefs and wave 1 quantity). Adolescents with higher levels of depressive symptoms and positive alcohol beliefs drink more frequently and at greater quantities, which is associated with initiating HED at a higher level and escalating HED more rapidly than peers with similar depressive symptoms who lack those beliefs. This suggests that, to the extent that positive alcohol beliefs can be tempered through public health campaigns, education and/or counseling, HED among depressed adolescents might be reduced.

High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model

Estimation of a conditional covariance matrix is an interesting and important research topic in statistics and econometrics. However, modelling ultra-high dimensional dynamic (conditional) covariance structures is known to suffer from the curse of dimensionality or the problem of singularity. To partially solve this problem, this paper establishes a model by combining the ideas of a factor model and a symmetric GARCH model to describe the dynamics of a high-dimensional conditional covariance matrix. Quasi maximum likelihood estimation (QMLE) and least square estimation (LSE) methods are used to estimate the parameters in the model, and the plug-in method is introduced to obtain the estimation of conditional covariance matrix. Asymptotic properties are established for the proposed method, and simulation studies are given to demonstrate its performance. A financial application is presented to support the methodology.

Application of Univariate Probability Distributions Fitting With Monte Carlo Simulation

In this study, we present a univariate probability distribution through application of the three Sub and Super Exponential heavier-longer and lighter-shorter tails fitting. This univariate family includes the Lognormal, Gamma and Weibull distribution, the adequacy of the distribution tails is obtained by adequate Fitting Tests and descriptive Criterion. It emphasizes on tail values and is independent of the number of intervals. In this regards the time series analysis for the last three centuries of the logarithm population data sets over to Karachi region (from1729 to1946 and from 1951 to 2018) is used, which contains irregular and regular length and peaks, That peaks /tails fitting is attained by methods for validation and normality tests and defined by stochastic depiction. In other hand, Weibull and Lognormal distribution tails are found as heavier distribution by two validation tests (Maximum Likelihood Estimation and probability of correct selection), In the final section, the univariate probability distributions are used to Monte Carlo simulation for generating the actual population data, it indicates that the heavy-tailed Lognormal and Weibull distributions are also fitted contract than the more commonly seen lighter tailed Gamma distribution. So, the Monte Carlo Simulation performs the appropriate Lognormal and Weibull distributions for irregular and regular data and generate data values (298 and 69) from duration of 1729 to 2020 and 1951 to 2020. Copyright(c) The Author

Optimization of Aeolus' aerosol optical properties by maximum-likelihood estimation

The European Space Agency (ESA) Earth Explorer Mission Aeolus was launched in August 2018, carrying the first Doppler wind lidar in space. Its primary payload, the Atmospheric LAser Doppler INstrument (ALADIN), is an ultraviolet (UV) high-spectral-resolution lidar (HSRL) measuring atmospheric backscatter from air molecules and particles in two separate channels. The primary mission product is globally distributed line-of-sight wind profile observations in the troposphere and lower stratosphere. Atmospheric optical properties are provided as a spin-off product. Being an HSRL, Aeolus is able to independently measure the particle extinction coefficients, co-polarized particle backscatter coefficients and the co-polarized lidar ratio (the cross-polarized return signal is not measured). This way, the retrieval is independent of a priori lidar ratio information. The optical properties are retrieved using the standard correct algorithm (SCA), which is an algebraic inversion scheme and therefore sensitive to measurement noise. In this work, we reformulate the SCA into a physically constrained maximum-likelihood estimation (MLE) problem and demonstrate a predominantly positive impact and considerable noise suppression capabilities. These improvements originate from the use of all available information by the MLE in conjunction with the expected physical bounds concerning positivity and the expected range of the lidar ratio. To consolidate and to illustrate the improvements, the new MLE algorithm is evaluated against the SCA on end-to-end simulations of two homogeneous scenes and for real Aeolus data collocated with measurements by a ground-based lidar and the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite. The largest improvements were seen in the retrieval precision of the extinction coefficients and lidar ratio ranging up to 1 order of magnitude or more in some cases due to effective noise dampening. In real data cases, the increased precision of MLE with respect to the SCA is demonstrated by increased horizontal homogeneity and better agreement with the ground truth, though proper uncertainty estimation of MLE results is challenged by the constraints, and the accuracy of MLE and SCA retrievals can depend on calibration errors, which have not been considered.

Generative adversarial network enables rapid and robust fluorescence lifetime image analysis in live cells

Fluorescence lifetime imaging microscopy (FLIM) is a powerful tool to quantify molecular compositions and study molecular states in complex cellular environment as the lifetime readings are not biased by fluorophore concentration or excitation power. However, the current methods to generate FLIM images are either computationally intensive or unreliable when the number of photons acquired at each pixel is low. Here we introduce a new deep learning-based method termed flimGANE (fluorescence lifetime imaging based on Generative Adversarial Network Estimation) that can rapidly generate accurate and high-quality FLIM images even in the photon-starved conditions. We demonstrated our model is up to 2,800 times faster than the gold standard time-domain maximum likelihood estimation (TD_MLE) and that flimGANE provides a more accurate analysis of low-photon-count histograms in barcode identification, cellular structure visualization, Förster resonance energy transfer characterization, and metabolic state analysis in live cells. With its advantages in speed and reliability, flimGANE is particularly useful in fundamental biological research and clinical applications, where high-speed analysis is critical.

Does the Type of Records Affect the Estimates of the Parameters?

The maximum likelihood estimation of the unknown parameters of inverse Rayleigh and exponential distributions are discussed based on lower and upper records. The aim is to study the effect of the type of records on the behavior of the corresponding estimators. Mean squared errors are calculated through simulation to study the behavior of the estimators. The results shall be of interest to those situations where the data can be obtained in the form of either of the two types of records and the experimenter must decide between these two for estimation of the unknown parameters of the distribution.