Maximum Log-likelihood Method Research Articles

Financial efficiency analysis of Hungarian agriculture, fisheries and forestry sector

In this study, we examine the efficiency of companies in Hungary's agriculture, fisheries and forestry sector. We analysed corporate efficiency by using stochastic frontier analysis (SFA). We used two methods to perform the SFA calculations – the Cobb-Douglas and translog functions. The result variable for the SFA calculation was gross value added (GVA), and the explanatory variables were tangibles, material costs, employee costs and other costs. The original database contained cross-sectional and time series data and was transformed into a panel database. We used the maximum log-likelihood method for parameter estimation. We performed the efficiency analysis in the case of the Cobb-Douglas and translog functions in two ways – first, without z variables (factor effects) and second, considering different factors (subsectors, workforce categories, ranking by total assets and ranking by total sales). Taking z variables into account increased the value of the efficiency coefficients. The latter model's results show that the companies' average performance in the sector examined was more than 70%. Further calculations also showed that the subsectors of the agriculture, fisheries and forestry sector differed in efficiency scores. The larger companies operated more efficiently than the smaller ones in the sector examined.

Finding acceptable parameter regions of stochastic Hill functions for multisite phosphorylation mechanism.

Multisite phosphorylation plays an important role in regulating switch-like protein activity and has been used widely in mathematical models. With the development of new experimental techniques and more molecular data, molecular phosphorylation processes emerge in many systems with increasing complexity and sizes. These developments call for simple yet valid stochastic models to describe various multisite phosphorylation processes, especially in large and complex biochemical networks. To reduce model complexity, this work aims at simplifying the multisite phosphorylation mechanism by a stochastic Hill function model. Furthermore, this work optimizes regions of parameter space to match simulation results from the stochastic Hill function with the distributive multisite phosphorylation process. While traditional parameter optimization methods have been focusing on finding the best parameter vector, in most circumstances, modelers would like to find a set of parameter vectors that generate similar system dynamics and results. This paper proposes a general α-β-γ rule to return an acceptable parameter region of the stochastic Hill function based on a quasi-Newton stochastic optimization algorithm. Different objective functions are investigated characterizing different features of the simulation-based empirical data, among which the approximate maximum log-likelihood method is recommended for general applications. Numerical results demonstrate that with an appropriate parameter vector value, the stochastic Hill function model depicts the multisite phosphorylation process well except the initial (transient) period.

Multivariate group-level analysis for task fMRI data with canonical correlation analysis

Task-based functional Magnetic Resonance Imaging (fMRI) has been widely used to determine population-based brain activations for cognitive tasks. Popular group-level analysis in fMRI is based on the general linear model and constitutes a univariate method. However, univariate methods are known to suffer from low sensitivity for a given specificity because the spatial covariance structure at each voxel is not taken entirely into account. In this study, a spatially constrained local multivariate model is introduced for group-level analysis to improve sensitivity at a given specificity for activation detection. The proposed model is formulated in terms of a multivariate constrained optimization problem based on the maximum log likelihood method and solved efficiently with numerical optimization techniques. Both simulated data mimicking real fMRI time series at multiple noise fractions and real fMRI episodic memory data have been used to evaluate the performance of the proposed method. For simulated data, the area under the receiver operating characteristic curves in detecting group activations increases for the subject and group level multivariate method by 20%, as compared to the univariate method. Results from real fMRI data indicate a significant increase in group-level activation detection, particularly in hippocampus, para-hippocampal area and nearby medial temporal lobe regions with the proposed method.

Deep learning algorithm for data-driven simulation of noisy dynamical system

We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Short-Term Memory (LSTM) network. It is shown that, when the numerical discretization is used, the function estimation problem can be solved by a multi-label classification problem. A penalized maximum log likelihood method is proposed to impose a smoothness condition in the prediction of the probability distribution. We show that the time evolution of the probability distribution can be computed by a high-dimensional integration of the transition probability of the LSTM internal states. A Monte Carlo algorithm to approximate the high-dimensional integration is outlined. The behavior of DE-LSTM is thoroughly investigated by using the Ornstein–Uhlenbeck process and noisy observations of nonlinear dynamical systems; Mackey–Glass time series and forced Van der Pol oscillator. It is shown that DE-LSTM makes a good prediction of the probability distribution without assuming any distributional properties of the stochastic process. For a multiple-step forecast of the Mackey–Glass time series, the prediction uncertainty, denoted by the 95% confidence interval, first grows, then dynamically adjusts following the evolution of the system, while in the simulation of the forced Van der Pol oscillator, the prediction uncertainty does not grow in time even for a 3,000-step forecast.

Calibration of the exponential Ornstein\u2013Uhlenbeck process when spot prices are visible through the maximum log-likelihood method. Example with gold prices

The purpose of this paper is to present a methodological procedure to estimate the parameters of the exponential Ornstein–Uhlenbeck process, also known as the Schwartz (J. Finance 52(3):923–973, 1997) one-factor model, in situations where the spot price of the commodity is observable. The proposal consists of looking at the probability function of the process as a function of the unknown parameters in discrete time, known as the likelihood function. Then the logarithm of that expression is calculated as it is easier to work with it. Finally, the problem of determining the values of the parameters that maximize the sum of the individual log-likelihoods (joint log-likelihood function) is solved to obtain the estimation equations explicitly. In that sense, this work is relevant because as spot prices are available, it is possible to estimate the parameters directly without the necessity of using more elaborate approaches like the Kalman filter. Finally, the paper applies this methodology to the concrete case of one precious metal that has an observable spot price and for which some empirical and theoretical studies suggest that it presents a mean-reverting pattern, gold. The estimated parameters are consistent with previous works and with the original data and the least squares method.

Regularization of Mars Reconnaissance Orbiter CRISM along‐track oversampled hyperspectral imaging observations of Mars

Mars Reconnaissance Orbiter Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) hyperspectral image data have been acquired in an along-track oversampled (ATO) mode with the intent of processing the data to better than the nominal ∼18m/pixel ground resolution. We have implemented an iterative maximum log-likelihood method (MLM) that utilizes the instrument spectral and spatial transfer functions and includes a penalty function to regularize the data. Products are produced both in sensor space and as projected hyperspectral image cubes at 12m/pixel. Preprocessing steps include retrieval of surface single scattering albedos (SSA) using the Hapke Function and DISORT-based radiative modeling of atmospheric gases and aerosols. Resultant SSA cubes are despiked to remove extrema and tested to ensure that the remaining data are Poisson-distributed, an underlying assumption for the MLM algorithm implementation. Two examples of processed ATO data sets are presented. ATO0002EC79 covers the route taken by the Curiosity rover during its initial ascent of Mount Sharp in Gale Crater. SSA data are used to model mineral abundances and grain sizes predicted to be present in the Namib barchan sand dune sampled and analyzed by Curiosity. CRISM based results compare favorably to in situ results derived from Curiosity's measurement campaign. ATO0002DDF9 covers Marathon Valley on the Cape Tribulation rim segment of Endeavour Crater. SSA spectra indicate the presence of a minor component of Fe3+ and Mg2+ smectites on the valley floor and walls. Localization to 12m/pixel provided the detailed spatial information needed for the Opportunity rover to traverse to and characterize those outcrops that have the deepest absorptions. The combination of orbital and rover-based data show that the smectite-bearing outcrops in Marathon Valley are impact breccias that are basaltic in composition and that have been isochemically altered in a low water to rock environment.

Analysis of the observed and intrinsic durations of gamma-ray bursts with known redshift

The duration distribution of 408 GRBs with measured both duration $T_{90}$ and redshift $z$ is examined. Mixtures of a number of distributions (standard normal, skew-normal, sinh-arcsinh, and alpha-skew-normal) are fitted to the observed and intrinsic durations using the maximum log-likelihood method. The best fit is chosen via the Akaike information critetion. The aim of this work is to assess the presence of the presumed intermediate GRB class, and to provide a phenomenological model more appropriate than the common mixture of standard Gaussians. While $\log T^{obs}_{90}$ are well described by a truly trimodal fit, after moving to the rest frame the statistically most significant fit is unimodal. To trace the source of this discrepancy, 334 GRBs observed only by $Swift$/BAT are examined in the same way. In the observer frame, this results in a number of statistically plausible descriptions, being uni- and bimodal, and with the number of components ranging from one to three. After moving to the rest frame, no unambiguous conclusions may be put forward. It is concluded that the size of the sample is not big enough to infer reliably GRB properties based on a univariate statistical reasoning only.

Analysis of the observed and intrinsic durations of Swift/BAT gamma-ray bursts

The duration distribution of 947 GRBs observed by Swift/BAT, as well as its subsample of 347 events with measured redshift, allowing to examine the durations in both the observer and rest frames, are examined. Using a maximum log-likelihood method, mixtures of two and three standard Gaussians are fitted to each sample, and the adequate model is chosen based on the value of the difference in the log-likelihoods, Akaike information criterion and Bayesian information criterion. It is found that a two-Gaussian is a better description than a three-Gaussian, and that the presumed intermediate-duration class is unlikely to be present in the Swift duration data.

Modeling of Kashmir Aftershock Decay Based on Static Coulomb Stress Changes and Laboratory-Derived Rate-and-State Dependent Friction Law

We model the spatial and temporal evolution of October 8, 2005 Kashmir earthquake’s aftershock activity using the rate-and-state dependent friction model incorporating uncertainties in computed coseismic stress perturbations. We estimated the best possible value for frictional resistance “Aσ n”, background seismicity rate “r” and coefficient of stress variation “CV” using maximum log-likelihood method. For the whole Kashmir earthquake sequence, we measure a frictional resistance Aσ n ~ 0.0185 MPa, r ~ 20 M3.7+ events/year and CV = 0.94 ± 0.01. The spatial and temporal forecasted seismicity rate of modeled aftershocks fits well with the spatial and temporal distribution of observed aftershocks that occurred in the regions with positive static stress changes as well as in the apparent stress shadow region. To quantify the effect of secondary aftershock triggering, we have re-run the estimations for 100 stochastically declustered catalogs showing that the effect of aftershock-induced secondary stress changes is obviously minor compared to the overall uncertainties, and that the stress variability related to uncertain slip model inversions and receiver mechanisms remains the major factor to provide a reasonable data fit.

Robust logistic regression modelling via the elastic net-type regularization and tuning parameter selection

The penalized logistic regression is a useful tool for classifying samples and feature selection. Although the methodology has been widely used in various fields of research, their performance takes a sudden turn for the worst in the presence of outlier, since the logistic regression is based on the maximum log-likelihood method which is sensitive to outliers. It implies that we cannot accurately classify samples and find important factors having crucial information for classification. To overcome the problem, we propose a robust penalized logistic regression based on a weighted likelihood methodology. We also derive an information criterion for choosing the tuning parameters, which is a vital matter in robust penalized logistic regression modelling in line with generalized information criteria. We demonstrate through Monte Carlo simulations and real-world example that the proposed robust modelling strategies perform well for sparse logistic regression modelling even in the presence of outliers.

INFLATION, INFLATION UNCERTAINTY AND GROWTH IN THE IRANIAN ECONOMY: AN APPLICATION OF BGARCH-M MODEL WITH BEKK APPROACH

This paper investigates the relationship between inflation, economic growth and their respective uncertainties in Iran for the period of 1988–2008 by using quarterly data. We employ a Bivariate Generalized Autoregressive Conditional Heteroskedasticity-in-Mean (BGARCH-M) model to examine in a unified empirical framework all the possible interactions between inflation uncertainty and growth in Iran. The model is simultaneously estimated by using the maximum log-likelihood method with the BEKK approach. The main findings of the present study are: (1) Inflation causes inflation uncertainty, supporting the Friedman-Ball hypothesis. (2) Inflation uncertainty affects the level of economic growth, supporting the Friedman (1977) hypothesis. (3) Growth uncertainty does not affect the level of economic growth, supporting the Friedman (1968) hypothesis. (4) And finally our empirical evidence shows that growth uncertainty affects the level of inflation, supporting the Deveraux (1989) hypothesis.

Using age-structured models to develop a stock recovery strategy for Kuwait's shrimp fishery

Shrimps are the most important fisheries resources in Kuwait. Shrimp resources have been decreasing due mostly to over-fishing. For protection of Kuwait's shrimp resources and to encourage a sustainable shrimp fishery, age-structured models were used to develop a stock recovery strategy. Age-structured models, including a modified Beverton–Holt stock–recruitment relationship, growth function and equations for catch-at-age analysis were used to fit the fisheries data from 1965 to 2004 and estimate four parameters: a, b and ɛ from the modified Beverton–Holt equation and the catchability q. The model fitting was conducted through comparing the estimated catches with the observed catches using the maximum log-likelihood method. The results showed a declining trend for both the recruitment and biomass before and after the 1991 Gulf War. The estimated maximum sustainable yield (MSY) for Kuwait's shrimp fishery is 2298 t with a corresponding fishing effort ( f MSY) of 9730 boat-days using a median natural mortality 2.9 per year. The model fitting with different natural mortalities and catchabilities showed that both parameters had limited effects on the MSY and f MSY. The trends in recruitment, biomass, catch and catch-per-unit-effort (CPUE) to year 2020 under different fishing effort were simulated by the fitted models. The simulations demonstrated that reducing the fishing effort will only slightly decrease the catch, but increase the recruitment, greatly increase biomass, and CPUE. Increasing the fishing effort, however, will result in a decline of recruitment, biomass, catch, and CPUE. The simulations also showed different season opening dates and duration affect the fishery. Delaying the season opening or advancing the close date will increase MSY and f MSY and reduce CPUE. While opening earlier and closing later will reduce the MSY, f MSY and increase the CPUE. We suggested that a good season management strategy should balance the high MSY, CPUE values and the size (price) of the shrimp catch. Based on the model fitting and simulation results, a management strategy to recover the shrimp stock was provided.

The V73M mutation in the hepatic lipase gene is associated with elevated cholesterol levels in four Dutch pedigrees with familial combined hyperlipidemia

Familial combined hyperlipidemia (FCHL) is a heritable lipid disorder characterized by multiple lipoprotein phenotypes within a single family. Previously, we have shown an increased incidence of mutations in the LPL gene which was associated with elevated levels of very low density lipoprotein (VLDL) and decreased levels of high density lipoprotein among the families studied. Now, we report the results of our study on the hepatic lipase gene. We found the HL V73M variant to be present in four FCHL families. By means of a pedigree-based maximum log-likelihood method we analyzed the effect of this variant on the lipid levels in these families. Carriers of the HL V73M variant revealed significantly higher levels of total cholesterol ( P<0.01) and apoB ( P<0.01). These findings show that the HL V73M mutant explains another part of the variability in the phenotype observed among FCHL family members, compared with mutations in the LPL gene. Family analysis shows that in these FCHL families, carriers of mutations in the LPL or HL genes have an increased risk for FCHL compared with their non-carrier relatives.