bayesian inference

Spectral induced polarization (SIP) is a useful tool in geophysical exploration for understanding the capacitive properties of materials beneath the surface. Unlike conventional methods, SIP analysis can be done in both the time domain and frequency domain. In the time domain, it measures the decay of electrical potential after transmitting a direct current pulse, while in the frequency domain, it measures the phase shift of an alternating current. The Cole-Cole model (CCM) is widely used to analyze SIP data, aiding in the comprehension of subsurface properties in different geological settings. Initially introduced by Cole and Cole (1941) and subsequently expanded upon by Pelton et al (1978), this model provides a description of the complex resistivity of materials. While initially developed for mineralized rock, CCM has been successfully adapted to characterize sedimentary formations lacking electronically conducting components. In such cases, the polarization arises from interactions between pore fluids and electrically charged mineral surfaces, forming an electric double layer. It is well established that frequency-dependent induced polarization measurements offer additional spectral information beyond a single measure of induced polarization amplitude, even though the universal mechanism is not fully understood. This spectral information, derived from the shape of the frequency response, can be linked to petrophysical and geochemical properties of the Earth’s subsurface, such as soil texture, water saturation, hydraulic conductivity, pH, and the dissemination of metallic minerals, through empirical relationships. In addition to advances in the fundamental understanding of induced polarization phenomena, the SIP method has seen significant progress and development across various research areas in recent years, including forward modeling, inversion, and equipment. However, the success of the SIP method is strongly dependent on providing a reliable and precise inversion algorithm aimed at retrieving the CCM parameters. Inverse problem theory refers to a mathematical framework that addresses the extraction of information about a parameterized physical system using observational data, theoretical relationships between model parameters and data (i.e., forward problem), and prior knowledge. To ensure accurate interpretation of the estimated models, it is crucial to understand the correlation between the parameters in the subsurface models. This research is significant because it explores the dependency and correlation of the CCM parameters using a Bayesian approach in a 2.5D inversion framework specifically designed for SIP data. The motivation for studying correlation analysis between model parameters arises from the challenges that high parameter correlation can pose to Markov chain Monte Carlo (McMC) sampling algorithms in probabilistic models. In other words, the objective is to enhance the understanding of subsurface properties and provide a more reliable interpretation of the estimated models by thoroughly analyzing parameter interdependencies. A novel 2.5D inversion code specifically developed for SIP data is introduced, leveraging Python-based libraries and advanced statistical methods. Through synthetic modeling and McMC sampling, the robustness of this approach across various subsurface scenarios is evaluated, including a homogeneous earth model, a two-layer medium, and a model featuring two anomalies within a homogeneous background. Our method enables the extraction of CCM parameters that reflect electrical properties, offering deeper insights into complex geological formations. Visualizations of McMC chains and corner plots effectively reveal the interdependencies among CCM parameters, illustrating the convergence and reliability of the parameter estimates. Validation against synthetic models highlights the precision and effectiveness of the proposed methodology. Overall, this study demonstrates the potential of Bayesian inversion to improve the interpretation of geophysical data and offers valuable insights into the correlation between CCM parameters across different geological environments.

Since the grade of elements in a mining area has spatial correlation, its statistical analysis is impossible with the usual statistical methods. Therefore, spatial statistics methods are used in their analysis to model the spatial correlation structure and predict the unknown grade values in arbitrary locations. For prediction, including dependence structures and trend following due to contextual factors (such as topography) helps improve the accuracy of response variable forecasting. In data analysis, the small number of observations, the presence of outlier observations, or data with a highly skewed distribution, causes an inaccurate estimation of the variogram. In this article, a Bayesian approach is used for the 3D modeling of the data, and an approximate Bayesian method known as Integrated Nested Laplace Approximations (INLA) is used to fit the proposed model. Since Geostatistical data are densely indexed, to ensure fast calculations using INLA, the spatial model defined on the study area was converted into a Gaussian Markov Random Field (GMRF) using triangulation and the Stochastic Partial Differential Equation (SPDE) approach. The implementation of the INLA+SPDE method on a 3D Geostatistical data set is a new topic in the field of mining data modeling.

The data obtained from observing a phenomenon over time is very common. One of the most popular models in time series and signal processing is the Autoregressive moving average model (ARMA). If the investigated time series has long memory, autoregressive fractional moving average model or in other words (ARFIMA), would be appropriate. The ARFIMA (p, d, q) model was first introduced by [1]. Classic methods for modeling, inference and estimating these processes lead to complex calculations of covariance structure and likelihood functions that make data processing difficult.Wavelet transform is one of the most powerful tools in analyzing such functions and best performs these functions from different time and location  perspectives as well as high and low frequencies. Wavelet transform due to the decreasing correlation property is a very efficient method in analysis and inference for estimating long-term memory processes.The values ​​obtained from wavelet transforms for long-term memory processes, in spite of the complex covariance structure of these processes, the wavelet coefficients are almost uncorrelated and thus much easier to handle [2]. The dense covariance structure of such processes makes it difficult to accurately calculate the maximum likelihood function of data sets [3]. In these cases, the Bayesian method can be easily used to calculate wavelet coefficients. In this paper, while briefly introducing wavelet transform in section two, the ARFIMA model and covariance matrix structure of this model is investigated in section three.  In section four, theBayesian estimation of ARFIMA parameters based on wavelets are calculated. At the end section, ‎we survey the theoretical outcomes with numerical computation by using simulation to described purpose estimation.

In this scheme, first we explain wavelet transformation, ARFIMA model and covariance matrix structure of this model. By using wavelet decomposition, Bayesian estimation of ARFIMA model parameters are calculated. The performance of purpose estimation is assessed with simulated data for comparing with respect to another estimators.

We discuss in detail wavelet transformation and autoregressive fractional  moving average model with long memory. The structure of covariance matrices of wavelet coefficients and Bayesian wavelet estimation of parameters are investigated.
At the end we used simulation study to examine our proposed estimation. Notice that, obtained results confirm that proposed estimation is better than another.

The following conclusions were drawn from this research.Wavelet transform due to the decreasing correlation property is very efficient method in estimating long-term memory processes.  The main purpose of this paper is to provide a new wavelet estimation of ARFIMA model parameters via Bayesian method.The main characteristic of this method is that it can be easily used and therefore many calculations are reduced.The proposed method can be applied for estimating of parameters in the simulation.According to the figures, we conclude   that Bayesian wavelet estimation of autoregressive process parameters is appropriate and better than with respect to other estimations.According to the table, by increasing the sample size, standard error of proposed estimator is decreased, so it was shown that the new proposed method is better with respect to others.

The instrumental variable (IV) regression is a common model in econometrics and other applied disciplines. This model is one of the proper candidate in dealing with endogeneity phenomenon which occurs in analyzing the multivariate regression when the errors are correlated with some covariates. One can consider IV regression as a special case of simultaneous equation models (SEM). There are some cases in which the normality assumption might not hold for the error term in these models and so the skew-normal distribution might be a suitable candidate. The present paper tackle the Bayesian inference based on Markov Chain Monte Carlo (MCMC) using this density for the error term while some instrumental variables are considered in the corresponding regression model. The proposed model is utilized to analysis the Iranian rural households income and expenditure collected in 2009.

The Exponentiated Gumbel (EG) distribution has been proposed to capture some aspects of the data that the Gumbel distribution fails to specify. In this paper, we estimate the EG's parameters in the Bayesian framework. We consider a 2-level hierarchical structure for prior distribution. As the posterior distributions do not admit a closed form, we do an approximated inference by using Gibbs and Metropolis-Hastings algorithm.

Longitudinal studies include the important parts of epidemiological surveys, clinical trials and social studies. In longitudinal studies, measurement of the responses is conducted repeatedly through time. Often, the main goal is to characterize the change in responses over time and the factors that influence the change. Recently, to analyze this kind of data, quantile regression has been taken into consideration. In this paper, quantile regression model, by adding an adaptive elastic net penalty term to the random effects, is proposed and analyzed from a Bayesian point of view. Since, in this model posterior distribution of the parameters are not in explicit form, the full conditional posterior distributions of the parameters are calculated and the Gibbs sampling algorithm is used for deduction. To compare the performance of the proposed method with the conventional methods, a simulation study was conducted and at the end, applications to a real data set are illustrated

In many medical studies، in order to describe the course of illness and treatment effects، longitudinal studies are used. In longitudinal studies، responses are measured frequently over time، but sometimes these responses are discrete and with two-state. Recently Binary quantile regression methods to analyze this kind of data have been taken into consideration. In this paper، quantile regression model with Lasso and adaptive Lasso penalty for longitudinal data with dichotomous responses is provided. Since in both methods posteriori distributions of the parameters are not in explicit form، thus the full conditional posteriori distributions of parameters are calculated and the Gibbs sampling algorithm is used to deduction. To compare the performance of the proposed methods with the conventional methods، a simulation study was conducted and at the end، applications to a real data set are illustrated.

In this paper، we study the applicability of probabilistic solutions for the alignment of tertiary structure of proteins and discuss its difference with the deterministic algorithms. For this purpose، we introduce two Bayesian models and address a solution to add amino acid sequence and type (primary structure) to protein alignment. Furthermore، we will study the parameter estimation with Markov Chain Monte Carlo sampling from the posterior distribution. Finally، in order to see the effectiveness of these methods in the protein alignment، we have compared the parameter estimations in a real data set.

There are several methods for inference about gene networks، but there are few cases in which the historical information have been considered. In this research we deal with Bayesian inference on gene network. We apply a Bayesian framework to use the available information. Assuming a proper prior distribution and taking the dependency of parameters into account، we seek a model to obtain promising results. We also deal with the hyper parameter estimation. Two methods are considered. The results will be compared by the use of a simulation based on Gibbs sampler. The strengths and weaknesses of each method are briefly mentioned.

Occurance of hazarious accident in nuclear power plants and industrial units usually lead to release of radioactive materials and pollutants in environment. These materials and pollutants can be transported to a far downstream by the wind flow. In this paper, we implemented an atmospheric dispersion code to solve the inverse problem. Having received and detected the pollutants in one region, we may estimate the rate and location of the unknown source. For the modeling, one needs a model with ability of atmospheric dispersion calculation. Furthermore, it is required to implement a mathematical approach to infer the source location and the related rates. In this paper the AERMOD software and Bayesian inference along the Markov Chain Monte Carlo have been applied. Implementing, Bayesian approach and Markov Chain Monte Carlo for the aforementioned subject is not a new approach, but the AERMOD model coupled with the said methods is a new and well known regulatory software, and enhances the reliability of outcomes. To evaluate the method, an example is considered by defining pollutants concentration in a specific region and then obtaining the source location and intensity by a direct calculation. The result of the caluclation estimates the average source location at a distance of 7km with an accuracy of 5m which is good enough to support the ability of the proposed algorithm.

In this article, we are going to interpret one of the queueing systems with a single server that has general and unknown distribution for the service and interarrival time using Bayesian view point.These General distributions may be well approximated by family of Mixed General Erlang distribution (MGE). This distribution is reparametrized such that it is possible to define a non-informative prior which allows using the MCMC method for estimating the parameters of models.Using the results of simulating parameters, we can estimate interesting measures that are based on recent results for known parameters in GI/G/1 frequently implemented queueing systems. At the end, we illustrate our approach for analyzing GI/G/1 systems with data from a bank.

Today, the predictive results of sporting events have become an important issue. Meanwhile, soccer is of particular importance in Iran and the need for a model that, not only can predict the result of a game, but also can predict the result of an entire league, is felt. Therefore, this paper attempts to present a statistical model for responding to this need by using Bayesian methods. Here, Poisson regression model is first introduced and then is used to obtain estimates of model parameters, using WinBUGS software. Finally, the model is used to fit on the data of the Iranian Premier League during the year 1388-89.