Search results for: Bayesian methods

Authors: Linda Smail, Zineb Azouz

Abstract:

Given a Bayesian network relative to a set I of discrete random variables, we are interested in computing the probability distribution P(S) where S is a subset of I. The general idea is to write the expression of P(S) in the form of a product of factors where each factor is easy to compute. More importantly, it will be very useful to give an interpretation of each of the factors in terms of conditional probabilities. This paper considers a semantic interpretation of the factors involved in computing marginal probabilities in Bayesian networks. Establishing such a semantic interpretations is indeed interesting and relevant in the case of large Bayesian networks.

Keywords: Bayesian networks, D-Separation, level two Bayesian networks, factorization of computation

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Authors: Georgiana Onicescu, Yuqian Shen

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Due to the complex nature of geo-referenced data, multicollinearity of the risk factors in public health spatial studies is a commonly encountered issue, which leads to low parameter estimation accuracy because it inflates the variance in the regression analysis. To address this issue, we proposed a two-stage variable selection method by extending the least absolute shrinkage and selection operator (Lasso) to the Bayesian spatial setting, investigating the impact of risk factors to health outcomes. Specifically, in stage I, we performed the variable selection using Bayesian Lasso and several other variable selection approaches. Then, in stage II, we performed the model selection with only the selected variables from stage I and compared again the methods. To evaluate the performance of the two-stage variable selection methods, we conducted a simulation study with different distributions for the risk factors, using geo-referenced count data as the outcome and Michigan as the research region. We considered the cases when all candidate risk factors are independently normally distributed, or follow a multivariate normal distribution with different correlation levels. Two other Bayesian variable selection methods, Binary indicator, and the combination of Binary indicator and Lasso were considered and compared as alternative methods. The simulation results indicated that the proposed two-stage Bayesian Lasso variable selection method has the best performance for both independent and dependent cases considered. When compared with the one-stage approach, and the other two alternative methods, the two-stage Bayesian Lasso approach provides the highest estimation accuracy in all scenarios considered.

Keywords: Lasso, Bayesian analysis, spatial analysis, variable selection

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Authors: Davood Shishebori, Mohammad Saber Fallah Nezhad, Sina Seifi

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In this paper, a variable multiple dependent state (MDS) sampling plan is developed based on the process capability index using Bayesian approach. The optimal parameters of the developed sampling plan with respect to constraints related to the risk of consumer and producer are presented. Two comparison studies have been done. First, the methods of double sampling model, sampling plan for resubmitted lots and repetitive group sampling (RGS) plan are elaborated and average sample numbers of the developed MDS plan and other classical methods are compared. A comparison study between the developed MDS plan based on Bayesian approach and the exact probability distribution is carried out.

Keywords: MDS sampling plan, RGS plan, sampling plan for resubmitted lots, process capability index (PCI), average sample number (ASN), Bayesian approach

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Authors: Mohammad Anwar, Shah Waliullah

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This study investigated panel data regression models. This paper used Bayesian and classical methods to study the impact of institutions on economic growth from data (1990-2014), especially in developing countries. Under the classical and Bayesian methodology, the two-panel data models were estimated, which are common effects and fixed effects. For the Bayesian approach, the prior information is used in this paper, and normal gamma prior is used for the panel data models. The analysis was done through WinBUGS14 software. The estimated results of the study showed that panel data models are valid models in Bayesian methodology. In the Bayesian approach, the effects of all independent variables were positively and significantly affected by the dependent variables. Based on the standard errors of all models, we must say that the fixed effect model is the best model in the Bayesian estimation of panel data models. Also, it was proved that the fixed effect model has the lowest value of standard error, as compared to other models.

Keywords: Bayesian approach, common effect, fixed effect, random effect, Dynamic Random Effect Model

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Authors: Al Omari Moahmmed Ahmed

Abstract:

In the Bayesian, we developed an approach by using non-informative prior with covariate and obtained by using Gauss quadrature method to estimate the parameters of the covariate and reliability function of the Weibull regression distribution with Type-I censored data. The maximum likelihood seen that the estimators obtained are not available in closed forms, although they can be solved it by using Newton-Raphson methods. The comparison criteria are the MSE and the performance of these estimates are assessed using simulation considering various sample size, several specific values of shape parameter. The results show that Bayesian with non-informative prior is better than Maximum Likelihood Estimator.

Keywords: non-informative prior, Bayesian method, type-I censoring, Gauss quardature

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

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In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.

Keywords: human action recognition, Bayesian HMM, Dirichlet process mixture model, Gaussian-Wishart emission model, Variational Bayesian inference, prior distribution and approximate posterior distribution, KTH dataset

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Authors: Viliam Makis, Farnoosh Naderkhani, Leila Jafari

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In this paper, we present a model and an algorithm for the calculation of the optimal control limit, average cost, sample size, and the sampling interval for an optimal Bayesian chart to control the proportion of defective items produced using a semi-Markov decision process approach. Traditional p-chart has been widely used for controlling the proportion of defectives in various kinds of production processes for many years. It is well known that traditional non-Bayesian charts are not optimal, but very few optimal Bayesian control charts have been developed in the literature, mostly considering finite horizon. The objective of this paper is to develop a fast computational algorithm to obtain the optimal parameters of a Bayesian p-chart. The decision problem is formulated in the partially observable framework and the developed algorithm is illustrated by a numerical example.

Keywords: Bayesian control chart, semi-Markov decision process, quality control, partially observable process

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Authors: Al Omari Moahmmed Ahmed

Abstract:

These papers describe the Bayesian Estimator using Markov Chain Monte Carlo and Lindley’s approximation and the maximum likelihood estimation of the Weibull distribution with Type-I censored data. The maximum likelihood method can’t estimate the shape parameter in closed forms, although it can be solved by numerical methods. Moreover, the Bayesian estimates of the parameters, the survival and hazard functions cannot be solved analytically. Hence Markov Chain Monte Carlo method and Lindley’s approximation are used, where the full conditional distribution for the parameters of Weibull distribution are obtained via Gibbs sampling and Metropolis-Hastings algorithm (HM) followed by estimate the survival and hazard functions. The methods are compared to Maximum Likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the better method in scale and shape parameters, the survival and hazard functions.

Keywords: weibull distribution, bayesian method, markov chain mote carlo, survival and hazard functions

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Authors: Chawarat Rotejanaprasert, Andrew Lawson

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Early detection of unusual health events depends on the ability to detect rapidly any substantial changes in disease, thus facilitating timely public health interventions. To assist public health practitioners to make decisions, statistical methods are adopted to assess unusual events in real time. We introduce a surveillance Kullback-Leibler (SKL) measure for timely detection of disease outbreaks for small area health data. The detection methods are compared with the surveillance conditional predictive ordinate (SCPO) within the framework of Bayesian hierarchical Poisson modeling and applied to a case study of a group of respiratory system diseases observed weekly in South Carolina counties. Properties of the proposed surveillance techniques including timeliness and detection precision are investigated using a simulation study.

Keywords: Bayesian, spatial, temporal, surveillance, prospective

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Authors: Golnaz Shahtahmassebi, Jose Maria Sarabia

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In this talk, we introduce a new class of conjugate prior distributions obtained from conditional specification methodology. We illustrate the application of such distribution in Bayesian change point detection in Poisson processes. We obtain the posterior distribution of model parameters using a general bivariate distribution with gamma conditionals. Simulation from the posterior is readily implemented using a Gibbs sampling algorithm. The Gibbs sampling is implemented even when using conditional densities that are incompatible or only compatible with an improper joint density. The application of such methods will be demonstrated using examples of simulated and real data.

Keywords: change point, bayesian inference, Gibbs sampler, conditional specification, gamma conditional distributions

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Authors: Darren Zou

Abstract:

Forecasting the stock market is a very challenging task. Various economic indicators such as GDP, exchange rates, interest rates, and unemployment have a substantial impact on the stock market. Time series models are the traditional methods used to predict stock market changes. In this paper, a machine learning method, Bayesian Additive Regression Tree (BART) is used in predicting stock market indexes based on multiple economic indicators. BART can be used to model heterogeneous treatment effects, and thereby works well when models are misspecified. It also has the capability to handle non-linear main effects and multi-way interactions without much input from financial analysts. In this research, BART is proposed to provide a reliable prediction on day-to-day stock market activities. By comparing the analysis results from BART and with time series method, BART can perform well and has better prediction capability than the traditional methods.

Keywords: BART, Bayesian, predict, stock

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Authors: Said Ali Al-Hadhrami, Amer Ibrahim Al-Omari

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In this paper, Bayesian estimation for the mean of exponential distribution is considered using Moving Extremes Ranked Set Sampling (MERSS). Three priors are used; Jeffery, conjugate and constant using MERSS and Simple Random Sampling (SRS). Some properties of the proposed estimators are investigated. It is found that the suggested estimators using MERSS are more efficient than its counterparts based on SRS.

Keywords: Bayesian, efficiency, moving extreme ranked set sampling, ranked set sampling

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Authors: Ersin Sener, Ibrahim Demir, Hasan Aykut Karaboga, Kadir Kilinc

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Bayesian methods, which have very wide range of applications, are implemented to the data obtained from the production of F class fly ash-based geopolymer bricks’ experimental design. In this study, dependent variable is compressive strength, independent variables are treatment type (oven and steam), treatment time, molding time, temperature, water absorbtion ratio and density. The effect of independent variables on compressive strength is investigated. There is no difference among treatment types, but there is a correlation between independent variables. Therefore, hierarchical Bayesian path analysis is applied. In consequence of analysis we specified that treatment time, temperature and density effects on compressive strength is higher, molding time, and water absorbtion ratio is relatively low.

Keywords: experimental design, F class fly ash, geopolymer bricks, hierarchical Bayesian path analysis

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Authors: Zhidong Zhang

Abstract:

This study established a mixed method model in assessing statistics learning with Bayesian network models. There are three variants in exploratory sequential designs. There are three linked steps in one of the designs: qualitative data collection and analysis, quantitative measure, instrument, intervention, and quantitative data collection analysis. The study used a scoring model of analysis of variance (ANOVA) as a content domain. The research study is to examine students’ learning in both semantic and performance aspects at fine grain level. The ANOVA score model, y = α+ βx1 + γx1+ ε, as a cognitive task to collect data during the student learning process. When the learning processes were decomposed into multiple steps in both semantic and performance aspects, a hierarchical Bayesian network was established. This is a theory-driven process. The hierarchical structure was gained based on qualitative cognitive analysis. The data from students’ ANOVA score model learning was used to give evidence to the hierarchical Bayesian network model from the evidential variables. Finally, the assessment results of students’ ANOVA score model learning were reported. Briefly, this was a mixed method research design applied to statistics learning assessment. The mixed methods designs expanded more possibilities for researchers to establish advanced quantitative models initially with a theory-driven qualitative mode.

Keywords: exploratory sequential design, ANOVA score model, Bayesian network model, mixed methods research design, cognitive analysis

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Authors: Mohamed Raouf Benmakrelouf, Wafa Karouche, Joseph Rynkiewicz

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In this paper, we propose an alternative method to construct a Bayesian Network (BN). This method relies on a convolutional neural network (CNN classifier), which determinates the edges of the network skeleton. We train a CNN on a normalized empirical probability density distribution (NEPDF) for predicting causal interactions and relationships. We have to find the optimal Bayesian network structure for causal inference. Indeed, we are undertaking a search for pair-wise causality, depending on considered causal assumptions. In order to avoid unreasonable causal structure, we consider a blacklist and a whitelist of causality senses. We tested the method on real data to assess the influence of education on the voting intention for the extreme right-wing party. We show that, with this method, we get a safer causal structure of variables (Bayesian Network) and make to identify a variable that satisfies the backdoor criterion.

Keywords: Bayesian network, structure learning, optimal search, convolutional neural network, causal inference

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Authors: P. Kooche Baghy, S. Eskandari, E.javanmard

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Neural network has been used as a predictive means of cold rolling force in this dissertation. Thus, imposed average force on rollers as a mere input and five pertaining parameters to its as a outputs are regarded. According to our study, feed-forward multilayer perceptron network has been selected. Besides, Bayesian algorithm based on the feed-forward back propagation method has been selected due to noisy data. Further, 470 out of 585 all tests were used for network learning and others (115 tests) were considered as assessment criteria. Eventually, by 30 times running the MATLAB software, mean error was obtained 3.84 percent as a criteria of network learning. As a consequence, this the mentioned error on par with other approaches such as numerical and empirical methods is acceptable admittedly.

Keywords: artificial neural network, Bayesian, cold rolling, force evaluation

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Authors: Redouane Tlemsani, Redouane, Belkacem Kouninef, Abdelkader Benyettou

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In this paper, our system is a Markovien system which we can see it like a Dynamic Bayesian Networks. One of the major interests of these systems resides in the complete training of the models (topology and parameters) starting from training data. The Bayesian Networks are representing models of dubious knowledge on complex phenomena. They are a union between the theory of probability and the graph theory in order to give effective tools to represent a joined probability distribution on a set of random variables. The representation of knowledge bases on description, by graphs, relations of causality existing between the variables defining the field of study. The theory of Dynamic Bayesian Networks is a generalization of the Bayesians networks to the dynamic processes. Our objective amounts finding the better structure which represents the relationships (dependencies) between the variables of a dynamic bayesian network. In applications in pattern recognition, one will carry out the fixing of the structure which obliges us to admit some strong assumptions (for example independence between some variables).

Keywords: Arabic on line character recognition, dynamic Bayesian network, pattern recognition, networks

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Authors: Ana Staneva, Vessela Stoimenova

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A parametric estimation of the MBP with Power Series offspring distribution family is considered in this paper. The MLE for the parameters is obtained in the case when the observable data are incomplete and consist only with the generation sizes of the family tree of MBP. The parameter estimation is calculated by using the Monte Carlo EM algorithm. The estimation for the posterior distribution and for the offspring distribution parameters are calculated by using the Bayesian approach and the Gibbs sampler. The article proposes various examples with bivariate branching processes together with computational results, simulation and an implementation using R.

Keywords: Bayesian, branching processes, EM algorithm, Gibbs sampler, Monte Carlo methods, statistical estimation

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Authors: B. Zerouali, M. Kara, B. Hamaidi, H. Mahdjoub, S. Rouabhia

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In this paper, a safety analysis for crude oil tanks to prevent undesirable events that may cause catastrophic accidents. The estimation of the probability of damage to industrial systems is carried out through a series of steps, and in accordance with a specific methodology. In this context, this work involves developing an assessment tool and risk analysis at the level of crude oil tanks system, based primarily on identification of various potential causes of crude oil tanks fire and explosion by the use of Fault Tree Analysis (FTA), then improved risk modelling by Bayesian Networks (BNs). Bayesian approach in the evaluation of failure and quantification of risks is a dynamic analysis approach. For this reason, have been selected as an analytical tool in this study. Research concludes that the Bayesian networks have a distinct and effective method in the safety analysis because of the flexibility of its structure; it is suitable for a wide variety of accident scenarios.

Keywords: bayesian networks, crude oil tank, fault tree, prediction, safety

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Authors: Xupin Zhang, Maria Caterina Bramati, Enrest Fokoue

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Understanding the career placement of graduates from the university is crucial for both the qualities of education and ultimate satisfaction of students. In this research, we adapt the capabilities of dynamic Bayesian networks to characterize and predict students’ job placement using data from various universities. We also provide elements of the estimation of the indicator (score) of the strength of the network. The research focuses on overall findings as well as specific student groups including international and STEM students and their insight on the career path and what changes need to be made. The derived Bayesian network has the potential to be used as a tool for simulating the career path for students and ultimately helps universities in both academic advising and career counseling.

Keywords: dynamic bayesian networks, indicator estimation, job placement, social networks

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Authors: Endeshaw Assefa Derso, Maria Gabriella Campolo, Angela Alibrandi

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Objectives:Early childhood malnutrition can have long-term and irreversible effects on a child's health and development. This study uses the Bayesian method with spatial variation to investigate the flexible trends of metrical covariates and to identify communities at high risk of injury. Methods: Cross-sectional data on underweight are collected from the 2016 Ethiopian Demographic and Health Survey (EDHS). The Bayesian geo-additive model is performed. Appropriate prior distributions were provided for scall parameters in the models, and the inference is entirely Bayesian, using Monte Carlo Markov chain (MCMC) stimulation. Results: The results show that metrical covariates like child age, maternal body mass index (BMI), and maternal age affect a child's underweight non-linearly. Lower and higher maternal BMI seem to have a significant impact on the child’s high underweight. There was also a significant spatial heterogeneity, and based on IDW interpolation of predictive values, the western, central, and eastern parts of the country are hotspot areas. Conclusion: Socio-demographic and community- based programs development should be considered compressively in Ethiopian policy to combat childhood underweight malnutrition.

Keywords: bayesX, Ethiopia, malnutrition, MCMC, semi-parametric bayesian analysis, spatial distribution, P- splines

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Authors: Farouk Metiri, Halim Zeghdoudi, Mohamed Riad Remita

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Credibility theory is an experience rating technique in actuarial science which can be seen as one of quantitative tools that allows the insurers to perform experience rating, that is, to adjust future premiums based on past experiences. It is used usually in automobile insurance, worker's compensation premium, and IBNR (incurred but not reported claims to the insurer) where credibility theory can be used to estimate the claim size amount. In this study, we focused on a popular tool in credibility theory which is the Bayesian premium estimator, considering Lindley distribution as a claim distribution. We derive this estimator under entropy loss which is asymmetric and squared error loss which is a symmetric loss function with informative and non-informative priors. In a purely Bayesian setting, the prior distribution represents the insurer’s prior belief about the insured’s risk level after collection of the insured’s data at the end of the period. However, the explicit form of the Bayesian premium in the case when the prior is not a member of the exponential family could be quite difficult to obtain as it involves a number of integrations which are not analytically solvable. The paper finds a solution to this problem by deriving this estimator using numerical approximation (Lindley approximation) which is one of the suitable approximation methods for solving such problems, it approaches the ratio of the integrals as a whole and produces a single numerical result. Simulation study using Monte Carlo method is then performed to evaluate this estimator and mean squared error technique is made to compare the Bayesian premium estimator under the above loss functions.

Keywords: bayesian estimator, credibility theory, entropy loss, monte carlo simulation

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Authors: Vahid Bayrami Rad

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In this research, common methods and techniques have been investigated with a focus on intelligent fault finding and monitoring systems in the oil industry. In fact, remote and intelligent control methods are considered a necessity for implementing various operations in the oil industry, but benefiting from the knowledge extracted from countless data generated with the help of data mining algorithms. It is a avoid way to speed up the operational process for monitoring and troubleshooting in today's big oil companies. Therefore, by comparing data mining algorithms and checking the efficiency and structure and how these algorithms respond in different conditions, The proposed (Bayesian) algorithm using data clustering and their analysis and data evaluation using a colored Petri net has provided an applicable and dynamic model from the point of view of reliability and response time. Therefore, by using this method, it is possible to achieve a dynamic and consistent model of the remote control system and prevent the occurrence of leakage in oil pipelines and refineries and reduce costs and human and financial errors. Statistical data The data obtained from the evaluation process shows an increase in reliability, availability and high speed compared to other previous methods in this proposed method.

Keywords: wireless sensors, petroleum equipment troubleshooting, Bayesian algorithm, colored Petri net, rapid miner, data mining-reliability

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Authors: Ching Louis Liu, Edmund Kazmierczak, Tim Miller

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Safety analysis for multi-agent systems is complicated by the, potentially nonlinear, interactions between agents. This paper proposes a method for analyzing the safety of multi-agent systems by explicitly focusing on interactions and the accident data of systems that are similar in structure and function to the system being analyzed. The method creates a Bayesian network using the accident data from similar systems. A feature of our method is that the events in accident data are labeled with HAZOP guide words. Our method uses an Ontology to abstract away from the details of a multi-agent implementation. Using the ontology, our methods then constructs an “Interaction Map,” a graphical representation of the patterns of interactions between agents and other artifacts. Interaction maps combined with statistical data from accidents and the HAZOP classifications of events can be converted into a Bayesian Network. Bayesian networks allow designers to explore “what it” scenarios and make design trade-offs that maintain safety. We show how to use the Bayesian networks, and the interaction maps to improve multi-agent system designs.

Keywords: multi-agent system, safety analysis, safety model, integration map

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Authors: Watcharin Sangma, Onsiri Chanmuang, Pitsanu Tongkhow

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A forecasting model for steel demand uncertainty in Thailand is proposed. It consists of trend, autocorrelation, and outliers in a hierarchical Bayesian frame work. The proposed model uses a cumulative Weibull distribution function, latent first-order autocorrelation, and binary selection, to account for trend, time-varying autocorrelation, and outliers, respectively. The Gibbs sampling Markov Chain Monte Carlo (MCMC) is used for parameter estimation. The proposed model is applied to steel demand index data in Thailand. The root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) criteria are used for model comparison. The study reveals that the proposed model is more appropriate than the exponential smoothing method.

Keywords: forecasting model, steel demand uncertainty, hierarchical Bayesian framework, exponential smoothing method

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Authors: Shima Soltanzadeh, Mohammad Hosain Fazel Zarandi, Mojtaba Barzegar Astanjin

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Diagnosis of male infertility by the laboratory tests is expensive and, sometimes it is intolerable for patients. Filling out the questionnaire and then using classification method can be the first step in decision-making process, so only in the cases with a high probability of infertility we can use the laboratory tests. In this paper, we evaluated the performance of four classification methods including naive Bayesian, neural network, logistic regression and fuzzy c-means clustering as a classification, in the diagnosis of male infertility due to environmental factors. Since the data are unbalanced, the ROC curves are most suitable method for the comparison. In this paper, we also have selected the more important features using a filtering method and examined the impact of this feature reduction on the performance of each methods; generally, most of the methods had better performance after applying the filter. We have showed that using fuzzy c-means clustering as a classification has a good performance according to the ROC curves and its performance is comparable to other classification methods like logistic regression.

Keywords: classification, fuzzy c-means, logistic regression, Naive Bayesian, neural network, ROC curve

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Authors: Nada Souissi, Mourad Mroua

Abstract:

The main purpose of this study is to examine the interaction between financial asset volatility, economic factors and investor's behavioral indicators related to both the company's and the markets stocks for the period from January 2000 to January2020. Using multiple linear regression and Bayesian Networks modeling, results show a positive and negative relationship between investor's psychology index, economic factors and predicted stock market return. We reveal that the application of the Bayesian Discrete Network contributes to identify the different cause and effect relationships between all economic, financial variables and psychology index.

Keywords: Financial asset return predictability, Economic factors, Investor's psychology index, Bayesian approach, Probabilistic networks, Parametric learning

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Authors: Randa Alharbi, Vladislav Vyshemirsky

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Systems biology is an important field in science which focuses on studying behaviour of biological systems. Modelling is required to produce detailed description of the elements of a biological system, their function, and their interactions. A well-designed model requires selecting a suitable mechanism which can capture the main features of the system, define the essential components of the system and represent an appropriate law that can define the interactions between its components. Complex biological systems exhibit stochastic behaviour. Thus, using probabilistic models are suitable to describe and analyse biological systems. Continuous-Time Markov Chain (CTMC) is one of the probabilistic models that describe the system as a set of discrete states with continuous time transitions between them. The system is then characterised by a set of probability distributions that describe the transition from one state to another at a given time. The evolution of these probabilities through time can be obtained by chemical master equation which is analytically intractable but it can be simulated. Uncertain parameters of such a model can be inferred using methods of Bayesian inference. Yet, inference in such a complex system is challenging as it requires the evaluation of the likelihood which is intractable in most cases. There are different statistical methods that allow simulating from the model despite intractability of the likelihood. Approximate Bayesian computation is a common approach for tackling inference which relies on simulation of the model to approximate the intractable likelihood. Particle Markov chain Monte Carlo (PMCMC) is another approach which is based on using sequential Monte Carlo to estimate intractable likelihood. However, both methods are computationally expensive. In this paper we discuss the efficiency and possible practical issues for each method, taking into account the computational time for these methods. We demonstrate likelihood-free inference by performing analysing a model of the Repressilator using both methods. Detailed investigation is performed to quantify the difference between these methods in terms of efficiency and computational cost.

Keywords: Approximate Bayesian computation(ABC), Continuous-Time Markov Chains, Sequential Monte Carlo, Particle Markov chain Monte Carlo (PMCMC)

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Authors: Sabyasachi Mukhopadhyay, Joseph Ogutu, Hans-Peter Piepho

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We aim to model dynamics of wildlife or pastoral livestock population for understanding of their population change and hence for wildlife conservation and promoting human welfare. The study is motivated by an age-sex structured population counts in different regions of Serengeti-Mara during the period 1989-2003. Developing reliable and realistic models for population dynamics of large herbivore population can be a very complex and challenging exercise. However, the Bayesian statistical domain offers some flexible computational methods that enable the development and efficient implementation of complex population dynamics models. In this work, we have used a novel Bayesian state-space model to analyse the dynamics of topi and hartebeest populations in the Serengeti-Mara Ecosystem of East Africa. The state-space model involves survival probabilities of the animals which further depend on various factors like monthly rainfall, size of habitat, etc. that cause recent declines in numbers of the herbivore populations and potentially threaten their future population viability in the ecosystem. Our study shows that seasonal rainfall is the most important factors shaping the population size of animals and indicates the age-class which most severely affected by any change in weather conditions.

Keywords: bayesian state-space model, Markov Chain Monte Carlo, population dynamics, conservation

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Authors: Najrullah Khan, Athar Ali Khan

Abstract:

The Topp-Leone distribution was introduced by Topp- Leone in 1955. In this paper, an attempt has been made to fit Topp-Leone Generalized exponential (TPGE) distribution. A real survival data set is used for illustrations. Implementation is done using R and JAGS and appropriate illustrations are made. R and JAGS codes have been provided to implement censoring mechanism using both optimization and simulation tools. The main aim of this paper is to describe and illustrate the Bayesian modelling approach to the analysis of survival data. Emphasis is placed on the modeling of data and the interpretation of the results. Crucial to this is an understanding of the nature of the incomplete or 'censored' data encountered. Analytic approximation and simulation tools are covered here, but most of the emphasis is on Markov chain based Monte Carlo method including independent Metropolis algorithm, which is currently the most popular technique. For analytic approximation, among various optimization algorithms and trust region method is found to be the best. In this paper, TPGE model is also used to analyze the lifetime data in Bayesian paradigm. Results are evaluated from the above mentioned real survival data set. The analytic approximation and simulation methods are implemented using some software packages. It is clear from our findings that simulation tools provide better results as compared to those obtained by asymptotic approximation.

Keywords: Bayesian Inference, JAGS, Laplace Approximation, LaplacesDemon, posterior, R Software, simulation

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