Purpose: Inflation has been a persistent and critical challenge in Iran's economy, necessitating Inflation has been a persistent and critical challenge in Iran's economy, necessitating a comprehensive understanding of its drivers and mechanisms for effective policy formulation. This study focuses on the interconnected roles of the key monetary policy tools, including liquidity, exchange rates, interest rates and base money, in inflation dynamics. Drawing upon the global perspective of inflation control, which includes exchange rate targeting, monetary aggregates and inflation targeting, the research adapts these insights to Iran's unique economic context.Using a Bayesian TVC-VAR model, the study captures the structural shifts and the evolving relationships among the corresponding variables from May 2014 to August 2024. The model’s strength lies in addressing the complex and interdependent nature of Iran’s macroeconomic variables, where changes in one variable can significantly impact others.The research highlights two pivotal periods: May 2018, marked by the U.S. withdrawal from the JCPOA, and August 2020, shaped by intensified sanctions and the COVID-19 pandemic. These periods underscore the importance of adaptive and coordinated monetary and exchange rate policies. The findings provide policymakers with workable insights to mitigate inflationary pressures and foster economic stability in an unpredictable environment.Methodology: This study employs the Bayesian TVC-VAR model, which builds on the traditional VAR framework by incorporating time-varying coefficients, enabling it to capture the evolving nature of economic relationships. The model uses monthly data spanning May 2014 to August 2024, sourced from the Central Bank of Iran. The key variables include the following:Inflation (CPI): A proxy for the general price level in the economyLiquidity: Representing the total money supply, influenced by the base money multiplier effectBase Money: High-powered money, including currency in circulation and bank reservesExchange Rate: The value of the Iranian Rial against foreign currenciesInterest Rate: Represented by the interbank rate, a proxy for general borrowing costsThe data were log-transformed and seasonally adjusted to ensure consistency. Unit root tests confirmed stationarity for all the variables except the interest rate, which required adjustments for structural breaks. To identify structural shocks, Cholesky decomposition was done, with the variables ordered as base money, exchange rate, liquidity, interest rate, and inflation. This hierarchy reflects the foundational role of base money in driving monetary aggregates and the lagged responses of inflation.The study focuses on two critical periods as follows:May 2018: The U.S. withdrawal from the JCPOA, which triggered significant economic and political uncertainty, leading to heightened exchange rate volatility and inflationary pressuresAugust 2020: A period of compounded economic crises due to the COVID-19 pandemic and intensified sanctions, which further disrupted economic stabilityFindings and discussion: The analysis reveals significant insights into the relationships between inflation and the key monetary policy variables. Shocks to liquidity had a moderate and short-lived impact on inflation. Following an increase in liquidity, inflation rose moderately, peaking after a few periods before stabilizing.The influence of liquidity was less pronounced than that of base money or exchange rate shocks, suggesting that the impact of liquidity on inflation is mediated through other variables.Exchange rate shocks exhibited the most immediate and significant impact on inflation. Depreciation of the Rial directly increased import prices, leading to a sharp and immediate rise in inflation.The magnitude of the impact was particularly pronounced in August 2020 due to combined economic crises. Inflation surged following an exchange rate shock and stabilized after approximately five periods.Interest rate shocks negatively affected inflation, demonstrating their effectiveness as a tool for controlling price levels. An increase in the interbank interest rate reduced inflation by curbing borrowing and aggregate demand.The effects of interest rate shocks were temporary, lasting for about 10 periods in May 2018 and 5 periods in August 2020 before inflation returned to its baseline.Shocks to base money had a pronounced and prolonged impact on inflation. Increases in base money, often used to finance government deficits, led to rapid inflationary pressures that persisted longer than those caused by liquidity shocks.The findings emphasize the critical role of base money as a driver of inflation, both directly and through its effects on liquidity and aggregate demand.Comparing the two critical periods, the study found consistent qualitative responses across the variables but differing magnitudes. The responses were more intense in August 2020, reflecting the heightened economic instability due to the combined effects of the COVID-19 pandemic and the external sanctions. The exchange rate shocks consistently had the most substantial impact on inflation, highlighting the critical importance of exchange rate stability in managing price levels.Conclusions and Policy Implications: This study underscores the significant role of monetary policy tools in shaping inflation dynamics in Iran. The Bayesian TVC-VAR model provided a nuanced understanding of the evolving relationships between inflation, exchange rates, interest rates, liquidity, and base money, offering valuable insights for policymakers:Exchange rate shocks have significant effects on inflation, making effective exchange rate management a policy priority. Implementing mechanisms to mitigate sharp currency fluctuations can play a crucial role in stabilizing prices and preventing sudden inflationary surges. This effort requires precise coordination between monetary and exchange rate policies.Given the positive impact of the interbank interest rate on controlling inflation, policymakers are advised to use this tool strategically while considering market conditions. Smart use of interest rates can help curb inflation by managing liquidity and channeling financial resources into productive economic sectors.The findings indicate that base money and liquidity shocks have substantial effects on inflation. Therefore, policymakers must closely monitor the growth of these two variables and prevent their excessive expansion. This requires implementing appropriate monetary policies and enhancing financial transparency to strengthen public trust and optimize policy effectiveness.The rapid response of the variables to exchange rate shocks underscores the need for policymakers to establish mechanisms and structures to quickly identify these shocks and adopt effective, timely responses. Building such frameworks, especially during crises, can prevent severe economic fluctuations and minimize their negative impacts.

A new continuous distribution called Lindley-Lindley distribution is defined and studied. Relevant mathematical properties are derived. We present three characterizations of the new distribution based on the truncated moments of certain functions of the random variable,the hazard function and in terms of the conditional expectation of a function of the random variable. Some new bivariate type distributions using Farlie Gumbel Morgenstern copula, modified Farlie Gumbel Morgenstern copula and Clayton copula are introduced. The main justification of this paper is to show how different frequentist estimators of the new model perform for different sample sizes and different parameter values and to provide a guideline for choosing the best estimation method for the parameters of the proposed model. The unknown parameters of the new distribution are estimated using the maximum likelihood, ordinary least squares, Cramer-Von-Mises, weighted least squares and Bayesian methods. The obtained estimators are compared using Markov Chain Monte Carlo simulations and observed that Bayesian estimators are generally more efficient than the other estimators.

Introduction: Genetic evaluation and estimation of breeding value are one of the most fundamental elements of breeding programmes for genetic improvement. Recently, genomic selection has become an efficient method to approach this aim. The accuracy of estimated Genomic breeding value is the most important factor in genomic selection. Different studies have been performed addressing the factors affecting the accuracy of estimated Genomic breeding value. The aim of this study was to evaluate the effect of beta and gamma distributions on the accuracy of genetic evaluation.Materials and Methods: A genome consisted of 10 chromosomes with 200 cm length was simulated. Markers were spaced on 0.2 cm intervals and different numbers of QTL with random distribution were simulated. Only additive gene effects were considered. The base population was simulated with an effective size of 100 animals and this structure continued up to generation 50 to creating linkage disequilibrium between the markers and QTL. The population size was increased to 1000 animals in generation 51 (reference generation). Marker effects were calculated from the genomic and phenotypic information. Genomic breeding value was computed in generations 52 to 57 (training generation). Effects of gamma 1 distribution (shape=0.4, scale=1.66), gamma 2 distribution (shape=0.4, scale=1) and beta distribution (shape1=3.11, shape2=1.16) were studied in the reference and training groups. The heritability values were 0.2 and 0.05.Results and Discussion: The results showed that accuracy of genomic breeding value reduced with passing generation (from 51 to 57) for two gamma distributions and beta distribution; this decrease may be due to two factors: recombination has negative impact on accuracy of genomic breeding value and selection reduces genetic variance as the number of generations increases. Accuracy of genomic estimated breeding value increased as the heritability increased so that the high heritability had more accuracy than low heritability in same QTL number. Number and distribution of genes is an important factor for accuracy of estimated breeding value. Duncan test was conducted by SPSS software. Results illustrated that there was no significant difference between the different distributions. Comparing accuracy of estimated breeding value showed that in the low heritability scenario with 10 and 20 QTL, gamma distribution 2 and gamma distribution 1 performed well, respectively, whilst in 50 and 100 QTL scenario, beta distribution was superior in both Lasso and Ridge methods. In the high heritability scenario with 50, 100 QTL gamma distributions 2 were superior in both Lasso and Ridge methods. With four QTL (10, 20, 50 & 100), in high heritability scenario, estimated genomic breeding value was often increased by increasing the number of QTL. This may be due to increasing linkage disequilibrium between markers and QTL. In general, the gamma distribution led to the increased accuracy of the estimations in both Lasso and Ridge methods.Conclusion: Marker density, method to estimate marker effects, QTL distribution, number of QTL, number of generations and trait heritability are some effective factors on accuracy of estimated genomic breeding value. The accuracy of estimated genomic breeding value is output of these factors and the distribution of genes is an important factor for accuracy of estimated genomic breeding value. We can conclude that, accuracy is reduced with increasing number of generations from base population to training population while the accuracy of estimated genomic breeding value is increased when breeding value of the reference group is used in lieu of the phenotypic records. In addition, accuracy of estimated genomic breeding value is enhanced by increasing heritability, so that, between three the distributions simulated in high heritability scenario, gamma 2 distribution increased accuracy of the estimates. Although, the size and distribution of QTL effects still greatly influence the effectiveness of the genomic prediction methods, but as a suggestion, models of genetic variation of genomic assessment should be considered, since a method of estimating breeding value may have (or produce) a better estimation with a specific model.

This paper introduces measures of information for Bayesian analysis when the support of data distribution is truncated progressively. The focus is on the lifetime distributions where the support is truncated at the current age t ³ 0. Notions of uncertainty and information are presented and operationalized by Shannon entropy, Kullback-Leibler information, and mutual information. Dynamic updatings of prior distribution of the parameter of lifetime distribution based on observing a survival at age t and observing a failure or the residual lifetime beyond t are presented. Dynamic measures of information provided by the data about the parameter of lifetime distribution, and dynamic predictive information are introduced. These measures are applied to two well-known lifetime models. The paper concludes with some remarks on use of generalized uncertainty and information measures, and some topics for further research.

The spatial prediction of an unknown quantity at a specific site is one of the most important topics in the fuzzy spatial analysis. Under the assumption that covariance is known, optimal prediction and mean square error of predictor are determinable by using fuzzy kriging methods. When the parameters of the parametric covariance function are unknown, their estimates are usually replaced in optimal prediction as real values. But, determination of this predictor and its mean square error are usually difficult. Therefore, to solve this problem, in this paper the Bayesian approach is used to extend the fuzzy kriging to a new method, namely Bayesian fuzzy kriging. Then, in an applied example, its accuracy is compared with other spatial predictors.

Background: The Bayesian methods have received more attention in medical research. It is considered as a natural paradigm for dealing with applied problems in the sciences and also an alternative to the traditional frequentist approach. However, its concept is somewhat difficult to grasp by nonexperts. This study aimed to explain the foundational ideas of the Bayesian methods through an intuitive example in medical science and to illustrate some simple examples of Bayesian data analysis and the interpretation of results delivered by Bayesian analyses. In this study, data sparsity, as a problem which could be solved by this approach, was presented through an applied example. Moreover, a common sense description of Bayesian inference was offered and some illuminating examples were provided for medical investigators and nonexperts. Methods: Data augmentation prior, MCMC, and Bayes factor were introduced. Data from the Khuzestan study, a 2-phase cohort study, were applied for illustration. Also, the effect of vitamin D intervention on pregnancy outcomes was studied. Results: Unbiased estimate was obtained by the introduced methods. Conclusion: Bayesian and data augmentation as the advanced methods provide sufficient results and deal with most data problems such as sparsity.