Variance Of Estimator Research Articles

Estimation of heterogeneous population variance using memory-type estimators based on EWMA statistic in the presence of measurement error for time-scaled surveys

In this present article, we have suggested memory-type ratio, exponential ratio, product and exponential product estimators based on exponentially weighted moving average statistic for the estimation of heterogeneous population variance using stratified sampling design in presence of measurement error for time-scaled surveys. Mathematical expressions of approximate mean square error are derived using Taylor and exponential expansions for the proposed memory-type estimators. We have also discussed the situations in which the memory-type estimators would perform efficiently than the conventional estimators. The results of extensive simulation study revealed that the proposed memory-type estimators based exponentially weighted moving average statistic would perform better than the conventional estimators in the presence measurement error for time-scaled surveys under certain condition.

Stochastic LQ optimal control for Markov jumping systems with multiplicative noise using reinforcement learning

The stochastic linear quadratic (LQ) problem of discrete-time linear Markov jumping systems with multiplicative noise is investigated in this paper. Two reinforcement learning algorithms, one model-based and one model-free, are designed. The algorithms can be readily adapted to handle nonlinear cases by employing an appropriate function approximator. In the linear case, the network structure is designed to enable the problem to be solved without succumbing to modeling errors. For the model-free algorithm, an approach based on moving averages is proposed to reduce estimation variance. A proof of convergence is also provided. Finally, the effectiveness of the proposed algorithms is demonstrated through a numerical example.

Improved estimation of population variance in stratified successive sampling using calibrated weights under non-response

This paper introduces a new method to estimate the population variance of a study variable in stratified successive sampling over two occasions, while accounting for random non-response. The method uses a logarithmic type estimator and leverages information from a highly positively correlated auxiliary variable. The paper also presents calibrated weights for the new estimator and examines its properties through numerical and simulation studies. The results indicate that the suggested estimator is more effective than the standard estimator for estimating the population variance.

Controlling underestimation bias in reinforcement learning via minmax operation

Obtaining the accurate value estimation and reducing the estimation bias are the key issues in reinforcement learning. However, current methods that address the overestimation problem tend to introduce underestimation, which face a challenge of precise decision-making in many fields. To address this issue, we conduct a theoretical analysis of the underestimation bias and propose the minmax operation, which allow for flexible control of the estimation bias. Specifically, we select the maximum value of each action from multiple parallel state-action networks to create a new state-action value sequence. Then, a minimum value is selected to obtain more accurate value estimations. Moreover, based on the minmax operation, we propose two novel algorithms by combining Deep Q-Network (DQN) and Double DQN (DDQN), named minmax-DQN and minmax-DDQN. Meanwhile, we conduct theoretical analyses of the estimation bias and variance caused by our proposed minmax operation, which show that this operation significantly improves both underestimation and overestimation biases and leads to the unbiased estimation. Furthermore, the variance is also reduced, which is helpful to improve the network training stability. Finally, we conduct numerous comparative experiments in various environments, which empirically demonstrate the superiority of our method.

Automated importance sampling via optimal control for stochastic reaction networks: A Markovian projection–based approach

We propose a novel alternative approach to our previous work (Ben Hammouda et al., 2023) to improve the efficiency of Monte Carlo (MC) estimators for rare event probabilities for stochastic reaction networks (SRNs). In the same spirit of Ben Hammouda et al. (2023), an efficient path-dependent measure change is derived based on a connection between determining optimal importance sampling (IS) parameters within a class of probability measures and a stochastic optimal control formulation, corresponding to solving a variance minimization problem. In this work, we propose a novel approach to address the encountered curse of dimensionality by mapping the problem to a significantly lower-dimensional space via a Markovian projection (MP) idea. The output of this model reduction technique is a low-dimensional SRN (potentially even one dimensional) that preserves the marginal distribution of the original high-dimensional SRN system. The dynamics of the projected process are obtained by solving a related optimization problem via a discrete L2 regression. By solving the resulting projected Hamilton–Jacobi–Bellman (HJB) equations for the reduced-dimensional SRN, we obtain projected IS parameters, which are then mapped back to the original full-dimensional SRN system, resulting in an efficient IS-MC estimator for rare events probabilities of the full-dimensional SRN. Our analysis and numerical experiments reveal that the proposed MP-HJB-IS approach substantially reduces the MC estimator variance, resulting in a lower computational complexity in the rare event regime than standard MC estimators.

Is Fisher inference inferior to Neyman inference for policy analysis?

The increasing computational power has led to an increasing interest in Fisher’s test in social science. As the Fisher and Neyman inference are based on different principles there is also an increasing interest in understanding the differential features of the two procedures. For example, Young (2018) found that the Fisher test has better size properties than the Neyman test in the situation with influential observations. Ding (2017), on the other hand, showed that the asymptotic variance of the mean-difference estimator (MDE) under Fisher inference is larger than that under Neyman inference, and that the asymptotic Fisher test is less powerful than the t-test even for the simplest case of homogeneous effect. Since MDE plays an important role for policy evaluation, these latter results are a concern for using Fisher’s test as argued in Young (2018). With the aim of providing an understanding of the usefulness of the exact Fisher test for inference to the sample and to the population, this paper clarifies the results in Ding (2017). Using a novel Monte Carlo simulation following the same data generating processes as in Ding (2017), we demonstrate that the Fisher test has no worse power properties than the t-test even with heterogeneous effects.

Identification of genomic regions and pathways associated with traits related to rumen acidosis in feedlot Nellore cattle.

There may be an increased risk of metabolic disorders, such as rumen acidosis, in cattle fed high-concentrate diets, particularly those from Bos taurus indicus genotypes, which have shown to be more sensitive to ruminal acidification. Therefore, this study aimed to estimate (co)variance components and identify genomic regions and pathways associated with ruminal acidosis in feedlot Nellore cattle fed high-concentrate diets. It was utilized a dataset containing a total of 642 Nellore bulls that were genotyped from seven feedlot nutrition studies. The GGP Indicus 35k panel was used with the single step genome-wide association study methodology in which the effects of the markers were obtained from the genomic values estimated by the GBLUP model. A bivariate model to estimate genetic correlations between the economically important traits and indicator traits for acidosis was used. The traits evaluated in this study that were nutritionally related to rumen acidosis included average daily gain (ADG), final body weight, time spent eating (TSE), time spent ruminating, rumenitis score (RUM), rumen absorptive surface area (ASA), rumen keratinized layer thickness (KER) and hot carcass weight (HCW). The identified candidate genes were mainly involved in the negative or non-regulation of the apoptotic process, salivary secretion, and transmembrane transport. The genetic correlation between HCW and ASA was low positive (0.27 ± 0.23), and between ADG and ASA was high moderate (0.58 ± 0.59). A positive genetic correlation between RUM and all performance traits was observed, and TSE correlated negatively with HCW (-0.33 ± 0.21), ASA (-0.75 ± 0.48), and KER (-0.40 ± 0.27). The genetic association between economically important traits and indicator traits for acidosis suggested that Nellore cattle may be more sensitive to acidosis in feedlot systems.

Scalable phylogenetic Gaussian process models improve the detectability of environmental signals on local extinctions for many Red List species

Abstract Conservation biologists have a daunting task of understanding the causes of species decline associated with anthropogenic factors and predicting the extinction risk of a growing number of endangered species. By reducing variances of estimates with information on closely related species, phylogenetic information among species can bridge gaps in information on species with small range sizes when modelling large numbers of endangered species. However, modelling many species with the Gaussian process (GP), which underlies the evolutionary process of phylogenetic random effects, remains a challenge owing to the computational burden in estimating the large variance–covariance matrix. Here, we applied a phylogenetic generalised mixed model with random slopes and random intercepts to 1010 endangered vascular plant taxa in Japan following phylogenetic GPs implemented by nearest neighbour GP (NNGP) approximation. NNGP enables flexibility in changing the proximity on the phylogenetic tree of species from which information is borrowed to reduce the variances of estimates with a realistic computational burden. We evaluated the effectiveness of phylogenetic models by comparing the predictive performance and descriptive power of phylogenetic and non‐phylogenetic models and identified the anthropogenic factors contributing to the decline of each of the studied endangered species. We found that the model with phylogenetic information had better prediction performance than the model without phylogenetic information. The results showed that across all explanatory variables, the phylogenetic model could detect interspecific differences in response to environmental factors in a number of species more clearly. Combined with the phylogenetic signal results, we could also detect a phylogenetic bias in the species that could benefit from the positive effects of protected areas but reduce the local extinctions of 95% of all studied taxa. In conclusion, our model, considering phylogenetic information with NNGP, allows the elucidation of factors causing the decline of many endangered species. In future analyses, the estimation of extinction probability linked to environmental change might be applied to future climate–land use scenarios, advancing the comprehensive assessment of biodiversity degradation and threats to species at multiple scales.

Functional analysis of variance (ANOVA) for carbon flux estimates from remote sensing data

Abstract. The constellation of Earth-observing satellites has now produced atmospheric greenhouse gas concentration estimates covering a period of several years. Their global coverage is providing additional information on the global carbon cycle. These products can be combined with complex inversion systems to infer the magnitude of carbon sources and sinks around the globe. Multiple factors, including the atmospheric transport model and satellite product aggregation method, can impact such flux estimates. Analysis of variance (ANOVA) is a well-established statistical framework for estimating common signals while partitioning variability across factors in the analysis of experiments. Functional ANOVA extends this approach with a statistical model that incorporates spatiotemporal correlation for each ANOVA component. The approach is illustrated on inversion experiments with different satellite retrieval aggregation methods and identifies consistent significant patterns in flux increments that span large spatial scales. Functional ANOVA identifies these patterns while accounting for the uncertainty at small spatial scales that is attributed to differences in the aggregation method. Functional ANOVA is also applied to a recent flux model intercomparison project (MIP), and the relative magnitudes of inversion system effects and data source (satellite versus in situ) are similar but exhibit slightly different importance for fluxes over different continents. In all examples, the unexplained residual variability is locally sizable in magnitude but with limited spatial and temporal correlation. These common behaviors across flux inversion experiments demonstrate the diagnostic capability for functional ANOVA to simultaneously distinguish the spatiotemporal coherence of carbon cycle processes and algorithmic factors.

Genetic correlation estimates between calving ease in primiparous cows and economically important traits in Nellore cattle.

This study aimed to estimate (co)variance components and genetic parameters for calving ease (CE) and their genetic correlations with growth, reproductive, carcass, and feed efficiency traits in Nellore cattle. Phenotypes for CE are scored in two categories: normal calving and assisted calving. The traits considered were probability of precocious calving, age at first calving, stayability, adjusted scrotal circumference at 365 days of age, accumulated cow productivity, age at puberty of males, gestation length, birth weight, adjusted weights at 210 and 450 days of age, adult cow weight, frame score, hip height, rib eye area, subcutaneous backfat thickness, rump fat thickness, intramuscular fat percentage, residual feed intake and dry matter intake. The estimation of genetic parameters was performed using a two-trait threshold-linear animal model, except for CE, stayability, and probability of precocious calving, which were evaluated through a two-trait threshold animal model. The direct (0.27) and maternal (0.19) heritability estimates for CE in heifers primiparous Nellore indicated that selecting for this trait is feasible. The selection to improve the female sexual precocity should consider CE during the selection and mating decisions to reduce calving problems. Genetic correlation estimates between CE and BW suggest that selecting low birth weight to reduce calving problems is not an appropriate strategy to improve calving ease in heifers Nellore. Therefore, adopting a multi-trait selection model with CE and BW in the Nellore breed would reduce calving difficulties, particularly in sexually precocious heifers, without impairing the growth, reproductive, feed efficiency conversion, and carcass indicator traits.

Effect of Increasing Sample Size on Multi-Collinearity in Multilevel Non-Linear Model

A multilevel logistic regression model demonstrating high correlations among predictor variables is susceptible to multi-collinearity. Multi-collinearity significantly impacts the robustness and interpretability of multilevel non-linear models. In multilevel non-linear models, the effects of multi-collinearity can be amplified, leading to distorted parameter estimates and inflated standard errors. This phenomenon contributes to an escalation in the variances of parameter estimates, thereby resulting in inaccurate inferences regarding the relationships between the response and explanatory factors. The primary objective of this study is to investigate the impact of multi-collinearity on multilevel non-linear models. The research aims to assess whether the quantity of independent variables influences the Multilevel Variance Inflation Factor and to explore the effect of altering the correlation degree at one level on multi-collinearity within a multilevel non-linear model. Additionally, the research seeks to determine how multi-collinearity affects the standard errors of parameters in a multilevel non-linear model. In a 2-level logistic regression, a binary variable was the dependent variable, while pre-established standard variables functioned as regressors. The Monte Carlo analysis incorporated three distinct correlation strengths (0.2, 0.5, and 0.9) and sample sizes (500, 100, and 30). The Multilevel Variance Inflation Factor was employed for multi-collinearity diagnosis. The outcomes revealed that, within the logistic multilevel regression model, an increase in sample size correlated with a reduction in multi-collinearity. Notably, the influence of multi-collinearity on standard errors in a multilevel non-linear model was more pronounced. It was observed that increasing the sample size remains an effective strategy to mitigate multi-collinearity errors in a multilevel non-linear model. This approach is particularly crucial due to the reliance on maximum likelihood estimation in logistic regression, as opposed to ordinary least squares (OLS) regression, which contrasts with the methodology of OLS regression.

Rescaling bootstrap variance estimation technique under dual frame surveys with unknown domain sizes

Dual frame (DF) surveys are a special case of multiple frame (MF) surveys considering two frames covering the entire population. Dual frame surveys are applicable in those situations, where, one frame may cover the entire population but is very expensive to sample; so an alternate frame may be available that does not cover the entire population but is easily available. Unbiased variance estimation in dual frame surveys can be difficult and complicated than corresponding estimators under single frame surveys. Again, the variance of dual frame estimator involves population variances of the individual domains which are generally unknown. Due to this reason, obtaining an unbiased estimate of the variance of the dual frame estimator is quite complex in the case of dual frame surveys. In this article, we propose a Post-stratified Rescaling Bootstrap with Unknown Domain size (PstRBUD) method for variance estimation of the dual frame estimator of population total. The proposed rescaled bootstrap method was compared to that of standard bootstrap methods in simulation analysis. The proposed PstRBUD method provides an unbiased estimation of the variance of the dual frame estimator of population total, according to simulation results.

Impact of individual level uncertainty of lung cancer polygenic risk score (PRS) on risk stratification.

Although polygenic risk score (PRS) has emerged as a promising tool for predicting cancer risk from genome-wide association studies (GWAS), the individual-level accuracy of lung cancer PRS and the extent to which its impact on subsequent clinical applications remains largely unexplored. Lung cancer PRSs and confidence/credible interval (CI) were constructed using two statistical approaches for each individual: (1) the weighted sum of 16 GWAS-derived significant SNP loci and the CI through the bootstrapping method (PRS-16-CV) and (2) LDpred2 and the CI through posteriors sampling (PRS-Bayes), among 17,166 lung cancer cases and 12,894 controls with European ancestry from the International Lung Cancer Consortium. Individuals were classified into different genetic risk subgroups based on the relationship between their own PRS mean/PRS CI and the population level threshold. Considerable variances in PRS point estimates at the individual level were observed for both methods, with an average standard deviation (s.d.) of 0.12 for PRS-16-CV and a much larger s.d. of 0.88 for PRS-Bayes. Using PRS-16-CV, only 25.0% of individuals with PRS point estimates in the lowest decile of PRS and 16.8% in the highest decile have their entire 95% CI fully contained in the lowest and highest decile, respectively, while PRS-Bayes was unable to find any eligible individuals. Only 19% of the individuals were concordantly identified as having high genetic risk (> 90th percentile) using the two PRS estimators. An increased relative risk of lung cancer comparing the highest PRS percentile to the lowest was observed when taking the CI into account (OR = 2.73, 95% CI: 2.12-3.50, P-value = 4.13 × 10-15) compared to using PRS-16-CV mean (OR = 2.23, 95% CI: 1.99-2.49, P-value = 5.70 × 10-46). Improved risk prediction performance with higher AUC was consistently observed in individuals identified by PRS-16-CV CI, and the best performance was achieved by incorporating age, gender, and detailed smoking pack-years (AUC: 0.73, 95% CI = 0.72-0.74). Lung cancer PRS estimates using different methods have modest correlations at the individual level, highlighting the importance of considering individual-level uncertainty when evaluating the practical utility of PRS.

The estimation of additive genetic variance of body size in a wild passerine is sensitive to the method used to estimate relatedness among the individuals.

Assessing additive genetic variance is a crucial step in predicting the evolutionary response of a target trait. However, the estimated genetic variance may be sensitive to the methodology used, e.g., the way relatedness is assessed among the individuals, especially in wild populations where social pedigrees can be inaccurate. To investigate this possibility, we investigated the additive genetic variance in tarsus length, a major proxy of skeletal body size in birds. The model species was the collared flycatcher (Ficedula albicollis), a socially monogamous but genetically polygamous migratory passerine. We used two relatedness matrices to estimate the genetic variance: (1) based solely on social links and (2) a genetic similarity matrix based on a large array of single-nucleotide polymorphisms (SNPs). Depending on the relatedness matrix considered, we found moderate to high additive genetic variance and heritability estimates for tarsus length. In particular, the heritability estimates were higher when obtained with the genetic similarity matrix instead of the social pedigree. Our results confirm the potential for this crucial trait to respond to selection and highlight methodological concerns when calculating additive genetic variance and heritability in phenotypic traits. We conclude that using a social pedigree instead of a genetic similarity matrix to estimate relatedness among individuals in a genetically polygamous wild population may significantly deflate the estimates of additive genetic variation.

Cooperative Multiagent Reinforcement Learning With Partial Observations

In this paper, we propose a distributed zeroth-order policy optimization method for Multi-Agent Reinforcement Learning (MARL). Existing MARL algorithms often assume that every agent can observe the states and actions of all the other agents in the network. This can be impractical in large-scale problems, where sharing the state and action information with multi-hop neighbors may incur significant communication overhead. The advantage of the proposed zeroth-order policy optimization method is that it allows the agents to compute the local policy gradients needed to update their local policy functions using local estimates of the global accumulated rewards that depend on partial state and action information only and can be obtained using consensus. Specifically, to calculate the local policy gradients, we develop a new distributed zeroth-order policy gradient estimator that relies on one-point residual-feedback which, compared to existing zeroth-order estimators that also rely on one-point feedback, significantly reduces the variance of the policy gradient estimates improving, in this way, the learning performance. We show that the proposed distributed zeroth-order policy optimization method with constant stepsize converges to the neighborhood of a policy that is a stationary point of the global objective function. The size of this neighborhood depends on the agents' learning rates, the exploration parameters, and the number of consensus steps used to calculate the local estimates of the global accumulated rewards. Moreover, we provide numerical experiments that demonstrate that our new zeroth-order policy gradient estimator is more sample-efficient compared to other existing one-point estimators.

Inferring community transmission of SARS-CoV-2 in the United Kingdom using the ONS COVID-19 Infection Survey

Key epidemiological parameters, including the effective reproduction number, R(t), and the instantaneous growth rate, r(t), generated from an ensemble of models, have been informing public health policy throughout the COVID-19 pandemic in the four nations of the United Kingdom of Great Britain and Northern Ireland (UK). However, estimation of these quantities became challenging with the scaling down of surveillance systems as part of the transition from the “emergency” to “endemic” phase of the pandemic.The Office for National Statistics (ONS) COVID-19 Infection Survey (CIS) provided an opportunity to continue estimating these parameters in the absence of other data streams. We used a penalised spline model fitted to the publicly-available ONS CIS test positivity estimates to produce a smoothed estimate of the prevalence of SARS-CoV-2 positivity over time. The resulting fitted curve was used to estimate the “ONS-based” R(t) and r(t) across the four nations of the UK. Estimates produced under this model are compared to government-published estimates with particular consideration given to the contribution that this single data stream can offer in the estimation of these parameters.Depending on the nation and parameter, we found that up to 77% of the variance in the government-published estimates can be explained by the ONS-based estimates, demonstrating the value of this singular data stream to track the epidemic in each of the four nations. We additionally find that the ONS-based estimates uncover epidemic trends earlier than the corresponding government-published estimates.Our work shows that the ONS CIS can be used to generate key COVID-19 epidemiological parameters across the four UK nations, further underlining the enormous value of such population-level studies of infection. This is not intended as an alternative to ensemble modelling, rather it is intended as a potential solution to the aforementioned challenge faced by public health officials in the UK in early 2022.

Purposeful co-design of OFDM signals for ranging and communications

This paper analyzes the fundamental trade-offs that occur in the co-design of pilot resource allocations in orthogonal frequency-division multiplexing signals for both ranging (via time-of-arrival estimation) and communications. These trade-offs are quantified through the Shannon capacity bound, probability of outage, and the Ziv–Zakai bound on range estimation variance. Bounds are derived for signals experiencing frequency-selective Rayleigh block fading, accounting for the impact of limited channel knowledge and multi-antenna reception. Uncompensated carrier frequency offset and phase errors are also factored into the capacity bounds. Analysis based on the derived bounds demonstrates how Pareto-optimal design choices can be made to optimize the communication throughput, probability of outage, and ranging variance. Different pilot resource allocation strategies are then analyzed, showing how Pareto-optimal design choices change depending on the channel.

Bias-free estimation of the covariance function and the power spectral density from data with missing samples including extended data gaps

Nonparametric estimation of the covariance function and the power spectral density of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Several common methods are tested for their systematic and random errors under the condition of variations in the distribution of the missing samples. In addition to random and independent outliers, the influence of longer and hence correlated data gaps on the performance of the various estimators is also investigated. The aim is to construct a bias-free estimation routine for the covariance function and the power spectral density from stationary stochastic processes under the condition of missing samples with an optimum use of the available information in terms of low estimation variance and mean square error, and that independent of the spectral composition of the data gaps. The proposed procedure is a combination of three methods that allow bias-free estimation of the desired statistical functions with efficient use of the available information: weighted averaging over valid samples, derivation of the covariance estimate for the entire data set and restriction of the domain of the covariance function in a post-processing step, and appropriate correction of the covariance estimate after removal of the estimated mean value. The procedures abstain from interpolation of missing samples as well as block subdivision. Spectral estimates are obtained from covariance functions and vice versa using Wiener–Khinchin’s theorem.

Times Square Sampling: An Adaptive Algorithm for Free Energy Estimation

Estimating free energy differences, an important problem in computational drug discovery and in a wide range of other application areas, commonly involves a computationally intensive process of sampling a family of high-dimensional probability distributions and a procedure for computing estimates based on those samples. The variance of the free energy estimate of interest typically depends strongly on how the total computational resources available for sampling are divided among the distributions, but determining an efficient allocation is difficult without sampling the distributions. Here we introduce the Times Square sampling algorithm, a novel on-the-fly estimation method that dynamically allocates resources in such a way as to significantly accelerate the estimation of free energies and other observables, while providing rigorous convergence guarantees for the estimators. We also show that it is possible, surprisingly, for on-the-fly free energy estimation to achieve lower asymptotic variance than the maximum-likelihood estimator MBAR, raising the prospect that on-the-fly estimation could reduce variance in a variety of other statistical applications. Supplementary materials for this article are available online.

Genetic background of juniper (Juniperus spp.) consumption predicted by fecal near-infrared spectroscopy in divergently selected goats raised in harsh rangeland environments

BackgroundJunipers (Juniperus spp.) are woody native, invasive plants that have caused encroachment problems in the U.S. western rangelands, decreasing forage productivity and biodiversity. A potential solution to this issue is using goats in targeted grazing programs. However, junipers, which grow in dry and harsh environmental conditions, use chemical defense mechanisms to deter herbivores. Therefore, genetically selecting goats for increased juniper consumption is of great interest for regenerative rangeland management. In this context, the primary objectives of this study were to: 1) estimate variance components and genetic parameters for predicted juniper consumption in divergently selected Angora (ANG) and composite Boer x Spanish (BS) goat populations grazing on Western U.S. rangelands; and 2) to identify genomic regions, candidate genes, and biological pathways associated with juniper consumption in these goat populations.ResultsThe average juniper consumption was 22.4% (± 18.7%) and 7.01% (± 12.1%) in the BS and ANG populations, respectively. The heritability estimates (realized heritability within parenthesis) for juniper consumption were 0.43 ± 0.02 (0.34 ± 0.06) and 0.19 ± 0.03 (0.13 ± 0.03) in BS and ANG, respectively, indicating that juniper consumption can be increased through genetic selection. The repeatability values of predicted juniper consumption were 0.45 for BS and 0.28 for ANG. A total of 571 significant SNP located within or close to 231 genes in BS, and 116 SNP related to 183 genes in ANG were identified based on the genome-wide association analyses. These genes are primarily associated with biological pathways and gene ontology terms related to olfactory receptors, intestinal absorption, and immunity response.ConclusionsThese findings suggest that juniper consumption is a heritable trait of polygenic inheritance influenced by multiple genes of small effects. The genetic parameters calculated indicate that juniper consumption can be genetically improved in both goat populations.