Highest Posterior Density Regions Research Articles

Phylogenomics reveals the history of host use in mosquitoes

Mosquitoes have profoundly affected human history and continue to threaten human health through the transmission of a diverse array of pathogens. The phylogeny of mosquitoes has remained poorly characterized due to difficulty in taxonomic sampling and limited availability of genomic data beyond the most important vector species. Here, we used phylogenomic analysis of 709 single copy ortholog groups from 256 mosquito species to produce a strongly supported phylogeny that resolves the position of the major disease vector species and the major mosquito lineages. Our analyses support an origin of mosquitoes in the early Triassic (217 MYA [highest posterior density region: 188–250 MYA]), considerably older than previous estimates. Moreover, we utilize an extensive database of host associations for mosquitoes to show that mosquitoes have shifted to feeding upon the blood of mammals numerous times, and that mosquito diversification and host-use patterns within major lineages appear to coincide in earth history both with major continental drift events and with the diversification of vertebrate classes.

Are There Differences between Methods Used for the Objective Estimation of Boar Sperm Concentration and Motility?

Artificial insemination in the swine industry, as in other species, demands adequate semen handling and accurate evaluation for the preparation of seminal doses. Sperm concentration and motility estimates are part of the semen evaluation process and are considered important for maximizing the yield of doses for insemination. In this study, methods were examined for their accuracy in the estimation of boar sperm concentration and motility. Assessments of sperm concentration were carried out using iSperm®, ISAS® v1, Open CASA v2, and the Accuread® photometer. Analyses of sperm motility were performed with iSperm®, ISAS® v1, and Open CASA v2 systems. In this study, boar semen samples were collected from 10 healthy males from two genetic lines. There were no relevant differences between sire lines when sperm concentration was assessed. A Bayesian analysis was applied to the four methods used to assess sperm concentration to examine whether there are relevant differences between them. Results suggested differences in the four methods, with a probability of relevance (PR) of 0.86-1.00. The iSperm® method revealed higher concentration values within the highest posterior density region at 95% confidence interval (HPD95%) = 167.0, 224.2 M/mL, whereas Open CASA v2 showed the lowest values, with HPD95% = 99.3, 155.9 M/mL. The iSperm® demonstrated higher reliability in measuring sperm concentration compared to other methods or devices within the given range of confidence. ANOVAs revealed relevant differences in the three methods of motility estimation. Overall, differences in boar sperm concentration and motility estimates were found using various methods, but further studies are needed for better characterization of these differences.

Existence of matching priors on compact spaces

Summary A matching prior at level $1-\alpha$ is a prior such that an associated $1-\alpha$ credible region is also a $1-\alpha$ confidence set. We study the existence of matching priors for general families of credible regions. Our main result gives topological conditions under which matching priors for specific families of credible regions exist. Informally, we prove that, on compact parameter spaces, a matching prior exists if the so-called rejection-probability function is jointly continuous when we adopt the Wasserstein metric on priors. In light of this general result, we observe that typical families of credible regions, such as credible balls, highest-posterior density regions, quantiles, etc., fail to meet this topological condition. We show how to design approximate posterior credible balls and highest-posterior density regions that meet these topological conditions, yielding matching priors. Finally, we evaluate a numerical scheme for computing approximately matching priors based on discretization and iteration. The proof of our main theorem uses tools from nonstandard analysis and establishes new results about the nonstandard extension of the Wasserstein metric that may be of independent interest.

Bayesian Estimation for the Two Log-Logistic Models Under Joint Type II Censoring Schemes

The present paper, discusses classical and Bayesian estimation of unknown combined parameters of two different log-logistic models with common shape parameters and different scale parameters under a new type of censoring scheme known as joint type II censoring scheme. Maximum likelihood estimators are derived. Bayes estimates of parameters are proposed under different loss functions. Classical asymptotic confidence intervals along with the Bayesian credible intervals and Highest Posterior Density region are also constructed. Markov Chain Monte Carlo approximation method is used for simulating the theoretic results. Comparative assessment of the classical and the Bayes results are illustrated through a real archived dataset.

Relapse, Mortality, and the Associated Factors in Children with Acute Lymphoblastic Leukemia; A Competing Risks Analysis

Background: Acute lymphoblastic leukemia (ALL) is the most frequent form of malignant neoplasia diagnosed in ages 0 to 14 years old. Efforts have not yet converted into a better prospect. Bone marrow relapse is still the leading cause of person-year of life lost in this malignancy. Objectives: This study aimed at identifying the associated risk factors for relapse and mortality for pediatric patients with ALL in standard and high-risk groups. Methods: This study included a cohort of pediatric (0 - 16 years old) patients with ALL referred to Sheikh Hospital, Mashhad, Iran from 2007 to 2016. The demographic, clinical, and laboratory information were considered. Hazard ration (HR) with 95% highest posterior density region was obtained, using a Bayesian competing risks model. Results: Of 424 patients with a mean age of 5.56 ± 3.75 years, 172 (40%) were female. Median follow-up time was 43.29 months, 10.6% had a relapse, and 17.2% had mortality related to ALL. Relapse-free survival rates at 1, 3, and 5 years were 97, 91, and 88%, respectively. Overall survival rates were 86, 83, and 82%, respectively. In the standard-risk group, tumor lysis syndrome (TLS) significantly increased either the relapse risk [HR: 13.47 (2.05 - 67.54)] or mortality risk [HR: 19.57 (2.24 - 32.18)]. In the high-risk group, the higher level of hemoglobin, platelet, and lactic acid dehydrogenase was significantly associated with higher relapse risk. TLS was associated with a higher risk of mortality in high-risk groups. Conclusions: It was suggested that TLS was a predictor for the disease relapse as well as mortality in pediatric patients with ALL. However, further evaluation on the larger population of patients is demanded to ascertain the precision of such parameters in leukemic management strategies.

A Bayesian analysis of boar spermatozoa kinematics and head morphometrics and their relationship with litter size fertility variables.

The semen movement and sperm head size patterns of boar ejaculates were analysed using computer-assisted semen analysis (CASA)-Mot and -Morph systems. The aim of the present study was to compare morphometric and kinematics variables from boars and to determine the relationship with sow fertility variables related to litter size. The females were from maternal crossing schemes such as the continuous 3-generation cross between York (Y), Landrace (L), and Pietrain (P) hybrid sows and Pietrain boars. Semen samples were collected from 11 sexually mature boars from two sire lines. Samples were analysed using the ISAS® v1 system to evaluate eight kinematic variables of sperm velocity, progressiveness and undulations. Four morphometric parameters of sperm head size (length, width, area and perimeter) were analysed. Bayesian analysis revealed relevant differences in four kinematic variables (VSL, LIN, STR and WOB) between sire lines, with a probability of relevance (PR ) of 0.79-0.91, and Pietrain boars were associated with higher progressive motility compared with Duroc x Pietrain boars. Moreover, there were relevant differences in all morphometric variables (PR =0.82-0.85) between sire lines. The dam line Y-L-50 (½ Y×½ L) had higher total born per litter and piglets born alive, and YLP-75 (1 /8 Y×1 /8 L×3 /4 P) was associated with higher values of litter weight at birth (highest posterior density region at 95%=9.92, 16.41kg). There are relevant differences in kinematic variables between the assessed sire lines and the differences in morphometric and litter size variables were also relevant. The York-Landrace hybrid sows had higher total born per litter and piglets born alive, and there were relevant differences when compared with YLP-50 (¼ York×¼ Landrace×½ Pietrain). Differences in kinematic and morphometric variables between sire and dam lines related to fertility need to be further studied.

New Approaches to Age Estimation Using Palatal Suture Fusion.

Palatal suture fusion has seen little testing and/or application due in part to an inadequately described relationship to formal age ranges. This study presents a modified scoring method that examines fusion on samples of modern documented adult males and compares two Bayesian approaches to age estimation. In the first analysis, American and Portuguese collections were used to derive univariate and multivariate transition analysis (TA) parameters, which combined with an informative prior, estimated age in a sample of modern Americans and Portuguese. For the second analysis, a Bayesian multiple linear regression (BMLR) used indicator statuses as the independent variables with age as the dependent variable. Highest posterior density regions (HPDRs) and highest posterior density intervals (HDI) were calculated for a holdout sample. Final age estimates for the methods were tested for accuracy using cumulative binomial tests at 75% and 90% coverages. The HPDRs from multivariate TA captured age better for younger individuals, but consistently underaged. The cumulative binomial tests on the BMLR results indicated the prediction intervals performed as expected, and we show they are narrower (more precise) and/or more accurate than the corresponding HPDR. The modified method presented here formally links palatal suture obliteration to age using two different approaches, one of which (BMLR) is new to the aging literature. The BMLR provided results free from bias and more reasonable age ranges while maintaining accuracy. We present a look-up table and a free, simple R file for users to download and run their own estimates with BMLR.

A theorem on a product of lognormal variables and hybrid models for children’s exposure to soil contaminants

This study developed hybrid Bayesian models to investigate the modeling process for children’s exposure to soil contaminants, which involves the intrinsic uncertainty of the exposure model, people’s judgments regarding random variables, and limited data resources. A hybrid Bayesian p-box was constructed, which was facilitated by a multiple integral dimensionality reduction (MIDR) theorem. The results indicated that exposure frequency (EF) dominated the exposure dose. The hybrid Bayesian p-box for the Frequentist-Bayesian (F–B) model at the 95th percentile of the simulated average daily dose (ADD) values corresponded to a 4.40 order-of-magnitude difference between the upper and lower bounds of the p-box. This considerable uncertainty was magnified by the combination of the highest posterior density (HPD) regions for three groups of the distribution parameters. For the Interior-Bayesian (I–B) hybrid model, the uncertainty of the outcomes, namely, [1.75 × 10−8, 2.18 × 10−8] mg kg−1d−1, was limited by the HPD regions for only one parameter unless the hyperparameters for the variables’ distributions were further evaluated. It was concluded that the hybrid models could provide a novel understanding of the complexity of the exposure modeling process compared to the traditional modeling method.

A Bayesian Approach to Age-at-Death Estimation from Osteoarthritis of the Shoulder in Modern North Americans.

Osteoarthritis (OA) is a marker of degeneration within the skeleton, frequently associated with age. This study quantifies the correlation between OA and age-at-death and investigates the utility of shoulder OA as a forensic age indicator using a modern North American sample of 206 individuals. Lipping, surface porosity, osteophyte formation, eburnation, and percentage of joint surface affected were recorded on an ordinal scale and summed to create composite scores that were assigned a specific phase. Spearman's correlation indicated a positive relationship between each composite score and age (right shoulder=0.752; left shoulder=0.734). Transition analysis revealed a tendency toward earlier degeneration of the right shoulder. Bayesian statistics generated phase-related age estimates based on highest posterior density regions. Best age estimates were into the seventh decade at the 90th and 50th percentile. The proposed method supplements traditional techniques by providing age estimates beyond a homogenous 50+ age cohort.

Data-dependent probability matching priors for likelihood ratio and adjusted likelihood ratio statistics

We consider likelihood ratio statistics based on the usual profile likelihood and the standard adjustments thereof proposed in the literature in the presence of nuisance parameters. The role of data-dependent priors in ensuring approximate frequentist validity of posterior credible regions based on the inversion of these statistics is investigated. Unlike what happens with data-free priors, it is seen that the resulting probability matching conditions readily admit solutions which entail approximate frequentist validity of the highest posterior density region as well.

Ages of 24 widespread tephras erupted since 30,000 years ago in New Zealand, with re-evaluation of the timing and palaeoclimatic implications of the Lateglacial cool episode recorded at Kaipo bog

Tephras are important for the NZ-INTIMATE project because they link all three records comprising the composite inter-regional stratotype developed for the New Zealand climate event stratigraphy (NZ-CES). Here we firstly report new calendar ages for 24 widespread marker tephras erupted since 30,000 calendar (cal.) years ago in New Zealand to help facilitate their use as chronostratigraphic dating tools for the NZ-CES and for other palaeoenvironmental and geological applications. The selected tephras comprise 12 rhyolitic tephras from Taupo, nine rhyolitic tephras from Okataina, one peralkaline rhyolitic tephra from Tuhua, and one andesitic tephra each from Tongariro and Egmont/Taranaki volcanic centres. Age models for the tephras were obtained using three methods: (i) 14C-based wiggle-match dating of wood from trees killed by volcanic eruptions (these dates published previously); (ii) flexible depositional modelling of a high-resolution 14C-dated age–depth sequence at Kaipo bog using two Bayesian-based modelling programs, Bacon and OxCal's P_Sequence function, and the IntCal09 data set (with SH offset correction −44 ± 17 yr); and (iii) calibration of 14C ages using OxCal's Tau_Boundary function and the SHCal04 and IntCal09 data sets. Our preferred dates or calibrated ages for the 24 tephras are as follows (youngest to oldest, all mid-point or mean ages of 95% probability ranges): Kaharoa AD 1314 ± 12; Taupo (Unit Y) AD 232 ± 10; Mapara (Unit X) 2059 ± 118 cal. yr BP; Whakaipo (Unit V) 2800 ± 60 cal. yr BP; Waimihia (Unit S) 3401 ± 108 cal. yr BP; Stent (Unit Q) 4322 ± 112 cal. yr BP; Unit K 5111 ± 210 cal. yr BP; Whakatane 5526 ± 145 cal. yr BP; Tuhua 6577 ± 547 cal. yr BP; Mamaku 7940 ± 257 cal. yr BP; Rotoma 9423 ± 120 cal. yr BP; Opepe (Unit E) 9991 ± 160 cal. yr BP; Poronui (Unit C) 11,170 ± 115 cal. yr BP; Karapiti (Unit B) 11,460 ± 172 cal. yr BP; Okupata 11,767 ± 192 cal. yr BP; Konini (bed b) 11,880 ± 183 cal. yr BP; Waiohau 14,009 ± 155 cal. yr BP; Rotorua 15,635 ± 412 cal. yr BP; Rerewhakaaitu 17,496 ± 462 cal. yr BP; Okareka 21,858 ± 290 cal. yr BP; Te Rere 25,171 ± 964 cal. yr BP; Kawakawa/Oruanui 25,358 ± 162 cal. yr BP; Poihipi 28,446 ± 670 cal. yr BP; and Okaia 28,621 ± 1428 cal. yr BP.Secondly, we have re-dated the start and end of the Lateglacial cool episode (climate event NZce-3 in the NZ-CES), previously referred to as the Lateglacial climate reversal, as defined at Kaipo bog in eastern North Island, New Zealand, using both Bacon and OxCal P_Sequence modelling with the IntCal09 data set. The ca 1200-yr-long cool episode, indicated by a lithostratigraphic change in the Kaipo peat sequence to grey mud with lowered carbon content, and a high-resolution pollen-derived cooling signal, began 13,739 ± 125 cal. yr BP and ended 12,550 ± 140 cal. yr BP (mid-point ages of the 95% highest posterior density regions, Bacon modelling). The OxCal modelling, generating almost identical ages, confirmed these ages. The Lateglacial cool episode (ca 13.8–12.6 cal. ka BP) thus overlaps a large part of the entire Antarctic Cold Reversal chronozone (ca 14.1–12.4 cal. ka BP or ca 14.6–12.8 cal. ka BP), and an early part of the Greenland Stadial-1 (Younger Dryas) chronozone (ca 12.9–11.7 cal. ka BP). The timing of the Lateglacial cool episode at Kaipo is broadly consistent with the latitudinal patterns in the Antarctic Cold Reversal signal suggested for the New Zealand archipelago from marine and terrestrial records, and with records from southern South America.

Recent Transmission of a Novel Alphacoronavirus, Bat Coronavirus HKU10, from Leschenault's Rousettes to Pomona Leaf-Nosed Bats: First Evidence of Interspecies Transmission of Coronavirus between Bats of Different Suborders

Although coronaviruses are known to infect various animals by adapting to new hosts, interspecies transmission events are still poorly understood. During a surveillance study from 2005 to 2010, a novel alphacoronavirus, BatCoV HKU10, was detected in two very different bat species, Ro-BatCoV HKU10 in Leschenault's rousettes (Rousettus leschenaulti) (fruit bats in the suborder Megachiroptera) in Guangdong and Hi-BatCoV HKU10 in Pomona leaf-nosed bats (Hipposideros pomona) (insectivorous bats in the suborder Microchiroptera) in Hong Kong. Although infected bats appeared to be healthy, Pomona leaf-nosed bats carrying Hi-BatCoV HKU10 had lower body weights than uninfected bats. To investigate possible interspecies transmission between the two bat species, the complete genomes of two Ro-BatCoV HKU10 and six Hi-BatCoV HKU10 strains were sequenced. Genome and phylogenetic analyses showed that Ro-BatCoV HKU10 and Hi-BatCoV HKU10 represented a novel alphacoronavirus species, sharing highly similar genomes except in the genes encoding spike proteins, which had only 60.5% amino acid identities. Evolution of the spike protein was also rapid in Hi-BatCoV HKU10 strains from 2005 to 2006 but stabilized thereafter. Molecular-clock analysis dated the most recent common ancestor of all BatCoV HKU10 strains to 1959 (highest posterior density regions at 95% [HPDs], 1886 to 2002) and that of Hi-BatCoV HKU10 to 1986 (HPDs, 1956 to 2004). The data suggested recent interspecies transmission from Leschenault's rousettes to Pomona leaf-nosed bats in southern China. Notably, the rapid adaptive genetic change in BatCoV HKU10 spike protein by ~40% amino acid divergence after recent interspecies transmission was even greater than the ~20% amino acid divergence between spike proteins of severe acute respiratory syndrome-related Rhinolophus bat coronavirus (SARSr-CoV) in bats and civets. This study provided the first evidence for interspecies transmission of coronavirus between bats of different suborders.

Invariance, model matching and probability matching

For an invariant statistical model we consider the induced right Haar prior distribution and the resulting right Haar posterior. Using this posterior distribution, HPD (highest posterior density) regions of constant posterior probability are constructed and shown to exhibit probability matching. Further, HPD regions for equivariant functions of the parameter are also shown to exhibit probability matching. A number of examples are considered.

Scale Parameter Estimation of the Laplace Model Using Different Asymmetric Loss Functions

In the last few decades, there has been an emergent interest in the construction of flexible parametric classes of probability distributions in Bayesian as compared to Classical approach. In present study Bayesian Analysis of Laplace model using Inverted Gamma, Inverted Chi-Squared informative, Levy and Gumbel Type-II priors is discussed. The properties of posterior distribution, credible interval, highest posterior density region (HPDR) and Bayes Factor are discussed in current study. Bayes estimators are derived under squared error loss function (SELF), precautionary loss function, weighted squared error loss function and modified (quadratic) squared error loss function. Hyperparameters are determined through Empirical Bayes method. The estimates are also compared using the posterior risks (PRs) under the said loss functions. The priors and loss functions are compared using a real life data set.

Bayesian genetic analysis of milk yield in Tunisian Holstein dairy cattle population

The genetic determinism of 305-d milk yield and its genetic parameters were investigated in Tunisian Holstein dairy cattle population through Bayesian segregation analyses using a Monte Carlo Markov Chains (MCMC) method. Data included 49,709 records of 305-d milk yield collected between 1996 and 2003 from 114 dairy herds. The postulated major gene was assumed to be additive biallelic locus with Mendelian transmission probabilities and priors used for variance components were uniform. Gibbs sampling was used to generate a chain of 500,000 samples, which were used to obtain posterior means of genetic parameters. Estimated marginal posterior means ± posterior standard deviations of variance components of milk yield were 402866.28 ± 23629.97, 271256.66 ± 34477.83, 68276.83 ± 233027.62 and 1098855.75 ± 10009.52 for polygenic variance (σ2u), permanent environmental variance (σ2ne), major gene variance (σ2G) and error variance (σ2e), respectively. The main finding of this paper showed the postulated major locus was not significant, since the 95% highest posterior density regions (HPDs95%) of most major gene parameters included 0, and particularly for the major gene variance. Estimated transmission probabilities for the 95% highest posterior density regions (HPDs95%) were overlapped. Genetic parameters of 305-d milk yield were very similar under both mixed inheritance and polygenic models. These results indicated that the genetic determinism of milk yield in Tunisian Holstein dairy cattle population is purely polygenic. Based on 50,000 Gibbs samples, heritability and repeatability estimates using polygenic model were h2 = 0.22 ± 0.012 and r = 0.38 ± 0.006, respectively.

A model‐based age estimate for Polynesian colonization of Hawai'i

ABSTRACT A model‐based Bayesian calibration using 14C data from paleoenvironmental cores and materials introduced to the islands by Polynesian colonists estimates that the islands were likely colonized sometime late in the first millennium AD. Two calibrations, one using 14C dates on floral materials and the other using 14C dates on floral and faunal materials, indicate that archaeological materials yield relatively imprecise estimates of the colonization event with 95% highest posterior density regions 3–5 centuries long. Materials introduced to the islands by Polynesians date to two periods, one that coincides with the colonization event, and another some 3–6 centuries later. A disparity between colonization and the first reliably dated archaeological evidence of human activity is identified and estimated to be 1–4 centuries long.

Complex Segregation Analysis of Total Milk Yield in Churra Dairy Ewes

The mode of inheritance of total milk yield and its genetic parameters were investigated in Churra dairy sheep through segregation analyses using a Monte Carlo Markov Chains (MCMC) method. Data which consisted of 7,126 lactations belonging to 5,154 ewes were collected between 1999 and 2002 from 15 Spanish Churra dairy flocks. A postulated major gene was assumed to be additive and priors used for variance components were uniform. Based on 50 000 Gibbs samples from ten replicates chains of 100,000 cycles, the estimated marginal posterior meansposterior standard deviations of variance components of milk yield were , , and for major gene variance (), polygenic variance (), permanent environmental variance () and error variance (), respectively. The results of this study showed the postulated major locus was not significant, and the 95% highest posterior density regions () of most major gene parameters included 0, and particularly for the major gene variance. The estimated transmission probabilities for the 95% highest posterior density regions () were overlapped. These results indicated that segregation of a major gene was unlikely and that the mode of inheritance of total milk yield in Churra dairy sheep is purely polygenic. Based on 50,000 Gibbs samples from ten replicates chains of 100,000 cycles, the estimated polygenic heritability and repeatability were and r=, respectively.

Genetic background and phenotypic characterization over two farrowings of leg conformation defects in Landrace and Large White sows1

A Bayesian threshold animal model was applied to evaluate the prevalence over 2 farrowings and genetic background of overall leg conformation score and the presence or absence of 6 specific leg defects (abnormal hoof growth, splay footed, plantigradism, straight pasterns, sickle-hocked legs, and the presence of swelling or injuries) in purebred Landrace and Large White sows. Data sets contained phenotypic records from 2,477 and 1,550 Landrace and Large White females, respectively, at the end of the growing period. Leg conformation data from first and second farrowings were available for 223 and 191 Landrace sows and 213 and 193 Large White sows, respectively. Overall leg conformation deteriorated with age, with statistically relevant differences between females at the end of the growing period, first farrowing (FF), and second farrowing (SF). In a similar way, the prevalence of the 6 specific leg defects increased between the end of the growing period and FF (with the exception of straight pasterns in the Landrace population). Differences between FF and second farrowing were statistically relevant for hoof growth (highest posterior density regions at 95% did not overlap), plantigradism, sickle-hocked legs, and overall leg conformation score in Landrace and for sickle-hocked leg and overall leg conformation score in Large White. The statistical relevance of the genetic background was tested through the Bayes factor (BF) between the model with the additive genetic component and the model with 0 heritability (nonheritable). Heritability (h(2)) was discarded (BF < 1) for sickle-hocked leg in both breeds, whereas decisive evidence (BF > 100) of genetic background was obtained for overall leg conformation score in Landrace and Large White sows (h(2) = 0.27 and 0.38, respectively), hoof growth in both breeds (h(2) = 0.22 and 0.26, respectively), and plantigradism (h(2) = 0.34) and the presence of swelling or injuries in Landrace (h(2) = 0.27). Note that a BF > 100 implies that the model with infinitesimal genetic effects was more than 100 times more suitable than the model without genetic effects, a conclusive estimate within the Bayesian framework. The remaining traits (splay footed and straight pasterns) registered BF values ranging from 11.6 to 35.1 and h(2) values ranging from 0.09 to 0.19. These results indicated a moderate genetic determinism for leg conformation in Landrace and Large White sows.

Simultaneous probability statements for Bayesian P-splines

P-splines are a popular approach for fitting nonlinear effects of continuous covariates in semiparametric regression models. Recently, a Bayesian version for P-splines has been developed on the basis of Markov chain Monte Carlo simulation techniques for inference. In this work, we adopt and generalize the concept of Bayesian contour probabilities to additive models with Gaussian or multicategorical responses. More specifically, we aim at computing the maximum credible level (sometimes called Bayesian p-value) for which a particular parameter vector of interest lies within the corresponding highest posterior density (HPD) region. We are particularly interested in parameter vectors that correspond to a constant, linear or, more generally, a polynomial fit. As an alternative to HPD regions, simultaneous credible intervals could be used to define pseudo contour probabilities. Efficient algorithms for computing contour and pseudo contour probabilities are developed. The performance of the approach is assessed through simulation studies. Two applications on the determinants of undernutrition in developing countries and the health status of trees show how contour probabilities may be used in practice to assist the analyst in the model building process.

Mixed Model Studies on Inheritance of Reproductive Traits in Laying Hens – A Bayesian Approach

Segregation analyses performed for many livestock species indicate a mixed inheritance model of reproductive traits. Additionally, depending on the population, a given trait can be determined by a number of genes with large effects. Genetic backgrounds of hatch-ability and fertility in poultry are still not known sufficiently. The objectives of this study are to verify the hypothesis on segregation of single genes (1 vs. 2) affecting fertility and hatchability and to estimate a heritability of these traits. Records from 2,040 and 2,015 dams from full-pedigreed strains of Rhode Island Red (R33) and New Hampshire (N88) from a pedigree farm were analyzed. The percentage of fertilized eggs and the percentage of the eggs hatched of fertilized eggs were registered for dams only. Fertility was checked by candling on the eighth day of incubation. To obtain a binomial phenotypic scale, 10 eggs per dam were included into the analysis. Animal single-trait threshold models were used for the analysis of data. The first model included the effects of 2 single genes, 2 fixed effects of year and season, additive polygenic effects, and permanent environmental effects. In the second model, only 1 single gene effect was included. Additionally, the analysis based on the polygenic threshold model was also performed. The Gibbs sampling procedure was used. The significance of single gene effects was verified by highest posterior density regions. The obtained results clearly gave evidence for the segregation of 1 major gene for hatchability in strain R33. Furthermore, the mixed inheritance model can also be suggested for fertility in this strain. After the analysis, the polygenic heritabilities were very low (<0.11), whereas major polygenic heritability ranged from 0.05 to 0.12.