Logarithmic Score Research Articles

Development of Novel Peripheral Blood Count-Based Prognostic Index for Multiple Myeloma

In multiple myeloma (MM), clonal plasma cells evade immune surveillance and proliferate within an inflammatory bone marrow microenvironment. During pathogenesis, monocyte-derived tumor-associated macrophages help myeloma cells to avoid apoptosis; effector T cell lymphocytes undergo senescence to enable preferential upregulation of their immunosuppressive regulatory T cell counterparts; and myeloma cells interact with hematopoietic stem cells to inhibit downstream megakaryocyte differentiation into platelets.1 Our prior research has suggested a prognostic role for the absolute monocyte count (AMC), absolute lymphocyte count (ALC), and platelet count as biomarkers. We have shown that abnormal AMC and decreased ALC and platelet count are associated with decreased overall survival (OS) among patients with MM at diagnosis and follow-up. Based on the easy accessibility of these peripheral blood markers and need for dynamic prognostication among patients with MM undergoing novel therapies, we created a categorical peripheral blood-based prognostic index for MM incorporating AMC, ALC and platelet count. We retrospectively evaluated this index in 10790 patients diagnosed with MM between 2000 and 2019 at Veterans Administration hospitals using cell counts obtained closest to diagnosis and up to 2.5 years thereafter. Patients were stratified into 3 levels based on a logarithmic risk score, where those with the lowest counts across all cell lines (AMC, ALC, and platelet count) were in level III and those with counts approaching normalcy were in level I. At diagnosis, 8% of patients were in level III and had the highest risk of death (hazard ratio [HR] 2.04; 95% confidence interval [CI] 1.85-2.24; P < .01) compared to those in levels I (HR 1.15; 95% CI, 1.08-1.23; P < .01) and II (HR 1.37; 95% CI, 1.28-1.46; P < .01). Moreover, the risk of inferior OS associated with level III status persisted during treatment and follow-up and existed independently of other known risk stratification tools (including Charlson comorbidity index, lactate dehydrogenase, International Staging System classification). With further validation, our findings support the use of our novel prognostic index, which potentially reflects the underlying tumor microenvironment, as an available tool for risk stratification during the MM disease course.

Validation of point process predictions with proper scoring rules

AbstractWe introduce a class of proper scoring rules for evaluating spatial point process forecasts based on summary statistics. These scoring rules rely on Monte Carlo approximations of expectations and can therefore easily be evaluated for any point process model that can be simulated. In this regard, they are more flexible than the commonly used logarithmic score and other existing proper scores for point process predictions. The scoring rules allow for evaluating the calibration of a model to specific aspects of a point process, such as its spatial distribution or tendency toward clustering. Using simulations, we analyze the sensitivity of our scoring rules to different aspects of the forecasts and compare it to the logarithmic score. Applications to earthquake occurrences in northern California, United States and the spatial distribution of Pacific silver firs in Findley Lake Reserve in Washington highlight the usefulness of our scores for scientific model selection.

Scoring and ranking probabilistic seismic hazard models: an application based on macroseismic intensity data

Abstract. A probabilistic seismic hazard model consists of a set of weighted models/branches that describes the center, the body and the range of seismic hazard. Owing to the intrinsic nature of this kind of analysis, the weight of each model/branch represents its scientific credibility. However, practical uses of this model may sometimes require the selection of one or a few hazard curves that are sampled from the whole model, which often consists of thousands of branches. Here we put forward an innovative procedure that facilitates the scoring, ranking and selection of the hazard curves to account for the requirements of a specific application. The approach consists of a careful quality check of the data used for scoring and the adoption of a proper scoring rule. To show the applicability of this approach, we present an example that consists of scoring and ranking a set of multiple models/branches constituting a recent seismic hazard model of Italy. To score these branches, hazard estimates produced by each of them are compared with time series of macroseismic observations available in the Italian macroseismic database for a carefully selected set of localities deemed sufficiently representative, homogeneously distributed in space and complete with respect to time and intensity levels. The proper scoring parameter used for such a comparison is the logarithmic score, which can always be applied independently of the distribution of the data.

Information-Based Probabilistic Verification Scores for Two-Dimensional Ensemble Forecast Data: A Madden–Julian Oscillation Index Example

Abstract Probabilistic forecasting is a common activity in many fields of the Earth sciences. Assessing the quality of probabilistic forecasts—probabilistic forecast verification—is therefore an essential task in these activities. Numerous methods and metrics have been proposed for this purpose; however, the probabilistic verification of vector variables of ensemble forecasts has received less attention than others. Here we introduce a new approach that is applicable for verifying ensemble forecasts of continuous, scalar, and two-dimensional vector data. The proposed method uses a fixed-radius near-neighbors search to compute two information-based scores, the ignorance score (the logarithmic score) and the information gain, which quantifies the skill gain from the reference forecast. Basic characteristics of the proposed scores were examined using idealized Monte Carlo simulations. The results indicated that both the continuous ranked probability score (CRPS) and the proposed score with a relatively small ensemble size (<25) are not proper in terms of the forecast dispersion. The proposed verification method was successfully used to verify the Madden–Julian oscillation index, which is a two-dimensional quantity. The proposed method is expected to advance probabilistic ensemble forecasts in various fields. Significance Statement In the Earth sciences, stochastic future states are estimated by solving a large number of forecasts (called ensemble forecasts) based on physical equations with slightly different initial conditions and stochastic parameters. The verification of probabilistic forecasts is an essential part of forecasting and modeling activity in the Earth sciences. However, there is no information-based probabilistic verification score applicable for vector variables of ensemble forecasts. The purpose of this study is to introduce a novel method for verifying scalar and two-dimensional vector variables of ensemble forecasts. The proposed method offers a new approach to probabilistic verification and is expected to advance probabilistic ensemble forecasts in various fields.

Probabilistic Forecast Reconciliation under the Gaussian Framework

Forecast reconciliation of multivariate time series maps a set of incoherent forecasts into coherent forecasts to satisfy a given set of linear constraints. Available methods in the literature either follow a projection matrix-based approach or an empirical copula-based reordering approach to revise the incoherent future sample paths to obtain reconciled probabilistic forecasts. The projection matrices are estimated either by optimizing a scoring rule such as energy or variogram score or simply using a projection matrix derived for point forecast reconciliation. This article proves that (a) if the incoherent predictive distribution is jointly Gaussian, then MinT (minimum trace) minimizes the logarithmic scoring rule for the hierarchy; and (b) the logarithmic score of MinT for each marginal predictive density is smaller than that of OLS (ordinary least squares). We illustrate these theoretical results using a set of simulation studies and the Australian domestic tourism dataset. The estimation of MinT needs to estimate the covariance matrix of the base forecast errors. We have evaluated the performance using the sample covariance matrix and shrinkage estimator. It was observed that the theoretical properties noted above are greatly impacted by the covariance matrix used and highlighted the importance of estimating it reliably, especially with high dimensional data.

PS-C23-2: GUT MICROBIOTA AND SUBCLINICAL CORONARY ARTERY CALCIFICATION IN A GENERAL POPULATION OF JAPANESE MEN

Objective: The gut microbiota of patients with coronary artery disease is being shown to differ from that of healthy individuals. However, it is unclear whether it is altered before the onset of the disease. The aim of this study is to investigate the association between gut microbiota and subclinical coronary artery calcification (CAC) in general Japanese men. Design and method: We randomly selected men from the general Japanese population, who underwent computed tomography and gut microbiology tests between 2010 and 2016. Among participants who underwent both tests, excluding those with myocardial infarction history, leaving a sample size of 653 participants in the analysis. DNA was extracted from fecal samples, the bacterial 16S ribosomal RNA gene was amplified using a two-step tail polymerase chain reaction method, and DNA sequencing was performed on a MiSeq System, followed by data analysis using QIIME2 algorithm. Agatston scores > = 100 was defined as the presence of CAC. LEfSe identified different taxa between with and without CAC, and Poisson regression analysis examined them when logarithmic LDA score was > = 3.5 and phylogenetic levels > = 3. Each taxon was ranked in quartiles (Q1–4) and the relative risk (RR) of CAC was calculated. Adjustment factors were age, smoking, drinking, body mass index, use of medication to treat hypertension, dyslipidemia, or diabetes, and history of cardiovascular events. Sensitivity analysis also delimited Agatston scores by 0 or 10. Results: Mean age of the participants was 68.3 years, and 215 (32.9%) participants had a CAC score > = 100. Relative abundance of phylum level was 55.1% and 53.2% for Firmicutes, and 32.4% and 34.3% for Bacteroidetes among participants with versus without CAC score > = 100, respectively. Among taxa identified by LEfSe, Poisson regression analysis revealed the genus Bacteroides was inversely associated and genus Ruminococcus was positively associated with CAC after multivariable adjustment (Bacteroides: RR [95%CI] = 0.62 [0.45–0.86] (Q4) vs. ref (Q1)) (Ruminococcus: RR [95%CI] = 1.69 [1.25–2.29] (Q4) vs. ref (Q1)). Sensitivity analysis showed similar results. Conclusions: The ratio of Firmicutes to Bacteroidetes was high from the beginning of atherosclerosis. Higher genus Ruminococcus and lower genus Bacteroides were associated with a CAC score > = 100 in general Japanese men.

MALDI-TOF MS Identification of Dromedary Camel Ticks and Detection of Associated Microorganisms, Southern Algeria.

This study used MALDI-TOF MS and molecular tools to identify tick species infesting camels from Tamanrasset in southern Algeria and to investigate their associated microorganisms. Ninety-one adult ticks were collected from nine camels and were morphologically identified as Hyalomma spp., Hyalomma dromedarii, Hyalomma excavatum, Hyalomma impeltatum and Hyalomma anatolicum. Next, the legs of all ticks were subjected to MALDI-TOF MS, and 88/91 specimens provided good-quality MS spectra. Our homemade MALDI-TOF MS arthropod spectra database was then updated with the new MS spectra of 14 specimens of molecularly confirmed species in this study. The spectra of the remaining tick specimens not included in the MS database were queried against the upgraded database. All 74 specimens were correctly identified by MALDI-TOF MS, with logarithmic score values ranging from 1.701 to 2.507, with median and mean values of 2.199 and 2.172 ± 0.169, respectively. One H. impeltatum and one H. dromedarii (2/91; 2.20%) tested positive by qPCR for Coxiella burnetii, the agent of Q fever. We also report the first detection of an Anaplasma sp. close to A. platys in H. dromedarii in Algeria and a potentially new Ehrlichia sp. in H. impeltatum.

Hierarchical mining with complex networks for music genre classification

Music genre is an important feature to identify a musical work. Thus, it is the most used label to organize musical datasets. However, this label is not always available and its identification is not a simple and direct task. Hence, in literature we can find many music genre classification (MGC) methods, with a variety of features and machine learning algorithms (MLA). In this paper, we propose an MGC system by using two levels of hierarchical mining, GLCM (gray level co-occurrence matrix) networks generated from the mel-spectrogram and a multi-hybrid feature strategy. Three types of complex networks were generated: GLCM network Gg, Superpixels network Gs, and GLCM network of each node of Gs (Ggsi network). The multi-hybrid features are formed by textural and topological measures of complex networks and acoustic measures. In the classification step, we used three datasets: GTZAN, Homburg, and ISMIR; two MLAs belonging to the classifier ensemble approach, and (10)-fold cross-validation repeated 100 times. Several experiments were performed using feature combinations of macro-mining (global features of Gg and Gs) and micro-mining (global features of Ggsi). For GTZAN, we performed a detailed analysis of individual class performance and calculated our new ranking logarithmic score (RLS) applied to the F1-score. For all datasets, the RLS and accuracy values were compared with several state-of-the-art methods. The accuracy obtained using micro-mining was >90%, which reveals a satisfactory result.

Decision Support System Based on CoCoSo Method with the Picture Fuzzy Information

Coronavirus disease 2019 (COVID‐19) is currently threatening the entire world, and a novel coronavirus is a virus from the corona family that has spread a new infection. The number of instances of this disease is increasing at an exponential, but there are now commercially accessible COVID‐19 vaccines. The weak symptoms of COVID‐19 disease, on the other hand, are treated with a variety of antiviral treatments. It is still choosing the optimal antiviral medicine to manage COVID‐19s. It is a challenging and difficult alternative to reduce the risk of infection. In this study, an improved combined compromise solution (CoCoSo) method is proposed to identify the ranking of alternatives. The introduction of a logarithmic picture fuzzy set is a more effective technique for representing variance, represented by three memberships (positive, neutral, and negative membership) degrees. This work introduces a fresh logarithmic picture fuzzy score function, to deal with the problem of comparison. The CoCoSo method‐based logarithmic picture fuzzy decision‐making algorithm is given. To achieve so, a new divergence measure for the logarithmic picture fuzzy number is introduced. To demonstrate the viability and efficacy of the established approach in real‐world applications, a case study of COVID‐19 disease drug selection is discussed.

Density Forecast of Financial Returns Using Decomposition and Maximum Entropy

Abstract We consider a multiplicative decomposition of the financial returns to improve the density forecasts of financial returns. The multiplicative decomposition is based on the identity that financial return is the product of its absolute value and its sign. Advantages of modeling the two components are discussed. To reduce the effect of the estimation error due to the multiplicative decomposition in estimation of the density forecast model, we impose a moment constraint that the conditional mean forecast is set to match with the sample mean. Imposing such a moment constraint operates a shrinkage and tilts the density forecast of the decomposition model to produce the improved maximum entropy density forecast. An empirical application to forecasting density of the daily stock returns demonstrates the benefits of using the decomposition and imposing the moment constraint to obtain the improved density forecast. We evaluate the density forecast by comparing the logarithmic score (LS), the quantile score (QS), and the continuous ranked probability score (CRPS). We contribute to the literature on the density forecast and the decomposition models by showing that the density forecast of the decomposition model can be improved by imposing a sensible constraint in the maximum entropy framework.

Molecular and MALDI-TOF MS identification of swallow bugs Cimex hirundinis (Heteroptera: Cimicidae) and endosymbionts in France

BackgroundThe Cimicidae are obligatory blood-feeding ectoparasites of medical and veterinary importance. We aim in the current study to assess the ability of MALDI-TOF MS to identify Cimex hirundinis swallow bugs collected in house martin nests.MethodsSwallow bugs were picked out from abandoned nests of house martin swallows and identified morphologically to the species level. The bugs were randomly selected, dissected and then subjected to MALDI-TOF MS and molecular analyses.ResultsA total of 65 adults and 50 nymphs were used in the attempt to determine whether this tool could identify the bug species and discriminate their developmental stages. Five adults and four nymphs of C. hirundinis specimens were molecularly identified to update our MS homemade arthropod database. BLAST analysis of COI gene sequences from these C. hirundinis revealed 98.66–99.12% identity with the corresponding sequences of C. hirundinis of the GenBank. The blind test against the database supplemented with MS reference spectra showed 100% (57/57) C. hirundinis adults and 100% (46/46) C. hirundinis nymphs were reliably identified and in agreement with morphological identification with logarithmic score values between 1.922 and 2.665. Ninety-nine percent of C. hirundinis specimens tested were positive for Wolbachia spp. The sequencing results revealed that they were identical to Wolbachia massiliensis, belonging to the new T-supergroup strain and previously isolated from C. hemipterus.ConclusionsWe report for the first time to our knowledge a case of human infestation by swallow bugs (C. hirundinis) in France. We also show the usefulness of MALDI-TOF MS in the rapid identification of C. hirundinis specimens and nymphs with minimal sample requirements. We phylogenetically characterized the novel Wolbachia strain (W. massiliensis) infecting C. hirundinis and compared it to other recognized Wolbachia clades.Graphical

Abstract 10150: Distinct Gut Microbiota Composition Among Older Adults with Impaired Left Ventricular Diastolic Function

Introduction: Recent research has demonstrated shifts in intestinal microbial composition in response to cardiovascular disease (CVD) development. Left ventricular (LV) diastolic dysfunction is an early manifestation of myocardial ageing. We aimed to examine whether gut microbial composition is associated with LV diastolic function among healthy older adults. Methods: Among community older adults, 15 subjects with preserved LV ejection fraction on echocardiography underwent gut microbial composition examination in this proof-of-concept cross-sectional study. Myocardial relaxation (diastolic function) was impaired in those subjects with lower ratios of peak early (E) to late diastolic (A, atrial contraction) velocities. Metagenomic reads from stool samples were analyzed after excluding human reference genome data, and classified into various microbial taxonomic groups using lowest-common-ancestor algorithm. Statistical analysis was performed using linear discriminant analysis (LDA). Results: The subjects (53% males, mean age 75±4 years) were stratified into Groups 1 (n=8) and 2 (n=7) with more severe and lesser diastolic dysfunction, respectively, based on E/A ratios (0.77 vs. 1.28, p<0.0001). In Group 1, there was significantly higher prevalence of certain bacteria (p<0.05), including Bacteroides sp, Ruminococcus sp., and Paraprevotella (Figure 1). The largest relative effect size was with Bacteroides sp., including Bacteroides xylanisolvens (logarithmic LDA score 3.0). In Group 2, there was significantly higher prevalence (p<0.05) of Oscillibacter sp., Peptostreptococcaceae, Clostridioides difficile, Prevotella timonensis, and Blautia producta. Relative effect size was largest with Oscillibacter sp. (log 2.8). Conclusions: Distinct gut microbiota were associated with more severe vs. lesser LV diastolic dysfunction. Future validation in larger cohorts is warranted for targeting the microbiome in myocardial ageing.

Considerations for Developing Predictive Spatial Models of Crime and New Methods for Measuring Their Accuracy

A literature review of the important trends in predictive crime modeling and the existing measures of accuracy was undertaken. It highlighted the need for a robust, comprehensive and independent evaluation and the need to include complementary measures for a more complete assessment. We develop a new measure called the penalized predictive accuracy index (PPAI), propose the use of the expected utility function to combine multiple measures and the use of the average logarithmic score, which measures accuracy differently than existing measures. The measures are illustrated using hypothetical examples. We illustrate how PPAI could identify the best model for a given problem, as well as how the expected utility measure can be used to combine different measures in a way that is the most appropriate for the problem at hand. It is important to develop measures that empower the practitioner with the ability to input the choices and preferences that are most appropriate for the problem at hand and to combine multiple measures. The measures proposed here go some way towards providing this ability. Further development along these lines is needed.

Using MALDI-TOF mass spectrometry to identify ticks collected on domestic and wild animals from the Democratic Republic of the Congo

Matrix-assisted laser desorption/ionization mass spectrometry (MALDI-TOF MS) has recently emerged as an alternative to morphological and molecular tools to identify tick species. In this study, we set out to evaluate and confirm the ability of MALDI-TOF MS to identify different species of ticks collected in the Democratic Republic of the Congo and preserved in 70% ethanol. A total of 575 ticks, of which 530 were collected from domestic pigs and 45 from wild animals, were subjected to MALDI-TOF MS analysis to evaluate the intraspecies reproducibility and interspecies specificity of MS profiles obtained from the different species. Morphologically, the ticks belonged to seven different species, namely Rhipicephalus complanatus, Rhipicephalus congolensis, Haemaphysalis muhsamae, Ixodes cumulatimpunctatus, Amblyomma exornatum, Amblyomma compressum and an unidentified Rhipicephalus sp. A total of 535/575 (93%) of the spectra obtained were of good enough quality to be used for our analyses. Our home-made MALDI-TOF MS arthropod database was upgraded with spectra obtained from between one and five randomly selected specimens per species. For these reference specimens, molecular identification of the ticks was also made using 16S, 12S rDNA genes and the Cox1 mtDNA gene sequencing. The remaining good quality spectra were then queried against the upgraded MALDI-TOF MS database, showing that 100% were in agreement with the morphological identification, with logarithmic score values (LSVs) between 1.813 and 2.51. The consistency between our morphological, molecular and MALDI-TOF MS identification confirms the capability and precision of MALDI-TOF MS for tick identification.

Predictive functional analysis reveals inferred features unique to cervicovaginal microbiota of African women with bacterial vaginosis and high-risk human papillomavirus infection.

Mounting evidence suggests that Lactobacillus species may not necessarily be the sine qua non of healthy cervicovaginal microbiota (CVM), especially among reproductive-age African women. A majority of African women have high-diversity non-Lactobacillus-dominated CVM whose bacterial functions remain poorly characterized. Functional profiling of the CVM is vital for investigating human host-microbiota interactions in health and disease. Here, we investigated the functional potential of L. iners-dominated and high-diversity non-Lactobacillus-dominated CVM of 75 African women with and without bacterial vaginosis (BV) and high-risk human papillomavirus (HR-HPV) infection. Functional contents were predicted using PICRUSt. Microbial taxonomic diversity, BV, and HR-HPV infection statuses were correlated with the inferred functional composition of the CVM. Differentially abundant inferred functional categories were identified using linear discriminant analysis (LDA) effect size (LEfSe) (p-value <0.05 and logarithmic LDA score >2.0). Of the 75 women, 56 (74.7%), 35 (46.7%), and 29 (38.7%) had high-diversity non-Lactobacillus-dominated CVM, BV, and HR-HPV infection, respectively. Alpha diversity of the inferred functional contents (as measured by Shannon diversity index) was significantly higher in women with high-diversity non-Lactobacillus-dominated CVM and BV than their respective counterparts (H statistic ≥11.5, q-value <0.001). Ordination of the predicted functional metagenome content (using Bray-Curtis distances) showed that the samples segregated according to the extent of microbial taxonomic diversity and BV (pseudo-F statistic ≥19.6, q-value = 0.001) but not HR-HPV status (pseudo-F statistic = 1.7, q-value = 0.159). LEfSe analysis of the inferred functional categories revealed that transport systems (including ABC transporters) and transcription factors were enriched in high-diversity CVM. Interestingly, transcription factors and sporulation functional categories were uniquely associated with high-diversity CVM, BV, and HR-HPV infection. Our predictive functional analysis reveals features unique to high-diversity CVM, BV and HR-HPV infections. Such features may represent important biomarkers of BV and HR-HPV infection. Our findings require proof-of-concept functional studies to examine the relevance of these potential biomarkers in women’s reproductive health and disease.

Beyond Strictly Proper Scoring Rules: The Importance of Being Local

AbstractThe evaluation of probabilistic forecasts plays a central role both in the interpretation and in the use of forecast systems and their development. Probabilistic scores (scoring rules) provide statistical measures to assess the quality of probabilistic forecasts. Often, many probabilistic forecast systems are available while evaluations of their performance are not standardized, with different scoring rules being used to measure different aspects of forecast performance. Even when the discussion is restricted to strictly proper scoring rules, there remains considerable variability between them; indeed strictly proper scoring rules need not rank competing forecast systems in the same order when none of these systems are perfect. The locality property is explored to further distinguish scoring rules. The nonlocal strictly proper scoring rules considered are shown to have a property that can produce “unfortunate” evaluations, particularly the fact that the continuous rank probability score prefers the outcome close to the median of the forecast distribution regardless of the probability mass assigned to the value at/near the median raises concern to its use. The only local strictly proper scoring rule, the logarithmic score, has direct interpretations in terms of probabilities and bits of information. The nonlocal strictly proper scoring rules, on the other hand, lack meaningful direct interpretation for decision support. The logarithmic score is also shown to be invariant under smooth transformation of the forecast variable, while the nonlocal strictly proper scoring rules considered may, however, change their preferences due to the transformation. It is therefore suggested that the logarithmic score always be included in the evaluation of probabilistic forecasts.

Statistical Postprocessing of Wind Speed Forecasts Using Convolutional Neural Networks

AbstractCurrent statistical postprocessing methods for probabilistic weather forecasting are not capable of using full spatial patterns from the numerical weather prediction (NWP) model. In this paper, we incorporate spatial wind speed information by using convolutional neural networks (CNNs) and obtain probabilistic wind speed forecasts in the Netherlands for 48 h ahead, based on KNMI’s deterministic HARMONIE-AROME NWP model. The probabilistic forecasts from the CNNs are shown to have higher Brier skill scores for medium to higher wind speeds, as well as a better continuous ranked probability score (CRPS) and logarithmic score, than the forecasts from fully connected neural networks and quantile regression forests. As a secondary result, we have compared the CNNs using three different density estimation methods [quantized softmax (QS), kernel mixture networks, and fitting a truncated normal distribution], and found the probabilistic forecasts based on the QS method to be best.

Evaluating epidemic forecasts in an interval format.

For practical reasons, many forecasts of case, hospitalization, and death counts in the context of the current Coronavirus Disease 2019 (COVID-19) pandemic are issued in the form of central predictive intervals at various levels. This is also the case for the forecasts collected in the COVID-19 Forecast Hub (https://covid19forecasthub.org/). Forecast evaluation metrics like the logarithmic score, which has been applied in several infectious disease forecasting challenges, are then not available as they require full predictive distributions. This article provides an overview of how established methods for the evaluation of quantile and interval forecasts can be applied to epidemic forecasts in this format. Specifically, we discuss the computation and interpretation of the weighted interval score, which is a proper score that approximates the continuous ranked probability score. It can be interpreted as a generalization of the absolute error to probabilistic forecasts and allows for a decomposition into a measure of sharpness and penalties for over- and underprediction.

Test positivity for Maedi–Visna virus and Mycobacterium avium ssp. paratuberculosis in Sarda ewes: Effects on milk composition and coagulation traits and heritability estimates for susceptibility

Maedi-Visna virus (MVV) and Mycobacterium avium ssp. paratuberculosis (MAP) are two pathogens that cause chronic, production-limiting diseases in dairy sheep. Although they are present worldwide, there are no detailed reports on their actual effects on milk traits in the literature. This study was designed to investigate the effects of test positivity to MVV and MAP on ovine milk yield, composition and coagulation properties, and curd-firming over time (CFt) variables in clinically healthy animals at the field level. The additive genetic variation and heritabilities of MVV and MAP positivity were also estimated. Milk samples were collected from 1,079 Sarda sheep kept on 23 farms, and pedigree information was obtained from the flock book. Milk yield was also recorded on the sampling date. Positivity for MVV and MAP was determined from milk samples using indirect ELISA test kits. Milk composition traits were measured by spectroscopy, milk coagulation properties were measured with a Formagraph (Foss Italia, Padua, Italy), and CFt traits were calculated using the data from the Formagraph diagram. The effects of MVV and MAP positivity on milk traits were determined through a set of mixed linear models, which took into account various sources of variation, such as days in milk, parity, and flock effects, and included the effects (positive or negative) of the 2 pathogens. A Bayesian threshold sire model with sire relationship was used to estimate genetic variation and heritability. The overall animal prevalence of MVV-positive ewes was 43.6%; on only 1 farm of the 23 tested were all sampled ewes negative. An overall animal prevalence of 10.6% was recorded for MAP, with 4 farms at 0%. Positivity for MVV significantly affected the logarithmic score of the bacterial count, curd firmness after 30 min and 45 min, and the curd-firming instant rate constant. We found significant effects of MAP infection on milk composition, pH, and rennet coagulation time. The mean of the posterior distributions of heritability estimates on the liability scale was 0.15 for MAP and 0.07 for MVV. Our results demonstrate that only a few traits are negatively affected by MVV and MAP positivity, and that there is exploitable genetic variation in MVV and MAP susceptibility in dairy sheep.

Additive Scoring Rules for Discrete Sample Spaces

In this paper, we develop strictly proper scoring rules that may be used to evaluate the accuracy of a sequence of probabilistic forecasts. In practice, when forecasts are submitted for multiple uncertainties, competing forecasts are ranked by their cumulative or average score. Alternatively, one could score the implied joint distributions. We demonstrate that these measures of forecast accuracy disagree under some commonly used rules. Furthermore, and most importantly, we show that forecast rankings can depend on the selected scoring procedure. In other words, under some scoring rules, the relative ranking of probabilistic forecasts does not depend solely on the information content of those forecasts and the observed outcome. Instead, the relative ranking of forecasts is a function of the process by which those forecasts are evaluated. As an alternative, we describe additive and strongly additive strictly proper scoring rules, which have the property that the score for the joint distribution is equal to a sum of scores for the associated marginal and conditional distributions. We give methods for constructing additive rules and demonstrate that the logarithmic score is the only strongly additive rule. Finally, we connect the additive properties of scoring rules with analogous properties for a general class of entropy measures.