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X-ray diffractometry (XRD) is commonly used to determine both aragonite:calcite ratio and Mg content (in calcite) in biogenic skeletal carbonate. Bimineral taxa, such as many abalone, combine aragonite and calcite, or sometimes two distinct calcites, in a single skeleton. At least some abalone shells are, however, formed of three discrete carbonate minerals: aragonite, high-Mg calcite, and low-Mg calcite. Here we develop and apply a new system based on a Bayesian calibration model, an extension of the Reference Intensity Ratio method that accommodates heteroskedastic noise, for determining relative proportions in trimineralic biogenic carbonate using XRD patterns. We describe the system, validate and assess the system using biomineral standards, and quantify sources of error. We then use the system to describe mineralogical variation within the sometimes-trimineralic New Zealand black-footed paua Haliotis iris. All specimens contained aragonite, and most contained low-Mg calcite, with older shell showing decreasing amounts of calcite (presumably due to wear of this external layer). Almost all specimens from Kaikoura contained at least some high-Mg calcite, thus being tri-mineralic. This mixture of three biogenic carbonates is most unusual, so we have used our new method of analysing XRD patterns to estimate the proportions of three co-occurring skeletal carbonate minerals in this marine invertebrate. We also provide the first detailed analysis of uncertainty and precision in XRD analysis of skeletal carbonate mineralogy.

\"Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years--at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information, even breaking Germany's Enigma code during World War II, and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security. Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.\"-- Provided by publisher.

Background Asthma is a heterogeneous disease that affects millions of children and adults. There is a lack of objective gold standard diagnosis that spans the ages; instead, diagnoses are made by clinician assessment based on a cluster of signs, symptoms and objective tests dependent on age. Yet, there is a clear morbidity associated with chronic asthma symptoms. Machine learning has become a popular tool to improve asthma diagnosis and classification. There is a paucity of literature on the use of Bayesian machine learning algorithms to predict asthma diagnosis in children. This paper develops a prediction model using the Bayesian additive regression trees (BART) and compares its performance to various machine learning algorithms in predicting the diagnosis of childhood asthma. Methods Clinically relevant variables collected at or before 3 years of age from 2794 participants in the CHILD Cohort Study were used to predict physician-diagnosed asthma at age 5. BART and six other commonly used machine learning algorithms, namely adaptive boosting, logistic regression, decision tree, neural network, random forest, and support vector machine were trained. Measures of performance including sensitivity, specificity, and area under the receiver operating characteristic (ROC) curve were calculated. The confidence intervals were calculated using Bootstrapping samples. Important predictors and interaction effects associated with asthma were also identified using BART. Results BART, logistic regression and random forest showed the highest area under the ROC curve compared to other machine learning algorithms. Based on BART, recurrent wheeze, respiratory infection and food sensitization at 3 years of age were the most important predictors. The three most important interaction effects were found to be interaction terms of respiratory infection at 3 years and recurrent wheezing at 3 years, maternal asthma and paternal asthma, and maternal wheezing and inhalant sensitization of child at 3 years. Conclusions BART demonstrated promising prediction performance when compared to other machine learning algorithms. Future research could validate the BART in an external cohort to evaluate its reliability and generalizability.

In medical research and clinical practice, Bayesian survival modeling is a powerful technique for assessing time-to-event data. It allows for the incorporation of prior knowledge about the model’s parameters and provides a more comprehensive understanding of the underlying hazard rate function. In this paper, we propose a Bayesian survival modeling strategy for proportional hazards regression models that employs the Sine-G family of distributions as baseline hazards. The Sine-G family contains flexible distributions that can capture a wide range of hazard forms, including increasing, decreasing, and bathtub-shaped hazards. In order to capture the underlying hazard rate function, we examine the flexibility and effectiveness of several distributions within the Sine-G family, such as the Gompertz, Lomax, Weibull, and exponentiated exponential distributions. The proposed approach is implemented using the R programming language and the STAN probabilistic programming framework. To evaluate the proposed approach, we use a right-censored survival dataset of gastric cancer patients, which allows for precise determination of the hazard rate function while accounting for censoring. The Watanabe Akaike information criterion and the leave-one-out information criterion are employed to evaluate the performance of various baseline hazards.

Background Real-world evaluation of large language models (LLMs) as clinical diagnostic aids is limited by the reliance on static vignettes and retrospective data, which inadequately reflect the dynamic, iterative nature of clinical decision-making and may overestimate LLMs’ performance. Here, we benchmark GPT-4o in a stepwise simulated diagnostic setting with real-world clinical data, comparing its diagnostic accuracy and information-seeking strategy with Bayesian-network-derived optimal policies and observed physician practice. Methods We assessed GPT-4o across 500 emergency department (ED) chest-pain encounters, drawn from a cohort of 202,632 cases spanning three EDs. A Bayesian network (BN) trained on the structured cohort data imputed clinical data not collected in the original encounter to create a more robust simulation environment. The BN furthermore enabled derivation of mutual-information-optimal query pathways. GPT-4o sequentially requested information from 136 structured clinical variables under three prompting regimes that varied in disease-prevalence cues and diagnostic category constraints. Diagnostic decisions encompassed one of seven predefined emergent conditions or Other Diagnosis . We measured diagnostic accuracy under each prompting strategy, as well as calculated rank-based overlap with the BN optimal pathway to benchmark the LLM’s information-seeking behavior. Results Across the full chest-pain cohort, life-threatening etiologies accounted for only 2.14% of encounters (from 1.04% acute coronary syndrome to 0.01% esophageal rupture). With baseline prompting, GPT-4o systematically over-predicted rare conditions (sensitivity 79.3%; specificity 45.2%); adding prevalence cues or removing diagnostic category constraints respectively increased specificity (83.0% and 94.7%) while reducing false alarms by 107 and 140 per 500, but at the cost of poor sensitivity (30.4% and 8.8%). Rank-biased overlap between GPT-4o’s information-seeking sequence and the Bayesian-network mutual-information optimum was low across diagnoses (range 0.060–0.097), and the model diverged from clinician behavior by requesting fewer vitals ( -fold) and labs ( -fold), while requesting 30%+ more imaging data. Conclusions In this simulated assessment, GPT-4o demonstrated diagnostic biases toward rare conditions and differed substantially from normative probabilistic models and physician practice patterns. These discrepancies could lead to unnecessary over-triage and resource utilization. Integrating LLMs within more rigorous probabilistic frameworks and calibrating them to realistic disease prevalences may be essential for effectively harnessing their potential as clinical decision-support tools.

In the present article we use geometric microliths (a specific type of arrowhead) and Approximate Bayesian Computation (ABC) in order to evaluate possible origin points and expansion routes for the Neolithic in the Iberian Peninsula. In order to do so, we divide the Iberian Peninsula in four areas (Ebro river, Catalan shores, Xúquer river and Guadalquivir river) and we sample the geometric microliths existing in the sites with the oldest radiocarbon dates for each zone. On this data, we perform a partial Mantel test with three matrices: geographic distance matrix, cultural distance matrix and chronological distance matrix. After this is done, we simulate a series of partial Mantel tests where we alter the chronological matrix by using an expansion model with randomised origin points, and using the distribution of the observed partial Mantel test’s results as a summary statistic within an Approximate Bayesian Computation-Sequential Monte-Carlo (ABC-SMC) algorithm framework. Our results point clearly to a Neolithic expansion route following the Northern Mediterranean, whilst the Southern Mediterranean route could also find support and should be further discussed. The most probable origin points focus on the Xúquer river area.

Ningxia wolfberry is the only wolfberry product with medicinal value in China. However, the nutritional elements, active ingredients, and economic value of the wolfberry vary considerably among different origins in Ningxia. It is difficult to determine the origin of wolfberry by traditional methods due to the same variety, similar origins, and external characteristics. In the study, we have for the first time used a multi-task residual fully convolutional network (MRes-FCN) under Bayesian optimized architecture for imaging from visible-near-infrared (Vis-NIR, 400–1000 nm) and near-infrared (NIR-1700 nm) hyperspectral imaging (HSI) technology to establish a classification model for near geographic origin of Ningxia wolfberries (Zhongning, Guyuan, Tongxin, and Huinong). The denoising auto-encoder (DAE) was used to generate augmented data, then principal component analysis (PCA) was combined with gray level co-occurrence matrix (GLCM) to extract the texture features. Finally, three datasets (HSI, DAE, and texture) were added to the multi-task model. The reshaped data were up-sampled using transposed convolution. After data-sparse processing, the backbone network was imported to train the model. The results showed that the MRes-FCN model exhibited excellent performance, with the accuracies of the full spectrum and optimum characteristic spectrum of 95.54% and 96.43%, respectively. This study has demonstrated that the MRes-FCN model based on Bayesian optimization and DAE data augmentation strategy may be used to identify the near geographical origin of wolfberries.

X-ray diffractometry (XRD) is commonly used to determine both aragonite:calcite ratio and Mg content (in calcite) in biogenic skeletal carbonate. Bimineral taxa, such as many abalone, combine aragonite and calcite, or sometimes two distinct calcites, in a single skeleton. At least some abalone shells are, however, formed of three discrete carbonate minerals: aragonite, high-Mg calcite, and low-Mg calcite. Here we develop and apply a new system based on a Bayesian calibration model, an extension of the Reference Intensity Ratio method that accommodates heteroskedastic noise, for determining relative proportions in trimineralic biogenic carbonate using XRD patterns. We describe the system, validate and assess the system using biomineral standards, and quantify sources of error. We then use the system to describe mineralogical variation within the sometimes-trimineralic New Zealand black-footed pāua Haliotis iris . All specimens contained aragonite, and most contained low-Mg calcite, with older shell showing decreasing amounts of calcite (presumably due to wear of this external layer). Almost all specimens from Kaikoura contained at least some high-Mg calcite, thus being tri-mineralic. This mixture of three biogenic carbonates is most unusual, so we have used our new method of analysing XRD patterns to estimate the proportions of three co-occurring skeletal carbonate minerals in this marine invertebrate. We also provide the first detailed analysis of uncertainty and precision in XRD analysis of skeletal carbonate mineralogy.

Almost all survival data is censored, and censor imputation is necessary. This study aimed to investigate the performance of the Bayesian Approach (BA) in the imputation of censored records in simulated and Breast Cancer (BC) data. Due to the difference in the distribution of time to event in survival analysis, two well-known the Weibull and Birnbaum-Saunders (BS) distributions have been used to test the performance of the BA. For each of the censored, 10,000 times were simulated using the BA in R and BUGS software, and their median or mean was imputed instead of each censor. The eligibility of both imputation methods was investigated using different curves, different censoring percentages, and sample sizes, as well as the Deviance Information Criteria (DIC), Effective Sample Size, and the Geweke diagnostic in simulated and especially real BC data. The BC data, which contains 220 patients who were identified and followed up between 2015 and 2023, was made accessible on February 1, 2023. The Kaplan-Meier, the BA, and other survival curves were drawn for the observed times. Findings indicated that the performance of the BA under the Weibull and BS distributions in simulated data is similar. The DIC index in the BC data under the BS distribution (1510) is less than the Weibull distribution (1698). Therefore, the BS distribution is preferred over the Weibull for imputation of censoring times in real BC data.