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Loss reserving generally focuses on identifying a single model that can generate superior predictive performance. However, different loss reserving models specialise in capturing different aspects of loss data. This is recognised in practice in the sense that results from different models are often considered, and sometimes combined. For instance, actuaries may take a weighted average of the prediction outcomes from various loss reserving models, often based on subjective assessments. In this paper, we propose a systematic framework to objectively combine (i.e. ensemble) multiple _stochastic_ loss reserving models such that the strengths offered by different models can be utilised effectively. Our framework contains two main innovations compared to existing literature and practice. Firstly, our criteria model combination considers the full distributional properties of the ensemble and not just the central estimate - which is of particular importance in the reserving context. Secondly, our framework is that it is tailored for the features inherent to reserving data. These include, for instance, accident, development, calendar, and claim maturity effects. Crucially, the relative importance and scarcity of data across accident periods renders the problem distinct from the traditional ensembling techniques in statistical learning. Our framework is illustrated with a complex synthetic dataset. In the results, the optimised ensemble outperforms both (i) traditional model selection strategies, and (ii) an equally weighted ensemble. In particular, the improvement occurs not only with central estimates but also relevant quantiles, such as the 75th percentile of reserves (typically of interest to both insurers and regulators). The framework developed in this paper can be implemented thanks to an R package, `ADLP`, which is available from CRAN.

We present the ARR2 prior, a joint prior over the auto-regressive components in Bayesian time-series models and their induced $R^2$. Compared to other priors designed for times-series models, the ARR2 prior allows for flexible and intuitive shrinkage. We derive the prior for pure auto-regressive models, and extend it to auto-regressive models with exogenous inputs, and state-space models. Through both simulations and real-world modelling exercises, we demonstrate the efficacy of the ARR2 prior in improving sparse and reliable inference, while showing greater inference quality and predictive performance than other shrinkage priors. An open-source implementation of the prior is provided.

Cycloids are particular Petri nets for modelling processes of actions and events, belonging to the fundaments of Petri's general systems theory. Defined by four parameters they provide an algebraic formalism to describe strongly synchronized sequential processes. To further investigate their structure, reduction systems of cycloids are defined in the style of rewriting systems and properties of reduced cycloids are proved. In particular the recovering of cycloid parameters from their Petri net structure is derived.

We detail for the first time a complete explicit description of the quasi-cyclic structure of all classical finite generalized quadrangles. Using these descriptions we construct families of quasi-cyclic LDPC codes derived from the point-line incidence matrix of the quadrangles by explicitly calculating quasi-cyclic generator and parity check matrices for these codes. This allows us to construct parity check and generator matrices of all such codes of length up to 400000. These codes cover a wide range of transmission rates, are easy and fast to implement and perform close to Shannon's limit with no visible error floors. We also include some performance data for these codes. Furthermore, we include a complete explicit description of the quasi-cyclic structure of the point-line and point-hyperplane incidences of the finite projective and affine spaces.

Robotic exploration has long captivated researchers aiming to map complex environments efficiently. Techniques such as potential fields and frontier exploration have traditionally been employed in this pursuit, primarily focusing on solitary agents. Recent advancements have shifted towards optimizing exploration efficiency through multiagent systems. However, many existing approaches overlook critical real-world factors, such as broadcast range limitations, communication costs, and coverage overlap. This paper addresses these gaps by proposing a distributed maze exploration strategy (CU-LVP) that assumes constrained broadcast ranges and utilizes Voronoi diagrams for better area partitioning. By adapting traditional multiagent methods to distributed environments with limited broadcast ranges, this study evaluates their performance across diverse maze topologies, demonstrating the efficacy and practical applicability of the proposed method. The code and experimental results supporting this study are available in the following repository: //github.com/manouslinard/multiagent-exploration/.

Differential abundance analysis is a key component of microbiome studies. While dozens of methods for it exist, currently, there is no consensus on the preferred methods. Correctness of results in differential abundance analysis is an ambiguous concept that cannot be evaluated without employing simulated data, but we argue that consistency of results across datasets should be considered as an essential quality of a well-performing method. We compared the performance of 14 differential abundance analysis methods employing datasets from 54 taxonomic profiling studies based on 16S rRNA gene or shotgun sequencing. For each method, we examined how the results replicated between random partitions of each dataset and between datasets from independent studies. While certain methods showed good consistency, some widely used methods were observed to produce a substantial number of conflicting findings. Overall, the highest consistency without unnecessary reduction in sensitivity was attained by analyzing relative abundances with a non-parametric method (Wilcoxon test or ordinal regression model) or linear regression (MaAsLin2). Comparable performance was also attained by analyzing presence/absence of taxa with logistic regression.

We present LinApart, a routine designed for efficiently performing the univariate partial fraction decomposition of large symbolic expressions. Our method is based on an explicit closed formula for the decomposition of rational functions with fully factorized denominators. We provide implementations in both the Wolfram Mathematica and C languages, made available at //github.com/fekeshazy/LinApart . The routine can provide very significant performance gains over available tools such as the Apart command in Mathematica.

We introduce a method for computing immediately human interpretable yet accurate classifiers from tabular data. The classifiers obtained are short Boolean formulas, computed via first discretizing the original data and then using feature selection coupled with a very fast algorithm for producing the best possible Boolean classifier for the setting. We demonstrate the approach via 13 experiments, obtaining results with accuracies comparable to ones obtained via random forests, XGBoost, and existing results for the same datasets in the literature. In most cases, the accuracy of our method is in fact similar to that of the reference methods, even though the main objective of our study is the immediate interpretability of our classifiers. We also prove a new result on the probability that the classifier we obtain from real-life data corresponds to the ideally best classifier with respect to the background distribution the data comes from.

Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of components is finite, for the Dirichlet process and Pitman--Yor process mixture models. We extend these results to additional Bayesian nonparametric priors such as Gibbs-type processes and finite-dimensional representations thereof. The latter include the Dirichlet multinomial process, the recently proposed Pitman-Yor, and normalized generalized gamma multinomial processes. We show that mixture models based on these processes are also inconsistent in the number of clusters and discuss possible solutions. Notably, we show that a post-processing algorithm introduced for the Dirichlet process can be extended to more general models and provides a consistent method to estimate the number of components.