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Several types of dynamics at stationarity can be described in terms of a Markov jump process among a finite number N of representative sites. Before dealing with the dynamical aspects, one basic problem consists in expressing the a priori steady-state occupation probabilities of the sites. In particular, one wishes to go beyond the mere black-box computational tools and find expressions in which the jump rate constants appear explicitly, therefore allowing for a potential design/control of the network. For strongly connected networks admitting a unique stationary state with all sites populated, here we express the occupation probabilities in terms of a formula that involves powers of the transition rate matrix up to order N − 1. We also provide an expression of the derivatives with respect to the jump rate constants, possibly useful in sensitivity analysis frameworks. Although we refer to dynamics in (bio)chemical networks at thermal equilibrium or under nonequilibrium steady-state conditions, the results are valid for any Markov jump process under the same assumptions. [ABSTRACT FROM AUTHOR]

Calculating the true probability that a signal will be transmitted between any pair of nodes in a network is computationally hard. Diffusion centrality, which counts the expected number of times that a signal will be transmitted, is often used as a heuristic for this probability. But this formula can lead to distorted results when used in this way, because its summation of probabilities does not take account of the inclusion–exclusion principle. This paper provides a simple new formula for the probabilities of node-to-node diffusion in networks, which uses De Morgan's laws to account for the inclusion–exclusion principle. Like diffusion centrality, this formula is based on the assumption that the probabilities of a signal travelling along each walk in a network are independent. The probabilities it calculates are therefore called Walk-Independence Probabilities (WIP). These probabilities provide two new centrality measures, WIP centrality and blocking centrality. Blocking centrality is a type of induced centrality which is calculated when some nodes block signals. • Calculating probabilities of diffusion in social networks is computationally hard • Diffusion centrality as a heuristic for these probabilities can lead to distortions • It omits the inclusion-exclusion principle, and can thereby overestimate inequality • The paper presents an alternative heuristic: Walk-Independence Probability (WIP) • WIP's formula uses De Morgan's laws to account for the inclusion–exclusion principle • It also provides two new centrality measures: WIP centrality and blocking centrality [ABSTRACT FROM AUTHOR]

This paper studies the mixed H 2 / H ∞ control for Takagi–Sugeno (T–S) fuzzy Markovian jump systems (MJSs) subject to random delays and multiple uncertain transition probabilities. In contrast to existing research, this study presents uncertainty parameters, external disturbance, random delays, and uncertain transition probabilities simultaneously in a unified T–S fuzzy model. Specifically, this study examines multiple Markov chains with partially unknown transition probabilities. These complex imperfections have a substantial adverse impact on system performance and the associated challenge of mixed H 2 / H ∞ control remains unresolved. Our innovative contributions are described as follows. The proposed approach utilizes free-weighting matrix technique and Lyapunov–Krasovskii functional to get the H 2 / H ∞ controller, which ensures that the stochastic T–S fuzzy systems exhibit stochastic stability and comply with the H ∞ performance index. [ABSTRACT FROM AUTHOR]

We introduce a general definition of a quantum committor in order to clarify reaction mechanisms and facilitate control in processes where coherent effects are important. With a quantum committor, we generalize the notion of a transition state to quantum superpositions and quantify the effect of interference on the progress of the reaction. The formalism is applicable to any linear quantum master equation supporting metastability for which absorbing boundary conditions designating the reactant and product states can be applied. We use this formalism to determine the dependence of the quantum transition state on coherences in a polaritonic system and optimize the initialization state of a conical intersection model to control reactive outcomes, achieving yields of the desired state approaching 100%. In addition to providing a practical tool, the quantum committor provides a conceptual framework for understanding reactions in cases when classical intuitions fail. [ABSTRACT FROM AUTHOR]

We will denote by $ \mathcal {M} $ M the space of Borel probabilities on the symbolic space $ \Omega =\{1,2\cdots,m\}^\mathbb {N} $ Ω={1,2⋯,m}N. $ \mathcal {M} $ M is equipped Monge–Kantorovich metric. We consider here the push-forward map $ \mathfrak {T}:\mathcal {M} \to \mathcal {M} $ T:M→M as a dynamical system. The space of Borel probabilities on $ \mathcal {M} $ M is denoted by $ \mathfrak {M} $ M. Given a continuous function $ A: \mathcal {M}\to \mathbb {R} $ A:M→R, an a priori probability $ \Pi _0 $ Π0 on $ \mathcal {M} $ M, and a certain convolution operation acting on pairs of probabilities on $ \mathcal {M} $ M, we define an associated Level-2 IFS Ruelle operator. We show the existence of an eigenfunction and an eigenprobability $ \hat {\Pi }\in \mathfrak {M} $ Π^∈M for such an operator. Under a normalization condition for A, we show the existence of some $ \mathfrak {T} $ T-invariant probabilities $ \hat {\Pi }\in \mathfrak {M}. $ Π^∈M. We are able to define the variational entropy of such $ \hat {\Pi } $ Π^ and a related maximization pressure problem associated to A. In some particular examples, we show how to get eigenprobabilities solutions on $ \mathfrak {M} $ M for the Level-2 Thermodynamic Formalism problem from eigenprobabilities on $ \mathcal {M} $ M for the classical (Level-1) Thermodynamic Formalism; this shows that our approach is a natural generalization of the classic case. [ABSTRACT FROM AUTHOR]

One of the premises of the argument from design is the need for the order of a designer. This premise has been explained in various ways, one of which is the calculus of probabilities. It posits that the likelihood of an ordered thing coming into existence by chance is so low that human beings consider it nearly impossible; therefore, this order requires an intelligent designer. However, some contemporary Muslim philosophers, such as Ayatollah Jawādī Āmulī, along with certain Western philosophers, have contested the validity of the calculus of probabilities. They argue that the calculus of probabilities does not reveal reality but is merely practically useful. They assert that undesigned states have the same probability as designed states. In this article, I address these objections, refute them, and ultimately demonstrate the soundness of the argument from design based on the calculus of probabilities. [ABSTRACT FROM AUTHOR]

This work presents ab initio calculations for the K α spectrum of manganese (Z = 25, [Ar] 3 d 5 4 s 2 ), a highly complex system due to the five open orbitals in the 3 d shell. The spectrum is composed of the canonical diagram line [ 1 s ] → [ 2 p ] and shake-off satellite lines [ 1 s n l ] → [ 2 p n l ] ( n l ∈ { 2 s , 2 p , 3 s , 3 p , 3 d , 4 s } ), where square brackets denote a hole state. The multiconfiguration Dirac–Hartree–Fock method with the active set approach provides the initial and final atomic wavefunctions. Results are presented as energy eigenvalue spectra for the diagram and satellite transitions. The calculated wavefunctions include over one hundred million configuration state functions and over 280,000 independent transition energies for the seven sets of spectra considered. Shake-off probabilities and Auger transition rates determine satellite intensities. The number of configuration state functions ensures highly-converged wavefunctions. Several measures of convergence demonstrate convergence in the calculated parameters. We obtain convergence of the transition energies in all eight transitions to within 0.06 eV and shake-off probabilities to within 4.5%. [ABSTRACT FROM AUTHOR]

A self-consistent method for studying second-order anharmonic effects on the basis of many-body quantum field theory is applied for the first time in calculating probabilities for 1 transitions between the ground state and the two-phonon state in the semimagic tin isotopes Sn. The approach used involves taking into account (i) self-consistency of the nuclear mean field and effective interaction on the basis of the energy density functional method with the parameters of the Fayans functional DF3-a, which were earlier found to provide good results; (ii) ground-state three-quasiparticle correlations; and (iii) nuclear-polarizablility effects. Good agreement with available experimental data, including those for Sn, is obtained. Values of ( 1) are predicted for Sn even–even nuclei. It is shown that dynamical ground-state three-quasiparticle correlations make a substantial contribution to the reduced probabilities for the 1 transitions in question, so that their inclusion is necessary for explaining experimental data. [ABSTRACT FROM AUTHOR]

For many applications of agent-based models (ABMs), an agent’s age influences important decisions (e.g. their contribution to/withdrawal from pension funds, their level of risk aversion in decision-making, etc.) and outcomes in their life cycle (e.g. their susceptibility to disease). These considerations make it crucial to accurately capture the age distribution of the population being considered. Often, empirical survival probabilities cannot be used in ABMs to generate the observed age structure. This may be due to discrepancies between samples (e.g. when empirical survival probabilities are calculated across the whole population, but only a subpopulation is being modelled) or models (between the survival model underpinning the ABM and the statistical model used to produce empirical survival probabilities). In these cases, imputing empirical survival probabilities will not generate the observed age structure of the population, and assumptions such as exogenous agent inflows are required (but not necessarily empirically valid). In this paper, we propose a method that allows for the preservation of agent age-structure without the exogenous influx of agents, even when only a subset of the population is being modelled. We demonstrate the flexibility and accuracy of our methodology by performing simulations of several real-world age distributions. This method is a useful tool for those developing ABMs across a broad range of applications. [ABSTRACT FROM AUTHOR]

This paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing random variations in the economic and financial environments. We prove a sufficient condition on the distribution of jumps of the business process ensuring the smoothness of the ruin probability as a function of the initial capital and obtain for this function an integro-differential equation. [ABSTRACT FROM AUTHOR]

The tail conditional allocation plays an important role in a number of areas, including economics, finance, insurance, and management. Fixed-margin confidence intervals and the assessment of their coverage probabilities are of much interest. In this paper, we offer a convenient way to achieve these goals via resampling. The theoretical part of the paper, which is technically demanding, is rigorously established under minimal conditions to facilitate the widest practical use. A simulation-based study and an analysis of real data illustrate the performance of the developed methodology. [ABSTRACT FROM AUTHOR]

In this paper, we present research results that extend and supplement our article recently published by MDPI. We derive the closed-form relations among the queue-length probabilities observed in the pre-arrival, random, and post-departure epochs for a complex, bulk-service, multi-server queueing system GI/M a , b /c. [ABSTRACT FROM AUTHOR]

We consider a continuous-time two-dimensional risk model, in which the claims from the two lines of insurance businesses satisfy an extensive asymptotic independence structure and the stochastic return is driven by a geometric Lévy process. Under a mild technical condition regarding the Laplace exponent of the Lévy process, we obtain explicit asymptotic expansions for both finite-time and infinite-time ruin probabilities when the claim sizes have regularly varying distributions. [ABSTRACT FROM AUTHOR]

AbstractThis article considers a non-standard bidimensional risk model with constant force of interest, in which every main claim may cause a random number of delayed claims in an uncertain period of time. Specifically, if both the main claims and delayed claims are subexponential and follow some dependence structure, we drive precise asymptotic formulae for finite-time ruin probabilities, which generalize the results of Lu and Yuan (2022) and Li (2023b) to some extent. [ABSTRACT FROM AUTHOR]

Quantum non-locality and contextuality can be simulated with quasi-probabilities, i.e. probabilities that take negative values. Here, we show that another quantum phenomenon, the observer effect, admits a quasi-probabilistic description too. We also investigate post-quantum observer effects based on the Specker's triangle scenario. This scenario comprises three observables, with the possibility of measuring two simultaneously. Represented as three boxes with a hidden ball, this scenario exhibits counterintuitive behaviour: regardless of the chosen pair of boxes, one box always contains the ball. Moreover, the scenario demonstrates a strong observer effect. When an observer selects and opens the first box, finding it empty, the ball is guaranteed to be in the second box, thereby allowing the observer to determine the ball's location among the remaining two boxes. We extend this scenario to include additional boxes and multiple balls. By employing negative probabilities, we demonstrate amplification of the observer effect. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'. [ABSTRACT FROM AUTHOR]

In the present work, analyses have been performed to determine spectroscopic parameters, including transition probabilities, and relative line strengths of discharge-produced xenon plasma. We present the transition probabilities of twenty-three emission lines originating from the 5p56p →5p56s transition array of neutral xenon covering the wavelength range from 450 to 1100 nm using a xenon-filled hollow cathode discharge lamp. The experimental absolute transition probabilities have been measured by combining the reported lifetimes of upper levels with the integrated spectral intensities of xenon transitions. The results agree well with the reported data in the NIST database, where available. The theoretical line strengths for all spectral transitions originating from the 5p56p→5p56s transition array have been calculated in the LS, LK, jj, and jck coupling schemes using the 3j, 6j, and 9j symbol relations. Furthermore, the normalized experimental line strengths have also been measured and compared with theoretical line strengths, which confirm that the jj and jck coupling scheme is more appropriate for the level designation of xenon. [ABSTRACT FROM AUTHOR]

The win ratio has in the recent decade gained popularity for analyzing prioritized multiple event data in clinical cohort studies, in particular within cardiovascular research. The literature on estimation of the win ratio using censored event data is however sparse. The methods that have been suggested have either an insufficient adjustment of the censoring or by assuming the the win and loss probabilities are proportional over time. The assumption of proportional win and loss probabilities will often in practice not be satisfied. In this paper, we present estimates for the win ratio, and win and loss probabilities, under independent right‐censoring and derive the asymptotic distribution of the estimates. The proposed win ratio estimate does not require the assumption of proportional win and loss probabilities. The small sample properties of the proposed method are studied in a simulation study showing that the variance formula is accurate even for small samples. The method is applied on two data sets. [ABSTRACT FROM AUTHOR]

Most statistical modeling applications involve the consideration of a candidate collection of models based on various sets of explanatory variables. The candidate models may also differ in terms of the structural formulations for the systematic component and the posited probability distributions for the random component. A common practice is to use an information criterion to select a model from the collection that provides an optimal balance between fidelity to the data and parsimony. The analyst then typically proceeds as if the chosen model was the only model ever considered. However, such a practice fails to account for the variability inherent in the model selection process, which can lead to inappropriate inferential results and conclusions. In recent years, inferential methods have been proposed for multimodel frameworks that attempt to provide an appropriate accounting of modeling uncertainty. In the frequentist paradigm, such methods should ideally involve model selection probabilities, i.e., the relative frequencies of selection for each candidate model based on repeated sampling. Model selection probabilities can be conveniently approximated through bootstrapping. When the Akaike information criterion is employed, Akaike weights are also commonly used as a surrogate for selection probabilities. In this work, we show that the conventional bootstrap approach for approximating model selection probabilities is impacted by bias. We propose a simple correction to adjust for this bias. We also argue that Akaike weights do not provide adequate approximations for selection probabilities, although they do provide a crude gauge of model plausibility. [ABSTRACT FROM AUTHOR]

Cytomegalovirus (CMV) has long been thought to have an association with glioblastoma multiforme (GBM), although the exact role of CMV and any subsequent implications for treatment have yet to be fully understood. This study addressed whether IGH complementarity determining region-3 (CDR3)-CMV protein chemical complementarity, with IGH CDR3s representing both tumor resident and blood-sourced IGH recombinations, was associated with overall survival (OS) distinctions. IGH recombination sequencing reads were obtained from (a) the Clinical Proteomic Tumor Analysis Consortium, tumor RNAseq files; and (b) the cancer genome atlas, blood exome-derived files. The Adaptive Match web tool was used to calculate chemical complementarity scores (CSs) based on hydrophobic interactions, and those scores were used to group GBM cases and assess survival probabilities. We found a higher OS probability for cases whose hydrophobic IGH CDR3-CMV protein chemical complementarity scores (Hydro CSs) were in the upper 50th percentile for several CMV proteins, including UL99 and UL123, as well as for CSs based on known B cell epitopes representing these proteins. We also identified multiple immune signature genes, including CD79A and TNFRSF17, for which higher RNA expression was associated with higher Hydro CSs. Results were consistent with the idea that stronger immunoglobulin responses to CMV are associated with better OS probabilities for GBM. [ABSTRACT FROM AUTHOR]

We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight q ∈ [ 1 , 4) . Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are beyond reach for other values of q than the FK-Ising model ( q = 2 ). Given the convergence of interfaces, the conjectural formulas for other values of q could be verified similarly with relatively minor technical work. The limit interfaces are variants of SLE κ curves (with κ = 16 / 3 for q = 2 ). Their partition functions, that give the connection probabilities, also satisfy properties predicted for correlation functions in conformal field theory (CFT), expected to describe scaling limits of critical random-cluster models. We verify these properties for all q ∈ [ 1 , 4) , thus providing further evidence of the expected CFT description of these models. [ABSTRACT FROM AUTHOR]

Bayesian predictive probabilities have become a ubiquitous tool for design and monitoring of clinical trials. The typical procedure is to average predictive probabilities over the prior or posterior distributions. In this paper, we highlight the limitations of relying solely on averaging, and propose the reporting of intervals or quantiles for the predictive probabilities. These intervals formalize the intuition that uncertainty decreases with more information. We present four different applications (Phase 1 dose escalation, early stopping for futility, sample size re-estimation, and assurance/probability of success) to demonstrate the practicality and generality of the proposed approach. [ABSTRACT FROM AUTHOR]

In recent years, there has been increasing interest in the joint modelling of compound extreme events such as high temperatures and low rainfall. The increase in the frequency of occurrence of these events in many regions has necessitated the development of models for estimating the concurrent probabilities of such compound extreme events. The current study discusses an application of copula models in predicting the concurrent probabilities of compound low rainfall and high-temperature events using data from the Lowveld region of the Limpopo province in South Africa. The second stage discussed two indicators for monitoring compound high temperature and low rainfall events. Empirical results from the study show that elevations ranging from 100–350 m, 350–700 m and 700–1200 m exhibit varying probabilities of experiencing drought, with mild droughts having approximately 64%, 66%, and 65% chances, moderate droughts around 36%, 39%, and 38%, and severe droughts at approximately 16%, 19%, and 18%, respectively. Furthermore, the logistic regression models incorporating the southern oscillation index as a covariate yielded comparable results of copula-based models. The methodology discussed in this paper is robust and can be applied to similar datasets in any regional setting globally. These findings could be useful to disaster management decision makers, helping them formulate effective mitigation strategies and emergency response plans. [ABSTRACT FROM AUTHOR]

We examined the human ability to encode and utilize local and global uncertainty information during a navigational task. Participants were tasked with navigating a virtual maze in which wall locations were obscured. Local cues and a global direction provided guidance. The validities of the global and local cues were separately and jointly varied across the two experiments. The results demonstrated that participants effectively utilized both global and local cues for navigation with a stronger reliance on local cues and a heightened precision in estimating their reliability. Our findings suggest that the representation of uncertainty for proximate events can be dissociated from that of distal events. Furthermore, humans effectively integrate both forms of information when making decisions during navigation tasks. This research advances our understanding of uncertainty processing and its implications for decision making in complex environments. [ABSTRACT FROM AUTHOR]

This article considers the challenge of designing football group draw mechanisms, which have a uniform distribution over all valid draw assignments, but are also entertaining, practical and transparent. Although this problem is trivial in completely symmetric problems, it becomes challenging when there are draw constraints that are not exchangeable across each of the competing teams, so that symmetry breaks down. We explain how to simulate the FIFA sequential draw method and compute the nonuniformity of its draws by comparison with a uniform rejection sampler. We then propose several practical methods of achieving the uniform distribution while still using balls and bowls in a way which is suitable for a televised draw. The solutions can also be carried out interactively. The general methodology we provide can readily be transported to different competition draws and is not restricted to football events. [ABSTRACT FROM AUTHOR]

Within a tensor framework, the notions of ergodicity, ever-reaching probabilities, and mean first passage times of Markov chains have recently been extended to higher order Markov chains. In this paper, we establish the relations between ergodicity of a higher order Markov chain and its ever-reaching probabilities and mean first passage times. In particular, we demonstrate the key role ergodicity plays in the existence and uniqueness of the mean first passage times. We exploit the structure of the tensor equation governing the mean first passage times and propose a block iterative algorithm and a block direct algorithm for computing these quantities. We show that ergodicity guarantees the convergence of the block iterative algorithm. Some illustrative numerical results comparing these algorithms with a brute-force direct method are also given. [ABSTRACT FROM AUTHOR]

There are many parameters that affect the seismic behavior of the bridge, especially in the new type of bridges. In this research, the seismic behavior of a cable-arch bridge as a new type of bridge with a hybrid system of an arch and stay cables has been studied considering the effect of seismic hazard probabilities and vertical excitations. By considering these parameters, the seismic analysis was investigated in three steps: Response spectrum analysis to obtain general seismic behavior of the bridge, time-history analysis using seismic ground motion records to capture dynamic responses, and pushover analysis to determine the capacity of the bridge. The performance of the bridge was monitored, and the significance of considering seismic hazard probabilities and vertical excitations was investigated. Pointing out the effects of these parameters on the seismic behavior of the bridge, the results indicated a requirement for considering them to provide the seismic safety of the bridge. [ABSTRACT FROM AUTHOR]

Background: A central goal of modern evidence-based medicine is the development of simple and easy to use tools that help clinicians integrate quantitative information into medical decision-making. The Bayesian Pre-test/Post-test Probability (BPP) framework is arguably the most well known of such tools and provides a formal approach to quantify diagnostic uncertainty given the result of a medical test or the presence of a clinical sign. Yet, clinical decision-making goes beyond quantifying diagnostic uncertainty and requires that that uncertainty be balanced against the various costs and benefits associated with each possible decision. Despite increasing attention in recent years, simple and flexible approaches to quantitative clinical decision-making have remained elusive. Methods: We extend the BPP framework using concepts of Bayesian Decision Theory. By integrating cost, we can expand the BPP framework to allow for clinical decision-making. Results: We develop a simple quantitative framework for binary clinical decisions (e.g., action/inaction, treat/no-treat, test/no-test). Let p be the pre-test or post-test probability that a patient has disease. We show that r ∗ = (1 - p) / p represents a critical value called a decision boundary. In terms of the relative cost of under- to over-acting, r ∗ represents the critical value at which action and inaction are equally optimal. We demonstrate how this decision boundary can be used at the bedside through case studies and as a research tool through a reanalysis of a recent study which found widespread misestimation of pre-test and post-test probabilities among clinicians. Conclusions: Our approach is so simple that it should be thought of as a core, yet previously overlooked, part of the BPP framework. Unlike prior approaches to quantitative clinical decision-making, our approach requires little more than a hand-held calculator, is applicable in almost any setting where the BPP framework can be used, and excels in situations where the costs and benefits associated with a particular decision are patient-specific and difficult to quantify. [ABSTRACT FROM AUTHOR]

This paper is a discussion note on Isaacs, Hájek and Hawthorne (2022) , which claims to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of that proposal. In particular, I show that if the proposal is applied to a bounded 3 -dimensional space, then one has to reject at least one of the following: • If A is at most as probable as B and B is at most as probable as C ⁠ , then A is at  most as probable as C ⁠. • Let A ∩ C = B ∩ C = ∅ ⁠. A is at most as probable as B if and only if (A ∪ C) is at  most as probable as (B ∪ C) ⁠. But rejecting either statement seems unattractive. [ABSTRACT FROM AUTHOR]

Objectives Pain is a leading cause of disability and a limiting factor in individuals' assessments of their own subjective health; however, its association with subjective longevity has yet to be explored. Subjective survival probabilities (SSPs), or one's own perceived chances of living to a given age, can influence individuals' behavior as they plan for their futures. This study assesses whether pain correlates to lower SSPs. Methods We use a repeated cross-section of the 2000–2018 waves of the Health and Retirement Study, a longitudinal and nationally representative survey of Americans aged 51 and older (N  = 31,773). Results Fractional logit regressions indicate that, across all age groups, respondents with severe and/or interfering pain reported significantly lower SSPs than those with no pain (Marginal Effect [ ME ] = −0.03 to −0.06, p  < .05). Controlling for all covariates, mild or moderate noninterfering pain was only associated with a significant reduction in SSPs among the youngest group reporting their chances of living to age 75 (ME  = −0.02, p  < .001). Descriptively and in the model results, respondents with mild or moderate noninterfering pain appeared to more closely resemble pain-free respondents than those with severe or interfering pain. Discussion These findings highlight the importance of pain on SSPs, and contribute to the growing evidence that pain interference is uniquely important in predicting meaningful health outcomes. [ABSTRACT FROM AUTHOR]

We analyze the implications of infectious diseases and social distancing in an extended SIS framework to allow for the presence of stochastic shocks with state dependent probabilities. Random shocks give rise to the diffusion of a new strain of the disease which affects both the number of infectives and the average biological characteristics of the pathogen causing the disease. The probability of such shock realizations changes with the level of disease prevalence and we analyze how the properties of the state-dependent probability function affect the long run epidemiological outcome which is characterized by an invariant probability distribution supported on a range of positive prevalence levels. We show that social distancing reduces the size of the support of the steady state distribution decreasing thus the variability of disease prevalence, but in so doing it also shifts the support rightward allowing eventually for more infectives than in an uncontrolled framework. Nevertheless, social distancing is an effective control measure since it concentrates most of the mass of the distribution toward the lower extreme of its support. [ABSTRACT FROM AUTHOR]

A Bernoulli scheme with unequal harmonic success probabilities is investigated, together with some of its natural extensions. The study includes the number of successes over some time window, the times to (between) successive successes and the time to the first success. Large sample asymptotics, statistical parameter estimation, and relations to Sibuya distributions and Yule–Simon distributions are discussed. This toy model is relevant in several applications including reliability, species sampling problems, record values breaking and random walks with disasters. [ABSTRACT FROM AUTHOR]

The multilevel Monte Carlo (MLMC) method is highly efficient for estimating expectations of a functional of a solution to a stochastic differential equation (SDE). However, MLMC estimators may be unstable and have a poor (noncanonical) complexity in the case of low regularity of the functional. To overcome this issue, we extend our previously introduced idea of numerical smoothing in [Quant. Finance, 23 (2023), pp. 209-227], in the context of deterministic quadrature methods to the MLMC setting. The numerical smoothing technique is based on root-finding methods combined with one-dimensional numerical integration with respect to a single well-chosen variable. This study is motivated by the computation of probabilities of events, pricing options with a discontinuous payoff, and density estimation problems for dynamics where the discretization of the underlying stochastic processes is necessary. The analysis and numerical experiments reveal that the numerical smoothing significantly improves the strong convergence and, consequently, the complexity and robustness (by making the kurtosis at deep levels bounded) of the MLMC method. In particular, we show that numerical smoothing enables recovering the MLMC complexities obtained for Lipschitz functionals due to the optimal variance decay rate when using the Euler--Maruyama scheme. For the Milstein scheme, numerical smoothing recovers the canonical MLMC complexity, even for the nonsmooth integrand mentioned above. Finally, our approach efficiently estimates univariate and multivariate density functions. [ABSTRACT FROM AUTHOR]

OBJECTIVE Use a referral dental clinic model to study how to calculate accurate 95% upper confidence limits for probabilities of workloads (total case duration, including turnover time) exceeding allocated times. ANIMALS Dogs and cats undergoing dental treatments. METHODS Managerial data (procedure date and duration) collected over 44 consecutive operative workdays were used to calculate the daily anesthetist workload. Workloads were compared with a normal distribution using the Shapiro-Wilk test, serial correlation was examined by runs test, and comparisons among weekdays were made using the KruskalWallis test. The 95% confidence limits for normally distributed workloads exceeding allocated times were estimated with a generalized pivotal quantity. The impact of a number of procedures was assessed with scatterplots, Pearson linear correlation coefficients, and multivariable linear regression. RESULTS Mean anesthetist’s workload was normally distributed (Shapiro-Wilk P = .25), without serial correlation (P = .45), and without significant differences among weekdays (P = .52). Daily workload, mean 9.39 hours and SD 3.06 hours, had 95% upper confidence limit of 4.47% for the probability that exceeding 16 hours (ie, 8 hours per each of 2 tables). There was a strong positive correlation between daily workload and the end of the workday (r = .85), significantly larger than the correlation between the end of the workday and the number of procedures (r = .64, P < .0001). CLINICAL RELEVANCE There are multiple managerial applications in veterinary anesthesia wherein the problem is to estimate risks of exceeding thresholds of workload, including the costs of hiring a locum, scheduling unplanned add-on cases, planning for late discharge of surgical patients to owners, and coordinating anesthetist breaks. [ABSTRACT FROM AUTHOR]

Currently, there are three main shortcomings in meteorological drought indices: first, they rely on historical climate probability functions; second, the timescale used in calculations has a certain degree of subjectivity; third, the same index value may correspond to vastly different levels of actual drought in different climate types of regions. The purpose of this article is to establish a meteorological drought index that does not rely on historical meteorological element probability functions. Through theoretical derivation, four drought‐level maintenance lines are established on the cumulative precipitation‐cumulative water surface evaporation coordinate plane, and the coordinate quadrant is divided into five drought‐level areas. Through forward daily rolling accumulation, the maximum distance point is selected from the dynamically changing coordinate points to determine the corresponding cumulative precipitation and cumulative evaporation. The meteorological drought index is established by the distance from the selected coordinate point to each drought‐level maintenance line. Using daily precipitation and evaporation data from meteorological observation stations, the index is calculated based on the established meteorological drought index model, and compared with actual drought evolution and drought disaster records. The results show that the index can capture the development of drought well, and its changes are very consistent with drought disaster records. The index is of great significance for drought monitoring or assessment, and can provide guidance for water resource allocation, crop layout, and urban planning. Furthermore, it can also provide a way of thinking that does not rely on historical element probabilities for future drought research. [ABSTRACT FROM AUTHOR]

This study explores the influence of socio-demographic characteristics on money mule recruitment types in South Korea. Analyzing data from 543 apprehended money mules, probabilities were calculated for each group's involvement in recruitment types. Using class membership probability estimates from six machine learning methods, the research investigates the probability relationship between socio-demographic characteristics and recruitment types. Findings indicate that unemployed individuals in their 20s with intermediate education levels are more likely to be recruited through social media, while offline recruitment is prevalent among unemployed teenagers with low education levels and men over 50s with criminal records. Highly educated unemployed individuals in their 20s and 30s show a higher probability of using online job search channels. The study provides valuable insights into the complex interplay between sociodemographic factors and money mule recruitment, offering potential implications for law enforcement agencies in developing effective crime prevention strategies. Further analysis will shed light on the underlying reasons behind these results. [ABSTRACT FROM AUTHOR]

This paper presents alternative techniques for inference on classical Bayesian networks in which all probabilities are fixed, and for synthesis problems when conditional probability tables (CPTs) in such networks contain symbolic parameters rather than concrete probabilities. The key idea is to exploit probabilistic model checking as well as its recent extension to parameter synthesis techniques for parametric Markov chains. To enable this, the Bayesian networks are transformed into Markov chains and their objectives are mapped onto probabilistic temporal logic formulas. For exact inference, we compare probabilistic model checking to weighted model counting on various Bayesian network benchmarks. We contrast symbolic model checking using multi-terminal binary (aka: algebraic) decision diagrams to symbolic inference using probabilistic sentential decision diagrams, symbolic data structures that are tailored to Bayesian networks. For the parametric setting, we describe how our techniques can be used for various synthesis problems such as computing sensitivity functions (and values), simple and difference parameter tuning and ratio parameter tuning. Our parameter synthesis techniques are applicable to arbitrarily many, possibly dependent, parameters that may occur in multiple CPTs. This lifts restrictions, e.g., on the number of parametrized CPTs, or on parameter dependencies between several CPTs, that exist in the literature. Experiments on several benchmarks show that our parameter synthesis techniques can treat parameter synthesis for Bayesian networks (with hundreds of unknown parameters) that are out of reach for existing techniques. [ABSTRACT FROM AUTHOR]

We report an algorithm based on renormalization to compute the probability that a particular state, or set thereof, is visited along the first passage or transition paths between two endpoint states of a finite Markov chain. The procedure is numerically stable and does not require dense storage of the transition matrix. [ABSTRACT FROM AUTHOR]

One of the key decisions in execution strategies is the choice between a passive (liquidity providing) or an aggressive (liquidity taking) order to execute a trade in a limit order book (LOB). Essential to this choice is the fill probability of a passive limit order placed in the LOB. This paper proposes a deep learning method to estimate the filltimes of limit orders posted in different levels of the LOB. We develop a novel model for survival analysis that maps time-varying features of the LOB to the distribution of filltimes of limit orders. Our method is based on a convolutional-Transformer encoder and a monotonic neural network decoder. We use proper scoring rules to compare our method with other approaches in survival analysis, and perform an interpretability analysis to understand the informativeness of features used to compute fill probabilities. Our method significantly outperforms those typically used in survival analysis literature. Finally, we carry out a statistical analysis of the fill probability of orders placed in the order book (e.g. within the bid-ask spread) for assets with different queue dynamics and trading activity. [ABSTRACT FROM AUTHOR]

Here we consider an application of the method of maximum entropy in the mean to solve an extension of the problem of finding a discrete probability distribution from the knowledge of its marginals. The extension consists of determining joint probabilities when, besides specifying the marginals, we specify the expected value of some given random variables. The proposed method can incorporate constraints as the the requirement that the joint probabilities have to fall within known ranges. To motivate, think of the marginal probabilities as demands or supplies, and of the joint probability as the fraction of the supplies to be shipped from the production sites to the demand sites, thus joint probabilities become transportation policies. Fixing the cost of a transportation policy is equivalent to requiring that the unknown probability yields a given value to some random variable, and prescribing the range for each unknown may have an economical interpretation. [ABSTRACT FROM AUTHOR]

The individual results of SARS-CoV-2 serological tests measured after the first pandemic wave of 2020 cannot be directly interpreted as a probability of having been infected. Plus, these results are usually returned as a binary or ternary variable, relying on predefined cut-offs. We propose a Bayesian mixture model to estimate individual infection probabilities, based on 81,797 continuous anti-spike IgG tests from Euroimmun collected in France after the first wave. This approach used serological results as a continuous variable, and was therefore not based on diagnostic cut-offs. Cumulative incidence, which is necessary to compute infection probabilities, was estimated according to age and administrative region. In France, we found that a "negative" or a "positive" test, as classified by the manufacturer, could correspond to a probability of infection as high as 61.8% or as low as 67.7%, respectively. "Indeterminate" tests encompassed probabilities of infection ranging from 10.8 to 96.6%. Our model estimated tailored individual probabilities of SARS-CoV-2 infection based on age, region, and serological result. It can be applied in other contexts, if estimates of cumulative incidence are available. [ABSTRACT FROM AUTHOR]

Natural frequencies are known to improve performance in Bayesian reasoning. However, their impact in situations with two binary events has not yet been completely examined, as most researchers in the last 30 years focused only on conditional probabilities. Nevertheless, situations with two binary events consist of 16 elementary probabilities and so we widen the scope and focus on joint probabilities. In this article, we theoretically elaborate on the importance of joint probabilities, for example, in situations like the Linda problem. Furthermore, we implemented a study in a 2x5x2 design with the factors information format (probabilities vs. natural frequencies), visualization type ("Bayesian text" vs. tree diagram vs. double tree diagram vs. net diagram vs. 2x2 table), and context (mammography vs. economics problem). Additionally, all four "joint questions" (i.e., P(A∩B), P(A∩B), P(A∩B), P(A∩B)) were asked for. The main factor of interest was whether there is a format effect in the five visualization types named above. Surprisingly, the advantage of natural frequencies was not found for joint probabilities and, most strikingly, the format interacted with the visualization type. Specifically, while people's understanding of joint probabilities in a double tree seems to be worse than the understanding of the corresponding natural frequencies (and, thus, the frequency effect holds true), the opposite seems to be true in the 2x2 table. Hence, the advantage of natural frequencies compared to probabilities in typical Bayesian tasks cannot be found in the same way when joint probability or frequency tasks are asked. [ABSTRACT FROM AUTHOR]

The present article discusses some recent advances in methods of critical evaluation of experimental data on wavelengths of spectral lines and theoretical data on transition probabilities and oscillator strengths for atoms and atomic ions. In particular, recently developed new statistical approaches to estimation of uncertainties of weighted means of multiple measurements are described, and a numerical toolbox implementing these new approaches is presented. There are also some new developments in estimation of uncertainties of theoretical transition probabilities. A short review of literature implementing these new procedures is provided, including a description of the methodology. [ABSTRACT FROM AUTHOR]

This paper concentrates on the finite-time  H ∞  control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT)  H ∞  state feedback controller and an SFT  H ∞  observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov–Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT  H ∞  boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes. [ABSTRACT FROM AUTHOR]

The problem of probabilities of conditionals is one of the long‐standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities of conditionals violate standard probability theory. This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. We address two common objections to Adams' view: that the relevant probabilities are 'probabilities only in name', and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. [ABSTRACT FROM AUTHOR]

This article is concerned with a reasonably generalized dual Binomial risk model where the periodic premium is one and in each period there is at most one claim and non-negative claim amounts are independent and identically distributed random variables. Our main purpose is to evaluate the probability of time to ruin and ruin probabilities. First, we present a formula for probability of time to ruin based on the convolution of claim amount. We derive a recursive expression for the finite time ruin probability based on the probability of time to ruin and classical ruin probability using the Markov property and law of total probability when surplus process stays below or at zero at least for some fixed duration of time. Moreover, we obtain an explicit expression for the corresponding infinite time ruin probability as a limiting case. Finally, to illustrate our method we calculate the numerical values of these probabilities for some different types of models of probability mass functions for claim amounts. [ABSTRACT FROM AUTHOR]

Surrogate reactions are a powerful tool to access neutron-induced reaction cross sections of short-lived nuclei. However, to infer neutron-induced reaction cross sections from measured deexcitation probabilities requires a consistent and rigorous theoretical framework describing both charged-particle and neutron-induced reactions. This work presents the first practical application of the new approach developed in O. Bouland, Phys. Rev. C 100, 064611 (2019) to Pu fissile isotopes, 237,238,240,242,244Pu*. Average neutron-induced reaction cross sections and deexcitation probabilities measured in surrogate reactions are simultaneously analyzed with an efficient Monte Carlo R -matrix-extended theory algorithm using a unique set of nuclear-structure parameters to describe both observables. Fission probabilities allow one to estimate fission-barrier heights, not otherwise accessible in fissile isotopes. The theoretical framework is here extended to model 'giant' resonance structures observed in the fission probabilities of some nuclides. A careful study of the impact of the uncertainties on nuclear parameters and on the populated compound system angular distribution has been carried out. This study raises questions on the normalization of some fission probabilities measured in the 70's in (t , p) reactions, that could not have been pointed out without the use of the here-presented complex technique. This finding is especially important for the peculiar 240Pu* system. In addition, our study reveals for the 237Pu* compound system a 10 to 30 % too high value of the only-performed low-energy neutron-induced fission cross section measurement (Gerasimov et al. , JINR-E–3-97-213 (1997)) and, subsequently of the evaluated fission cross section below 50 keV for the 236Pu. [ABSTRACT FROM AUTHOR]

Experts often communicate probabilities verbally (e.g., unlikely) rather than numerically (e.g., 25% chance). Although criticism has focused on the vagueness of verbal probabilities, less attention has been given to the potential unintended, biasing effects of verbal probabilities in communicating probabilities to decision-makers. In four experiments (Ns = 201, 439, 435, 696), we showed that probability format (i.e., verbal vs. numeric) influenced participants' inferences and decisions following a hypothetical financial expert's forecast. We observed a format effect for low probability forecasts: verbal probabilities were interpreted more pessimistically than numeric equivalents. We attributed the difference to directionality, a linguistic property that biases attention toward an outcome. In the high-probability conditions, the directionality of verbal and numeric probabilities aligned (both were positive), whereas they differed in the low-probability conditions (verbal probabilities were more negative). Participants inferred recommendations congruent with the communicated direction and these inferences mediated the effect of probability format on decisions. [ABSTRACT FROM AUTHOR]

This contribution deals with a model of one-dimensional Bernoulli-like random walk with the position of the walker controlled by varying transition probabilities. These probabilities depend explicitly on the previous move of the walker and, therefore, implicitly on the entire walk history. Hence, the walk is not Markov. The article follows on the recent work of the authors, the models presented here describe how the logits of transition probabilities are changing in dependence on the last walk step. In the basic model this development is controlled by parameters. In the more general setting these parameters are allowed to be time-dependent. The contribution focuses mainly on reliable estimation of model components via the MLE procedures in the framework of the generalized linear models. [ABSTRACT FROM AUTHOR]

AbstractBivariate copulas for two dependent non homogeneous compound Poisson processes (NCPP) are considered. In this scenario, the arrival times of events are assumed to follow two independent non homogeneous Poisson processes (NHPP), but the corresponding renewal variables are dependent through a bivariate copula. The article aims to provide a computational tool for the estimation of the probability that the random sum associated with the first NCPP is less than the other random sum by a truncated time. The proposed ML and Bayesian estimation methods in a general setting can be applied using bivariate copulas such as Gumbel (for upper tail dependency), Clayton (for lower tail dependency), and Frank (for symmetric dependency). Power Law (PL) intensity function for the NHPPs and Inverse-Gaussian as renewal distribution are considered as examples. Bayes estimates of NHPPs parameters use gamma priors, and for Bayes estimates of Inverse-Gaussian distribution, an MCMC algorithm is employed. Our method has a broad range of practical applications, especially in the insurance sector, where the renewal variable may represent the dollar amount associated with a claim. To illustrate our approach, we analyze injury claims in North Carolina and South Carolina over a specific period, using a dataset sourced from docs.databricks.com. [ABSTRACT FROM AUTHOR]