Explore the vast range of titles available.

There are two main interrelated goals of this paper. Firstly we investigate the sums

A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position and survey state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of logic programming languages such as Prolog, which have been considered for over 20 years.

Starting with the category of probabilistic approach groups, we show that the category of approach groups can be embedded into the category of probabilistic approach groups as a bicoreflective subcategory; further, considering a category of probabilistic topological convergence groups, we show that the category of probabilistic topological convergence groups is isomorphic to the category of probabilistic approach groups under so-called triangle function τ: Δ⁺ × Δ⁺ −→ Δ⁺, where Δ⁺ is the set of all distance distribution functions that plays a central role for probabilistic metric spaces. Moreover, if we allow this triangle function τ to be sup-continuous, then we can show that the category of probabilistic metric groups can be embedded into the category of probabilistic approach groups as a coreflective subcategory. Furthermore, we demonstrate that every T₁ probabilistic topological convergence group satisfying so-called (PM) axiom is probabilistic metrizable. Finally, among others, introducing a category of probabilistic approach transformation groups, we show that the category of probabilistic topological convergence transformation groups is isomorphic to the category of probabilistic approach transformation groups; this solves an open problem that proposed in one of our earlier papers. Moreover, we prove that the category of probabilistic metric transformation groups is isomorphic to the category of probabilistic metric probabilistic convergence transformation groups.

Assume that the moment-generating function of the random variable Y exists in a neighborhood of the origin. The aim of this paper is to investigate the probabilistic type 2 Bernoulli polynomials associated with Y and the probabilistic type 2 Euler polynomials associated with Y , along with the probabilistic type 2 cosine-Bernoulli polynomials associated with Y , the probabilistic type 2 sine-Bernoulli polynomials associated with Y , the probabilistic type 2 cosine-Euler polynomials associated with Y , and the probabilistic type 2 sine-Euler polynomials associated with Y . We deal with their properties, related identities and explicit expressions.

Introducing the notion of probabilistic convergence ring, and probabilistic limit ring, our motivations among others are, to focus at two vital issues, such as, (a) to provide characterization theorems on probabilistic convergence rings, (b) probabilistic uniformizability of probabilistic limit rings, and discuss some results on probabilistic Cauchy rings, and their relationship with probabilistic convergence rings. In doing so, we produce various examples, particularly, from function space structure of continuous probabilistic convergence. Moreover, we observe that the category of probabilistic convergence ring in the sense of Richardson-Kent is a reflective subcategory of the category of probabilistic convergence rings in our sense.

Probabilistic programming allows for automatic Bayesian inference on user-defined probabilistic models. Recent advances in Markov chain Monte Carlo (MCMC) sampling allow inference on increasingly complex models. This class of MCMC, known as Hamiltonian Monte Carlo, requires gradient information which is often not readily available. PyMC3 is a new open source probabilistic programming framework written in Python that uses Theano to compute gradients via automatic differentiation as well as compile probabilistic programs on-the-fly to C for increased speed. Contrary to other probabilistic programming languages, PyMC3 allows model specification directly in Python code. The lack of a domain specific language allows for great flexibility and direct interaction with the model. This paper is a tutorial-style introduction to this software package.

Spivey found a remarkable recurrence relation for Bell numbers, which was generalized to that for Bell polynomials by Gould-Quaintance. The aim of this article is to generalize their recurrence relation for Bell polynomials to that for the probabilistic Dowling polynomials associated with and also that for the probabilistic -Dowling polynomials associated with . Here is a random variable whose moment generating function exists in a neighborhood of the origin.

Evidence regarding whether imaging can be used effectively to select patients for endovascular thrombectomy (EVT) is scarce. We aimed to investigate the association between baseline imaging features and safety and efficacy of EVT in acute ischaemic stroke caused by anterior large-vessel occlusion. In this meta-analysis of individual patient-level data, the HERMES collaboration identified in PubMed seven randomised trials in endovascular stroke that compared EVT with standard medical therapy, published between Jan 1, 2010, and Oct 31, 2017. Only trials that required vessel imaging to identify patients with proximal anterior circulation ischaemic stroke and that used predominantly stent retrievers or second-generation neurothrombectomy devices in the EVT group were included. Risk of bias was assessed with the Cochrane handbook methodology. Central investigators, masked to clinical information other than stroke side, categorised baseline imaging features of ischaemic change with the Alberta Stroke Program Early CT Score (ASPECTS) or according to involvement of more than 33% of middle cerebral artery territory, and by thrombus volume, hyperdensity, and collateral status. The primary endpoint was neurological functional disability scored on the modified Rankin Scale (mRS) score at 90 days after randomisation. Safety outcomes included symptomatic intracranial haemorrhage, parenchymal haematoma type 2 within 5 days of randomisation, and mortality within 90 days. For the primary analysis, we used mixed-methods ordinal logistic regression adjusted for age, sex, National Institutes of Health Stroke Scale score at admission, intravenous alteplase, and time from onset to randomisation, and we used interaction terms to test whether imaging categorisation at baseline modifies the association between treatment and outcome. This meta-analysis was prospectively designed by the HERMES executive committee but has not been registered. Among 1764 pooled patients, 871 were allocated to the EVT group and 893 to the control group. Risk of bias was low except in the THRACE study, which used unblinded assessment of outcomes 90 days after randomisation and MRI predominantly as the primary baseline imaging tool. The overall treatment effect favoured EVT (adjusted common odds ratio [cOR] for a shift towards better outcome on the mRS 2·00, 95% CI 1·69–2·38; p<0·0001). EVT achieved better outcomes at 90 days than standard medical therapy alone across a broad range of baseline imaging categories. Mortality at 90 days (14·7% vs 17·3%, p=0·15), symptomatic intracranial haemorrhage (3·8% vs 3·5%, p=0·90), and parenchymal haematoma type 2 (5·6% vs 4·8%, p=0·52) did not differ between the EVT and control groups. No treatment effect modification by baseline imaging features was noted for mortality at 90 days and parenchymal haematoma type 2. Among patients with ASPECTS 0–4, symptomatic intracranial haemorrhage was seen in ten (19%) of 52 patients in the EVT group versus three (5%) of 66 patients in the control group (adjusted cOR 3·94, 95% CI 0·94–16·49; pinteraction=0·025), and among patients with more than 33% involvement of middle cerebral artery territory, symptomatic intracranial haemorrhage was observed in 15 (14%) of 108 patients in the EVT group versus four (4%) of 113 patients in the control group (4·17, 1·30–13·44, pinteraction=0·012). EVT achieves better outcomes at 90 days than standard medical therapy across a broad range of baseline imaging categories, including infarcts affecting more than 33% of middle cerebral artery territory or ASPECTS less than 6, although in these patients the risk of symptomatic intracranial haemorrhage was higher in the EVT group than the control group. This analysis provides preliminary evidence for potential use of EVT in patients with large infarcts at baseline. Medtronic.

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the derangement polynomials, the derangement polynomials of type 2 and the r-derangement numbers, namely the probabilistic derangement polynomials associated with Y, the probabilistic derangement polynomials of type 2 associated with Y and the probabilistic r-derangement numbers associated Y, respectively. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers. In addition, we consider the special case that Y is the gamma random variable with parameters α, β > 0.

Uncertainty is a significant challenge in tsunami hazard analysis. Tsunami heights are affected by complex factors and change constantly during propagation. The heights of tsunami have random characteristics. This study proposes that the water depths (related to seabed topography) are the most important factors that affect tsunami height. But across the globe, a considerable area of seabed topography has not been measured. So it is necessary to use the method of uncertainty to consider the water depth. The Wiener process is utilized to quantify the random changes of the water depth, which can better describe the situation that water depths change in a non-monotonic way. Considering the uncertainty of water depth, a Weiner process-based probabilistic model was established for predicting the maximum tsunami height, which is different from the maximum tsunami height deterministic or stochastic model previously studied with higher prediction efficiency and good prediction accuracy. The probability distribution of maximum tsunami heights was calculated using the stochastic model. The mean value of the maximum tsunami heights was very similar to the average value of 165 actual observations of maximum tsunami heights collected from 1997 to 2017.