Average fuel prices in the United States started the week at $2.26 per gallon, showing little change from the last month or last week, and may remain flat.

The USS Montgomery and the USNS Cesar Chavez sailed into the South China Sea this week in support of the West Capella drill ship, according to U.S. Indo-Pacific Command.

Montana Superintendent Denise Juneau said it would be "in the best interest of our students" to let districts cancel Smarter Balanced testing if necessary.

In addition to a delay, Wisconsin had to eliminate certain questions from its Smarter Balanced exam, after opting not to use the adaptive testing feature of the test.

The U.S. Supreme Court agreed to review a decision by Montana's highest court that struck down a tuition tax-credit program allowing tuition scholarships to benefit students at private religious schools.

This Quality Counts 2019 Highlights Report captures all the data you need to assess your state's performance on key educational outcomes.

This Quality Counts 2020 Highlights Report captures all the data you need to assess your state's performance on key educational outcomes.

Brain -- Diseases.

Berlin : T. Trautwein, 1842.

Paris : Didot le jeune, 1831.

Londres : Paris, 1860.

A state law aimed at encouraging—or prodding—small, rural districts to merge has hit some speed bumps on the road to implementation.

Vermont doles out none of its K-12 education aid explicitly for technology, but it has tried to use federal and private grant money to make educational technology resources available for school districts.

State of the States: Education highlights from latest governor's address before the legislature.

The latest approvals mean 12 of the 17 state plans submitted so far for Every Student Succeeds Act implementation have been given the federal go-ahead.

In his annual speech to the legislature, the governor proposed leasing the state lottery, with $25 million of the proceeds going to property-tax relief and $25 million to modernization of school buildings.

State Education Secretary Rebecca Holcombe has been officiating over the state's politically thorny district consolidation process, and many are asking for it to be placed on hold until the state board replaces her.

A group of Vermont high school students backed by a powerful conservative Christian legal organization is accusing the state of religious discrimination.

In the Green Mountain State, education leaders discuss their focus on the whole child.

This Quality Counts 2019 Highlights Report captures all the data you need to assess your state's performance on key educational outcomes.

This Quality Counts 2020 Highlights Report captures all the data you need to assess your state's performance on key educational outcomes.

Monte Carlo simulation is useful to compute or estimate expected functionals of random elements if those random samples are possible to be generated from the true distribution. However, when the distribution has some unknown parameters, the samples must be generated from an estimated distribution with the parameters replaced by some estimators, which causes a statistical error in Monte Carlo estimation. This paper considers such a statistical error and investigates the asymptotic distributions of Monte Carlo-based estimators when the random elements are not only the real valued, but also functional valued random variables. We also investigate expected functionals for semimartingales in details. The consideration indicates that the Monte Carlo estimation can get worse when a semimartingale has a jump part with unremovable unknown parameters.

Jere Koskela, Paul A. Jenkins, Adam M. Johansen, Dario Spanò.

Source: The Annals of Statistics, Volume 48, Number 1, 560--583.

Abstract:
We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines. We consider the genealogical tree embedded into such particle systems, and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman $n$-coalescent in the infinite system size limit in the sense of finite-dimensional distributions. Thus, the tractable $n$-coalescent can be used to predict the shape and size of SMC genealogies, as we illustrate by characterising the limiting mean and variance of the tree height. SMC genealogies are known to be connected to algorithm performance, so that our results are likely to have applications in the design of new methods as well. Our conditions for convergence are strong, but we show by simulation that they do not appear to be necessary.

L. F. South, A. N. Pettitt, C. C. Drovandi.

Source: Bayesian Analysis, Volume 14, Number 3, 773--796.

Abstract:
Sequential Monte Carlo (SMC) methods for sampling from the posterior of static Bayesian models are flexible, parallelisable and capable of handling complex targets. However, it is common practice to adopt a Markov chain Monte Carlo (MCMC) kernel with a multivariate normal random walk (RW) proposal in the move step, which can be both inefficient and detrimental for exploring challenging posterior distributions. We develop new SMC methods with independent proposals which allow recycling of all candidates generated in the SMC process and are embarrassingly parallelisable. A novel evidence estimator that is easily computed from the output of our independent SMC is proposed. Our independent proposals are constructed via flexible copula-type models calibrated with the population of SMC particles. We demonstrate through several examples that more precise estimates of posterior expectations and the marginal likelihood can be obtained using fewer likelihood evaluations than the more standard RW approach.

Airing on the aquarium's Twitch channel at 4 p.m. EST today, the two-hour session will focus on the video game's diverse insect population

64-year-old John Neville, in agony and needing his wisdom tooth extracted, has been navigating a complex tangle of COVID-19 restrictions in an unsuccessful attempt at getting emergency dental care.