We investigate Bayesian alternatives to classical Monte Carlo methods for evaluating integrals. Bayesian Monte Carlo (BMC) allows the incorporation ofprior knowledge, such as smoothness of the integrand, into the estimation. In a simple problem we show that this outperforms any classical importance sampling method. We also attempt more challenging multidimensionalintegrals involved in computing marginal likelihoods ofstatistical models (a.k.a.
Rafael Nadal once again showed why he is the greatest clay court player in the history of the game with a dominant run to the title at the Monte Carlo Masters, his 11th in the Principality of Monaco. The Spaniard defeated Kei Nishikori in straight sets in the final on Sunday and won the title without dropping a set throughout the tournament. He has now won 36 straight sets since the start of the 2017 French Open, where he captured his 10th title last year. Nadal's win in Monte Carlo was more significant as it was his first ATP event of 2018 having struggled with a hip injury since January 2018. He withdrew from the Australian Open with the injury which subsequently saw him withdraw from the Mexican Open, the Indian Wells Masters and the Miami Open.
World No. 1 Rafael Nadal will look to capture his 11th Monte Carlo Masters title on Sunday when he faces Kei Nishikori in the final. Betting site Betfair Exchange lists Nadal as a 1/14 favorite, while Nishikori is a 59/5 longshot. Nadal, who owns just a 100-point lead on No. 2 Roger Federer, defeated No. 5 Grigor Dimitrov 6-4 6-1 on Saturday, after No. 36 Nishikori held off No. 4 Alexander Zverev, 3-6 6-3 6-4. The Spaniard needs a victory Sunday to remain No. 1. Federer has been inactive since an upset loss to Thanasi Kokkinakis at the Miami Open on March 24. Prior to the start of the Monte Carlo Masters, Nadal was the overwhelming favorite with 8/11 odds and has done little to shed doubt of his frontrunner status.
This technical report is the union of two contributions to the discussion of the Read Paper "Riemann manifold Langevin and Hamiltonian Monte Carlo methods" by B. Calderhead and M. Girolami, presented in front of the Royal Statistical Society on October 13th 2010 and to appear in the Journal of the Royal Statistical Society Series B. The first comment establishes a parallel and possible interactions with Adaptive Monte Carlo methods. The second comment exposes a detailed study of Riemannian Manifold Hamiltonian Monte Carlo (RMHMC) for a weakly identifiable model presenting a strong ridge in its geometry.
Novak Djokovic turned to a familiar face as he looked to get back to winning ways following his recent split with Andre Agassi and Radek Stepanek, going into the clay court swing of the 2018 season. The Serbian reunited with former coach Marian Vajda ahead of the Monte Carlo Masters, but it is not confirmed whether their association will be long-term, with the statement on the player's website stating they will go "one step at a time." Djokovic ended his decade long association with Vajda in the early part of the 2017 season before hiring Agassi prior to the start of last year's French Open. It was a shock at first, as the former played a key role in taking the Serb to 12 men's singles Grand Slam titles. In this picture, Novak Djokovic of Serbia plays a shot against Benoit Paire of France during Day 5 of the Miami Open at the Crandon Park Tennis Center on March 23, 2018, in Key Biscayne, Florida.