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A standard way to move particles in a SMC sampler is to apply several steps of a MCMC (Markov chain Monte Carlo) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste-free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its output is consistent and asymptotically normal. We use the expression of the asymptotic variance to develop various insights on how to implement the algorithm in practice. We develop in particular a method to estimate, from a single run of the algorithm, the asymptotic variance of any particle estimate. We show empirically, through a range of numerical examples, that waste-free SMC tends to outperform standard SMC samplers, and especially so in situations where the mixing of the considered MCMC kernels decreases across iterations (as in tempering or rare event problems)., revised version

Summary The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis–Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.

Background Deep infiltrating endometriosis (DIE) is presented as a disease with high recurrence risk. Bladder DIE is the most frequent location in cases of urinary endometriosis. Surgical removal has been recommended for bladder DIE but long-term outcomes remains unevaluated. The objectives of this study are to evaluate the rate of recurrence after partial cystectomy for patients presenting with bladder DIE and to outline the surgical modalities for handling associated posterior DIE nodules. Methods Seventy-five consecutive patients with histologically proved bladder DIE were enrolled at a single tertiary academic center between June 1992 and December 2007. A partial cystectomy was performed for each patient. Complete surgical exeresis of all associated symptomatic DIE lesions was carried out during the same surgical procedure. Bladder DIE patients were classified into three groups: patients with isolated bladder DIE (Group A); patients with associated symptomatic posterior DIE (Group B); patients with associated asymptomatic posterior DIE (Group C). Bladder DIE recurrence was defined as a clinical reappearance of the disease or radiological evidence that mandated a new surgical procedure. We assessed pelvic pain symptoms pre- and post-operatively using a 10-cm visual analogue scale. Results In a series of 627 patients with DIE, we observed 75 patients (12%) with bladder DIE. With a 50.9 +/- 44.6 months mean follow-up after partial cystectomy no patient presented evidence of bladder DIE recurrence. Post-operatively, we observed a significant improvement with respect to pain symptoms, with only two patients (2.7%) developing major complications during follow-up. Among patients with non-operated associated asymptomatic posterior DIE lesions (n = 15), a second surgical procedure indicated for pain symptoms was necessary in only one patient (6.7%). Conclusions For patients presenting with bladder DIE, no patients required further surgery for bladder recurrence after radical surgery consisting in partial cystectomy. Exeresis of associated posterior DIE nodules is indicated only when they are symptomatic.

Background This study was designed to investigate the intra-operative characteristics and the risk of intra- and post-operative complications in cases of total laparoscopic hysterectomy (TLH) in overweight, obese and non-obese patients. Methods This cohort study includes all patients undergoing TLH for benign pathologies between January 1993 and June 2007 in Cochin university hospital (Paris). Demographic and surgical data were analysed. A comparison between overweight and obese patients versus non-obese patients and multivariate analyses were performed. Results Of 1460 patients undergoing TLH, 101 patients (6.9%) had a BMI of 30 or higher and 338 (23.2%) were overweight. After adjustment with respect to the patients' characteristics and past history (age, parity, past history of laparotomies, previous Cesarean section, menopausal status), no significant difference was found whether in terms of intra-operative (haemorrhage, transfusion, thrombosis, ureter, bladder or bowel injuries) or post-operative complications (hyperthermia, infections, fistula). Concerning the intra- and post-operative characteristics of these patients, only a significantly longer operating time was noted in the case of obesity (RR = 1.80; CI 95%: 1.16-2.81). Conclusions In our experience, provided that the operating technique is meticulous, the intra- and post-operative complications are not increased in the case of obesity, although the operating time is longer.

Background Laparoscopic hysterectomy is indicated as an alternative to laparotomy when the vaginal route is potentially difficult because of an immobile uterus and a poor vaginal accessibility. The aim of this study was to evaluate the rate, the risk factors for bladder injuries in a series of 1501 laparoscopic hysterectomies indicated for benign uterine pathologies. Methods This study was conducted retrospectively from January 1993 to 2000 and prospectively from 2001 to July 2007.The indications, patients' characteristics and complications were recorded. The overall rate of bladder injuries, the comparison of means (t test) and percentages (exact chi(2) test) between the cases and the population with no injury, the odd ratios (OR) and multivariate analysis were performed using the statistical package for the social sciences software. Results The rate of bladder injuries was 1% (15 patients). Risks factors were previous Caesarian section [OR: 4.33, 95% confidence interval (CI): 1.53-12.30] and previous laparotomy (OR: 4.69, 95% CI: 1.59-13.8). The rate of injury decreases with the surgeons' experience and reaches a plateau of 0.4% after 100 hysterectomies performed. Conclusions The rate of bladder injury during total laparoscopic hysterectomy is low and decreases with the surgeon's experience. Bladder injury is not linked to an increase of post-operative morbidity when recognized and repaired during the same laparoscopic procedure. The comparison with other routes of hysterectomies should take into account these risk factors.

Background Transvaginal ultrasonography (TVUS) has important advantages compared with transrectal ultrasonography (TRUS): it is less invasive, is cost-effective, is a familiar and well-accepted approach, and anesthesia is not required. We compared the accuracy of TVUS and TRUS for diagnosing rectal wall involvement in patients presenting with histologically proved deeply infiltrating endometriosis (DIE). Methods Prospective study of 134 patients with histologically proved DIE underwent preoperative investigations using both TVUS and TRUS. The radiologist (TVUS) and sonographer (TRUS) were unaware of the clinical findings but knew that DIE was suspected. Results DIE was confirmed histologically for all the patients. A rectal wall involvement was histologically proved for 75 patients (56%). For the diagnosis of infiltration of the intestinal wall, TVUS and TRUS, respectively, had a sensitivity of 90.7% and 96.0%, a specificity of 96.5% and 100.0%, a positive predictive value of 97.1% and 100.0% and a negative predictive value of 88.9% and 95.2%. Conclusions TVUS and TRUS have similar degrees of accuracy for predicting intestinal involvement. TVUS must be the first-line imaging process to perform for patients presenting with clinically suspected DIE. The question for the coming years is to define if it is necessary for TRUS to be carried out systematically in cases of clinically suspected DIE.

BACKGROUND: The aim of this study was to evaluate the risk of ureteral injuries and to discuss how to avoid their occurence after laparoscopic hysterectomy indicated for benign uterine pathologies. METHODS: This observational study covers the period from January 1993 to December 2005 (retrospective study from 1993 to 2000 and prospective from 2001). We reviewed incidence, methods of diagnosis and management of ureteral injuries. RESULTS: The rate of ureteral injuries was 0.3% (four patients). Three patients presented a ureteral fistula diagnosed secondarily some time after the operation. The fourth patient presented a ureteral injury that was diagnosed peroperatively. Three out of four of the lesions were observed on the right side. In every case, there were preoperative risk factors connected with a past history of surgery, or the lateral location of uterine myomas. All four patients needed ureterovesical reimplantation. The outcome was good in all four cases. CONCLUSIONS: The rate of ureter complications after laparoscopic hysterectomy is low and comparable to that observed after hysterectomy by laparotomy. The risk should not prevent laparoscopic hysterectomy being used more widely. Prevention depends on training in the technique and the surgeon’s experience.

SummaryThe system equation of a hidden Markov model is rewritten to label the components by order of appearance, and to make explicit the random behaviour of the number of components, mt. We argue that this reformulation is often a good way to achieve identifiability, as it facilitates the interpretation of the posterior density, and the estimation of the number of components that have appeared in a given sample. We develop a sequential Monte Carlo algorithm for estimating the reformulated model, which relies on particle filtering and Gibbs sampling. Our algorithm has a computational cost that is similar to that of a Markov chain Monte Carlo sampler and is much less likely to be affected by label switching, i.e. the possibility of becoming trapped in a local mode of the posterior density. The extension to transdimensional priors is also considered. The approach is illustrated by two real data examples.

BACKGROUND: To investigate whether knowledge of the anatomical distribution of histologically proven deeply infiltrating endometriosis (DIE) lesions contributes to understanding the pathogenesis. METHODS: Observational study between June 1992 and December 2004 (retrospective study between 1992 and 2000; prospective study between 2001 and 2004). Continuous series of 426 patients suffering from pelvic pain who underwent complete surgical exeresis of DIE. DIE lesions were classified according to four different possibilities: (i) Firstly, DIE lesions were classified as located in the anterior or posterior pelvic compartment. (ii) Secondly, DIE were classified as left, median and right. (iii) Thirdly, DIE lesions were classified as pelvic or abdominal. (iv) Fourthly, DIE lesions that could present in a right and/or left location were classified as unilateral or bilateral. RESULTS: These 426 patients presented 759 histologically proven DIE lesions: bladder (48 lesions; 6.3%); uterosacral (USL) (400 lesions; 52.7%); vagina (123 lesions; 16.2%); ureter (16 lesions; 2.1%) and intestine (172, 22.7%). DIE lesions are significantly more often located in the pelvis (n = 730 lesions) than in the abdomen (n = 29 lesions) (P < 0.0001). Pelvic DIE lesions are significantly more often located in the posterior compartment of the pelvis [682 DIE lesions (93.4%) versus 48 DIE lesions (6.6%); P < 0.0001]. Pelvic DIE lesions are significantly more frequently located on the left side. For patients with unilateral pelvic DIE lesions, the anatomical distribution is significantly different in the three groups: left (172 lesions; 32.0%), median (284 lesions; 52.8%) and right (82 lesions; 15.2%) (P < 0.0001). For patients with lateral lesions, left DIE lesions (172 lesions; 67.8%) were found significantly more frequently than right DIE lesions (82 lesions; 32.2%) (P < 0.0001). A similar predisposition was observed when we included patients with bilateral pelvic DIE lesions (P = 0.0031). The same significantly asymmetric distribution is observed for total (pelvic and abdominal) DIE lesions. CONCLUSIONS: Our results demonstrate that distribution of DIE lesions is asymmetric. It is possible that this is related to the anatomical difference between the left and right hemipelvis and to the flow of peritoneal fluid. These findings support the hypothesis that retrograde menstruation of regurgitated endometrial cells is implicated in the pathogenesis of DIE.

SUMMARY Particle filter methods are complex inference procedures, which combine importance sampling and Monte Carlo schemes in order to explore consistently a sequence of multiple distributions of interest. We show that such methods can also offer an efficient estimation