A regeneration proof of the central Llmit theorem for uniformly ergodic Markov chains

Central limit theorems for functionals of general state space Markov chains are of crucial importance in sensible implementation of Markov chain Monte Carlo algorithms as well as of vital theoretical interest. Different approaches to proving this type of results under diverse assumptions led to a large variety of CLT versions. However due to the recent development of the regeneration theory of Markov chains, many classical CLTs can be reproved using this intuitive probabilistic approach, avoiding technicalities of original proofs. In this paper we provide a characterization of CLTs for ergodic Markov chains via regeneration and then use the result to solve the open problem posed in [Roberts & Rosenthal 2005]. We then discuss the difference between one-step and multiple-step small set condition

A progress report on a prospective randomised trial of open and robotic prostatectomy

A randomised trial of robotic and open prostatectomy commenced in October 2010 and is progressing well. Clinical and quality of life outcomes together with economic costs to individuals and the health service are being examined critically to compare outcomes

Can atorvastatin with metformin change the natural history of prostate cancer as characterized by molecular, metabolomic, imaging and pathological variables? A randomized controlled trial protocol

Background Atorvastatin and metformin are known energy restricting mimetic agents that act synergistically to produce molecular and metabolic changes in advanced prostate cancer (PCa). This trial seeks to determine whether these drugs favourably alter selected parameters in men with clinically-localized, aggressive PCa. Methods/design This prospective phase II randomized, controlled window trial is recruiting men with clinically significant PCa, confirmed by biopsy following multiparametric MRI and intending to undergo radical prostatectomy. Ethical approval was granted by the Royal Brisbane and Women's Hospital Human and The University of Queensland Medical Research Ethics Committees.Participants are being randomized into four groups: metformin with placebo; atorvastatin with placebo; metformin with atorvastatin; or placebo alone. Capsules are consumed for 8weeks, a duration selected as the most appropriate period in which histological and biochemical changes may be observed while allowing prompt treatment with curative intent of clinically significant PCa. At recruitment and prior to RP, participants provide blood, urine and seminal fluid. A subset of participants will undergo 7Tesla magnetic resonance spectroscopy to compare metabolites in-vivo with those in seminal fluid and biopsied tissue.The primary end point is biochemical evolution, defined using biomarkers (serum prostate specific antigen; PCA3 and citrate in seminal fluid and prostatic tissue). Standard pathological assessment will be undertaken. Discussion This study is designed to assess the potential synergistic action of metformin and atorvastatin on PCa tumour biology. The results may determine simple methods of tumour modulation to reduce disease progression