This paper introduces an extension of the Markov switching GARCH model where the volatility in each state is a convex combination of two different GARCH components with time varying weights. This model has the dynamic behaviour to capture the variants of shocks. The asymptotic behavior of the second moment is investigated and an appropriate upper bound for it is evaluated. The estimation of the parameters by using the Bayesian method via Gibbs sampling algorithm is studied. Finally we illustrate the efficiency of the model by simulation and empirical analysis. We show that this model provides a much better forecast of the volatility than the Markov switching GARCH model.
The current study endeavored to closely compare the detection rate of 68-Gallium labelled prostate-specific membrane antigen ([68Ga]Ga-PSMA) versus [18F]Fluorocholine in men with prostate cancer (PC), to investigate the benefits and pitfalls of each modality in the setting of various patient characteristics. We retrospectively analyzed 29 biopsy-proven PC patients in two categories, staging and restaging, who underwent both scans within a maximum of 30 days of each other. Variables including patient demographics, prostate specific antigen (PSA) level, Gleason score, clinical course, and following treatments were recorded. The number and location of suspicious lesions as well as uptake values were noted. A total of 148 suspicious lesions were detected, of which 70.9% (105/148) were concordantly visualized in both imaging modalities. [68Ga]Ga-PSMA positron emission tomography/computed tomography (PET/CT) revealed a higher number of metastatic lesions per patients (91% vs 78%). The mean of maximum standardized uptake value (SUV max) in concordant lesions was significantly higher in [68Ga]Ga-PSMA compared to [18F]Fluorocholine PET/CT (14.6 ± 8.44 vs. 6.9 ± 3.4, p = 0.001). Discordant lesions were detected by both modalities, but more frequently by [68Ga]Ga-PSMA PET/CT (20.3% in [68Ga]Ga-PSMA versus 8.8% by [18F]Fluorocholine PET/CT). In patients with PSA levels below 1.0 ng/mL and <2.0 ng/mL, [18F]Fluorocholine PET/CT detection rate was half (57% and 55%, respectively) that of [68Ga]Ga-PSMA PET/CT. Tumor, nodes and metastases (TNM) staging, and subsequently patient management, was only influenced in 4/29 patients (14%), particularly by [68Ga]Ga-PSMA PET/CT with PSA values under 0.5 ng/mL. [68Ga]Ga-PSMA PET/CT revealed superior diagnostic performance to [18F]Fluorocholine PET/CT in staging and restaging of PC patients, especially in cases with low PSA levels. However, in a few hormone resistant high-risk PC patients, [18F]Fluorocholine PET/CT may improve overall diagnostic accuracy.
A new Markov switching asymmetric GARCH model is proposed where each state follows a logistic smooth transition structure between effects of positive and negative shocks. This consideration provides better forecasts in many financial time series. The asymptotic finiteness of the second moment is investigated. The parameters of the model are estimated by applying MCMC methods through Gibbs and griddy Gibbs sampling. Applying the log return of some part of S&P 500 indices, we show the competing performance of in sample fit and out of sample forecast volatility and value at risk of the proposed model. The Diebol-Mariano test shows that the presented model outperforms all competing models in forecast volatility.
The Bayesian estimation of the stress-strength parameter in Lomax distribution under the progressive hybrid censored sample is considered in three cases. First, assuming the stress and strength are two random variables with a common scale and different shape parameters. The Bayesian estimations of these parameters are approximated by Lindley method and the Gibbs algorithm. Second, assuming the scale parameter is known, the exact Bayes estimation of the stress-strength parameter is obtained. Third, assuming all parameters are unknown, the Bayesian estimation of the stressstrength parameter is derived via the Gibbs algorithm. Also, the maximum likelihood estimations are calculated, and the usefulness of the Bayesian estimations is confirmed, in comparison with them. Finally, the different methods are evaluated utilizing the Monte Carlo simulation and one real data set is analyzed.
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