The Metropolis-Hastings (MH) algorithm is a way to IID sample a provided target distribution π(x). It works by repeatedly sampling a separate proposal distribution T (x, x′) to generate a random walk {x(t)} which converges to a set of samples of π. Here, we introduce a T -updating phase after the cooling period and before sampling begins. In the updating phase, {x(t)} is used to update T at t a...

Particle filtering has a great potential for solving highly nonlinear and non-Gaussian estimation problems, generally intractable within a standard linear Kalman filtering based framework. However, the implementation of particle filters (PFs) is rather computationally involved, which nowadays prevents them from practical real-world application. A natural idea to make PFs feasible for “real-time...

Background: Cancer incidence is increasing annually in all countries. So, it nowadays a great burden for the different nations of world. Research new therapeutics becoming an urgent need, particularly intractable and chemoresistant cancer cases. The solutions can still be found by investigating natural products which are recognized as promising sources bioactive compounds with potential discove...

In general, the transition probability P of the Markov chain depends on some tuning parameter θ defined on some space Θ which can be either finite dimensional or infinite dimensional. The success of the MCMC procedure depends crucially upon a proper choice of θ. To illustrate, consider the standard Metropolis-Hastings (MH) algorithm. For simplicity, we assume that π has a density also denoted b...