Medical researchers may be interested in disease processes‎  ‎that are not‎ ‎directly observable‎. ‎Imperfect diagnostic‎ ‎tests may be used repeatedly to monitor the‎ ‎condition of a patient in the absence of a gold standard.‎ ‎We consider parameter identifiability and estimability‎ ‎in a Markov model for alternating binary longitudinal ‎responses that may be misclassified.‎ ‎Exactly ...

Customer Journey Maps (CJMs) summarize the behavior of customers by displaying the most common sequences of steps they take when engaging with a company or product. In many practical applications, the challenge lies in automatically discovering these prototypical sequences from raw event logs for thousands of customers. We propose a novel, probabilistic approach based on a mixture of Markov mod...

Often, at the time when a performance model is built, some of its input parameters are not known exactly. This can be for a variety of reasons, such as the system itself not having been completed, a benchmarking process not yet having been carried out, or that precise estimates for the parameters are very difficult to obtain. In these situations, interval values can be used to express the uncer...

This paper provides a precise error analysis for the maximum likelihood estimate $\hat{a}_{\text{ML}}(u_1^n)$ of parameter $a$ given samples $u_1^n = (u_1, \ldots, u_n)'$ drawn from nonstationary Gauss-Markov process $U_i U_{i-1} + Z_i,~i\geq 1$, where $U_0 0$, $a> and $Z_i$'s are independent Gaussian random variables with zero mean variance $\sigma^2$. We show tight nonasymptotic exponentially...

AbstractThis paper surveys the analysis of parametric Markov models whose transitions are labelled with functions over a finite set parameters. These symbolic representations uncountable many concrete probabilistic models, each obtained by instantiating We consider various problems for given logical specification \(\varphi \): do all parameter instantiations within region values satisfy \)?, wh...

An autoregressive model with Markov regime-switching is analyzed that reflects on the properties of the quasi-likelihood ratio test developed by Cho and White (2007). For such a model, we show that consistency of the quasi-maximum likelihood estimator for the population parameter values, on which consistency of the test is based, does not hold. We describe a condition that ensures consistency o...