An adaptive covariance inflation scheme is proposed for the ensemble Kalman filter (EnKF) to mitigate for the loss of ensemble variance. Adaptive inflation methods are mostly based on a Bayesian approach, which considers the inflation factor as a random variable with a given prior probability distribution, and then combines it with the inflation likelihood through Bayes’ rule to obtain its posterior distribution. In this work, we introduce a numerical implementation of this generic Bayesian approach that uses a particle filter (PF) to compute a Monte Carlo approximation of the inflation posterior distribution. To alleviate the sample attrition issue, the proposed PF employs an artificial dynamical model for the inflation factor based on the well-known smoothing-kernel West and Liu model. The positivity constraint on the inflation factor is further imposed through an inverse-Gamma transition density, whose parameters suggest analytical expressions. The resulting PF-EnKF scheme is straightforward to implement, and can use different number of particles in its EnKF and PF components. Numerical experiments are conducted with the Lorenz-96 model to demonstrate the effectiveness of the proposed method under various experimental scenarios.