Connection strength estimation is widely used in detecting the topology of neuronal networks and assessing their synaptic plasticity. A recently proposed model-based method using the leaky integrate-and-fire model neuron estimates membrane potential from spike trains by calculating the maximum a posteriori (MAP) path. We further enhance the MAP path method using variational Bayes and dynamic causal modeling. Several simulations demonstrate that the proposed method can accurately estimate connection strengths with an error ratio of less than 20%. The results suggest that the proposed method can be an effective tool for detecting network structure and synaptic plasticity.