The electrical behavior of neurons depends on their morphology as well as various biophysical characteristics including passive membrane and intracellular properties and the identities and densities of voltage-gated ion channels. However, some of these parameters are often not sufficiently constrained by the available experimental data and need to be inferred from the response of the neuron to specific external stimuli. Data-driven models have proved to be useful in this context; one approach is to tune the unknown parameters in the model until the output of the model best approximates the target data. However, the reliability and precision of the estimates obtained via fitting-based methods typically remains undetermined, and it is also unknown how the results are affected by the properties of the noise that is present in the experimental data. To solve these issues, we combined the simulation of neuronal models with Bayesian probabilistic inference to obtain the full joint probability distribution of the unknown parameters. We applied this method to estimate passive biophysical parameters and to infer the distribution of ion channels from somatic and dendritic whole-cell recordings in CA1 pyramidal neurons. We found that the experimental noise had long time-scale correlations, and this strongly affected the estimates of biophysical parameters. Specifically, the resulting value of the axial resistivity (20-40 Ohm cm) was much lower than previous estimates. We also concluded that the spatial distribution of the leak conductance cannot be reliably estimated based on data from a single (somatic or dendritic) recording site.