diff --git a/CHANGELOG.md b/CHANGELOG.md
index bee1c84..16824f2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -36,6 +36,7 @@
 * Fix `io_pymc3.py` to handle models with `potentials` (#1043)
 * Fix several inconsistencies between schema and `from_pymc3` implementation
   in groups `prior`, `prior_predictive` and `observed_data` (#1045)
+* Stabilize covariance matrix for `plot_kde_2d` (#1075)
 
 ### Deprecation
 
diff --git a/arviz/plots/backends/matplotlib/traceplot.py b/arviz/plots/backends/matplotlib/traceplot.py
index 437f925..e181417 100644
--- a/arviz/plots/backends/matplotlib/traceplot.py
+++ b/arviz/plots/backends/matplotlib/traceplot.py
@@ -1,5 +1,6 @@
 """Matplotlib traceplot."""
 
+import warnings
 import matplotlib.pyplot as plt
 from matplotlib.lines import Line2D
 import numpy as np
@@ -48,8 +49,8 @@ def plot_trace(
     rug : bool
         If True adds a rugplot. Defaults to False. Ignored for 2D KDE. Only affects continuous
         variables.
-    lines : tuple
-        Tuple of (var_name, {'coord': selection}, [line, positions]) to be overplotted as
+    lines : tuple or list
+        list of tuple of (var_name, {'coord': selection}, [line_positions]) to be overplotted as
         vertical lines on the density and horizontal lines on the trace.
     combined : bool
         Flag for combining multiple chains into a single line. If False (default), chains will be
@@ -124,6 +125,21 @@ def plot_trace(
 
     _, axes = plt.subplots(len(plotters), 2, squeeze=False, figsize=figsize, **backend_kwargs)
 
+    # Check the input for lines
+    if lines is not None:
+        all_var_names = set(plotter[0] for plotter in plotters)
+
+        invalid_var_names = set()
+        for line in lines:
+            if line[0] not in all_var_names:
+                invalid_var_names.add(line[0])
+        if invalid_var_names:
+            warnings.warn(
+                "A valid var_name should be provided, found {} expected from {}".format(
+                    invalid_var_names, all_var_names
+                )
+            )
+
     for idx, (var_name, selection, value) in enumerate(plotters):
         value = np.atleast_2d(value)
 
@@ -219,6 +235,10 @@ def plot_trace(
                 line_values = [vlines]
             else:
                 line_values = np.atleast_1d(vlines).ravel()
+                if not np.issubdtype(line_values.dtype, np.number):
+                    raise ValueError(
+                        "line-positions should be numeric, found {}".format(line_values)
+                    )
             axes[idx, 0].vlines(line_values, *ylims[0], colors="black", linewidth=1.5, alpha=0.75)
             axes[idx, 1].hlines(
                 line_values, *xlims[1], colors="black", linewidth=1.5, alpha=trace_kwargs["alpha"]
diff --git a/arviz/plots/plot_utils.py b/arviz/plots/plot_utils.py
index 3d1c189..a611401 100644
--- a/arviz/plots/plot_utils.py
+++ b/arviz/plots/plot_utils.py
@@ -818,7 +818,9 @@ def _cov(data):
         x -= avg[:, None]
         prod = _dot(x, x.T.conj())
         prod *= np.true_divide(1, ddof)
-        return prod.squeeze()
+        prod = prod.squeeze()
+        prod += 1e-6 * np.eye(prod.shape[0])
+        return prod
     else:
         raise ValueError("{} dimension arrays are not supported".format(data.ndim))
 

diff --git a/arviz/tests/test_plots_matplotlib.py b/arviz/tests/test_plots_matplotlib.py
index a688a79..c0fa4ae 100644
--- a/arviz/tests/test_plots_matplotlib.py
+++ b/arviz/tests/test_plots_matplotlib.py
@@ -156,6 +156,21 @@ def test_plot_trace_max_subplots_warning(models):
     assert axes.shape
 
 
+@pytest.mark.parametrize("kwargs", [{"var_names": ["mu", "tau"], "lines": [("hey", {}, [1])]}])
+def test_plot_trace_invalid_varname_warning(models, kwargs):
+    with pytest.warns(UserWarning, match="valid var.+should be provided"):
+        axes = plot_trace(models.model_1, **kwargs)
+    assert axes.shape
+
+
+@pytest.mark.parametrize(
+    "bad_kwargs", [{"var_names": ["mu", "tau"], "lines": [("mu", {}, ["hey"])]}]
+)
+def test_plot_trace_bad_lines_value(models, bad_kwargs):
+    with pytest.raises(ValueError, match="line-positions should be numeric"):
+        plot_trace(models.model_1, **bad_kwargs)
+
+
 @pytest.mark.parametrize("model_fits", [["model_1"], ["model_1", "model_2"]])
 @pytest.mark.parametrize(
     "args_expected",
@@ -701,7 +716,6 @@ def test_plot_posterior_point_estimates(models, point_estimate):
     "kwargs", [{"insample_dev": False}, {"plot_standard_error": False}, {"plot_ic_diff": False}]
 )
 def test_plot_compare(models, kwargs):
-
     model_compare = compare({"Model 1": models.model_1, "Model 2": models.model_2})
 
     axes = plot_compare(model_compare, **kwargs)

plot_trace lines is unclear and it may yield unexpected results
**Describe the bug**
The argument `lines` for the function `plot_trace` can give unexpected results. Moreover, the documentation is a bit nebulous.
 
**To Reproduce**
A toy example is defined
```python
import pymc3 as pm
import arviz as az
import numpy as np

# fake data
mu_real = 0
sigma_real = 1
n_samples = 150

Y = np.random.normal(loc=mu_real, scale=sigma_real, size=n_samples)

with pm.Model() as model:
    mu = pm.Normal('mu', mu=0, sigma=10)  
    sigma = pm.HalfNormal('sigma', sigma=10)
    likelihood = pm.Normal('likelihood', mu=mu, sigma=sigma, observed=Y)
    trace = pm.sample()
```
As per [documentation](https://arviz-devs.github.io/arviz/generated/arviz.plot_trace.html#arviz.plot_trace), the argument `lines` accepts a tuple in the form `(var_name, {‘coord’: selection}, [line, positions])`. So, the command 
```python
az.plot_trace(trace, lines=(('mu', {}, mu_real),))
```
yields correctly 
![image](https://user-images.githubusercontent.com/18400141/69927034-b7327f80-1484-11ea-8f4c-5f52563413be.png)

I can also pass a list of tuples or a list of tuples and lists and it will work fine:
```
az.plot_trace(trace, lines=[('mu', {}, mu_real)]) # list of tuples
az.plot_trace(trace, lines=[['mu', {}, mu_real]]) # list of lists
az.plot_trace(trace, lines=[['mu', {}, mu_real], ('sigma', {}, sigma_real)]) # list of lists and tuples
```
however, I cannot pass a simple tuple because I will get a `KeyError: 0`
```python
az.plot_trace(trace, lines=(['mu', {}, mu_real]))
az.plot_trace(trace, lines=(('mu', {}, mu_real)))
```
Also, I can pass a variable or coordinate name that do not exist and Arviz will not complain---but not lines will be plotted (here I would expect a warning)
```python
az.plot_trace(trace, lines=[('hey', {}, mu_real)])
az.plot_trace(trace, lines=[('mu', {'hey'}, mu_real)])
```
![image](https://user-images.githubusercontent.com/18400141/69927389-d251bf00-1485-11ea-8d5c-7630a6763728.png)
The weird behavior happens when I pass a string:
```python
az.plot_trace(trace, lines=[('mu', {}, 'hey')])
```
![image](https://user-images.githubusercontent.com/18400141/69927502-32e0fc00-1486-11ea-8f6a-3f012017e932.png)

**Expected behavior**
The [documentation](https://arviz-devs.github.io/arviz/generated/arviz.plot_trace.html#arviz.plot_trace) could be improved and the function could check the inputs. In addition to what described above, the placeholder `[line, positions]` in `(var_name, {‘coord’: selection}, [line, positions])` should be something like `[line_positions]` otherwise one may think (like myself :) ) that two values should be inserted (one for `line` and one for `positions`).

**Additional context**
I am using Win10, fresh conda environment with PyMC3 and Arviz from master.

Possibly related https://github.com/pymc-devs/pymc3/issues/3495, https://github.com/pymc-devs/pymc3/issues/3497
arviz/tests/test_plots_matplotlib.py::test_plot_trace_invalid_varname_warning[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_trace_bad_lines_value[bad_kwargs0]
arviz/tests/test_plots_matplotlib.py::test_plot_density_float[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_density_float[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_density_float[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_density_float[kwargs3] arviz/tests/test_plots_matplotlib.py::test_plot_density_float[kwargs4] arviz/tests/test_plots_matplotlib.py::test_plot_density_float[kwargs5] arviz/tests/test_plots_matplotlib.py::test_plot_density_float[kwargs6] arviz/tests/test_plots_matplotlib.py::test_plot_density_float[kwargs7] arviz/tests/test_plots_matplotlib.py::test_plot_density_float[kwargs8] arviz/tests/test_plots_matplotlib.py::test_plot_density_bad_kwargs arviz/tests/test_plots_matplotlib.py::test_plot_trace[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_trace[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_trace[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_trace[kwargs3] arviz/tests/test_plots_matplotlib.py::test_plot_trace[kwargs4] arviz/tests/test_plots_matplotlib.py::test_plot_trace[kwargs5] arviz/tests/test_plots_matplotlib.py::test_plot_trace[kwargs6] arviz/tests/test_plots_matplotlib.py::test_plot_trace[kwargs7] arviz/tests/test_plots_matplotlib.py::test_plot_trace[kwargs8] arviz/tests/test_plots_matplotlib.py::test_plot_trace[kwargs9] arviz/tests/test_plots_matplotlib.py::test_plot_trace_max_subplots_warning arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected0-model_fits0] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected0-model_fits1] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected1-model_fits0] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected1-model_fits1] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected2-model_fits0] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected2-model_fits1] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected3-model_fits0] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected3-model_fits1] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected4-model_fits0] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected4-model_fits1] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected5-model_fits0] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected5-model_fits1] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected6-model_fits0] arviz/tests/test_plots_matplotlib.py::test_plot_forest[args_expected6-model_fits1] arviz/tests/test_plots_matplotlib.py::test_plot_forest_rope_exception arviz/tests/test_plots_matplotlib.py::test_plot_forest_single_value arviz/tests/test_plots_matplotlib.py::test_plot_forest_bad[model_fits0] arviz/tests/test_plots_matplotlib.py::test_plot_forest_bad[model_fits1] arviz/tests/test_plots_matplotlib.py::test_plot_energy[kde] arviz/tests/test_plots_matplotlib.py::test_plot_energy[hist] arviz/tests/test_plots_matplotlib.py::test_plot_energy_bad arviz/tests/test_plots_matplotlib.py::test_plot_parallel_raises_valueerror arviz/tests/test_plots_matplotlib.py::test_plot_parallel[None] arviz/tests/test_plots_matplotlib.py::test_plot_parallel[normal] arviz/tests/test_plots_matplotlib.py::test_plot_parallel[minmax] arviz/tests/test_plots_matplotlib.py::test_plot_parallel[rank] arviz/tests/test_plots_matplotlib.py::test_plot_parallel_exception[None] arviz/tests/test_plots_matplotlib.py::test_plot_parallel_exception[mu] arviz/tests/test_plots_matplotlib.py::test_plot_parallel_exception[var_names2] arviz/tests/test_plots_matplotlib.py::test_plot_joint_bad arviz/tests/test_plots_matplotlib.py::test_plot_kde[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_kde[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_kde[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_kde[kwargs3] arviz/tests/test_plots_matplotlib.py::test_plot_kde[kwargs4] arviz/tests/test_plots_matplotlib.py::test_cov[x0] arviz/tests/test_plots_matplotlib.py::test_cov[x1] arviz/tests/test_plots_matplotlib.py::test_cov[x2] arviz/tests/test_plots_matplotlib.py::test_plot_kde_cumulative[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_kde_cumulative[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_kde_cumulative[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_kde_cumulative[kwargs3] arviz/tests/test_plots_matplotlib.py::test_plot_dist[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_dist_2d_kde[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_dist_2d_kde[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_dist_2d_kde[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_kde_quantiles[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_kde_quantiles[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_kde_quantiles[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_kde_inference_data arviz/tests/test_plots_matplotlib.py::test_plot_pair[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_pair[kwargs3] arviz/tests/test_plots_matplotlib.py::test_plot_pair[kwargs4] arviz/tests/test_plots_matplotlib.py::test_plot_pair[kwargs5] arviz/tests/test_plots_matplotlib.py::test_plot_pair_2var[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_pair_2var[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_pair_2var[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_pair_bad arviz/tests/test_plots_matplotlib.py::test_plot_pair_divergences_warning[True] arviz/tests/test_plots_matplotlib.py::test_plot_pair_divergences_warning[False] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[False-None-kde] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[False-None-cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[False-None-scatter] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[False-0.2-kde] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[False-0.2-cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[False-0.2-scatter] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[False-1-kde] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[False-1-cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[False-1-scatter] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[True-None-kde] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[True-None-cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[True-None-scatter] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[True-0.2-kde] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[True-0.2-cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[True-0.2-scatter] arviz/tests/test_plots_matplotlib.py::test_plot_ppc[True-1-kde] 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arviz/tests/test_plots_matplotlib.py::test_plot_ppc_multichain[True-0.1-cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_multichain[True-0.1-scatter] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_multichain[True-1-kde] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_multichain[True-1-cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_multichain[True-1-scatter] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_multichain[True-3-kde] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_multichain[True-3-cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_multichain[True-3-scatter] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_discrete[False-cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_discrete[True-cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_grid arviz/tests/test_plots_matplotlib.py::test_plot_ppc_bad[kde] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_bad[cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_bad[scatter] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_ax[kde] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_ax[cumulative] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_ax[scatter] arviz/tests/test_plots_matplotlib.py::test_plot_ppc_bad_ax arviz/tests/test_plots_matplotlib.py::test_plot_violin[None] arviz/tests/test_plots_matplotlib.py::test_plot_violin[mu] arviz/tests/test_plots_matplotlib.py::test_plot_violin[var_names2] arviz/tests/test_plots_matplotlib.py::test_plot_violin_ax arviz/tests/test_plots_matplotlib.py::test_plot_violin_layout arviz/tests/test_plots_matplotlib.py::test_plot_autocorr_short_chain arviz/tests/test_plots_matplotlib.py::test_plot_autocorr_uncombined arviz/tests/test_plots_matplotlib.py::test_plot_autocorr_combined arviz/tests/test_plots_matplotlib.py::test_plot_autocorr_var_names[None] arviz/tests/test_plots_matplotlib.py::test_plot_autocorr_var_names[mu] arviz/tests/test_plots_matplotlib.py::test_plot_autocorr_var_names[var_names2] arviz/tests/test_plots_matplotlib.py::test_plot_rank[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_rank[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_rank[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_rank[kwargs3] arviz/tests/test_plots_matplotlib.py::test_plot_rank[kwargs4] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs3] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs4] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs5] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs6] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs7] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs8] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs9] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs10] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs11] arviz/tests/test_plots_matplotlib.py::test_plot_posterior[kwargs12] arviz/tests/test_plots_matplotlib.py::test_plot_posterior_bad arviz/tests/test_plots_matplotlib.py::test_plot_posterior_point_estimates[mode] arviz/tests/test_plots_matplotlib.py::test_plot_posterior_point_estimates[mean] arviz/tests/test_plots_matplotlib.py::test_plot_posterior_point_estimates[median] arviz/tests/test_plots_matplotlib.py::test_plot_hpd[kwargs0] arviz/tests/test_plots_matplotlib.py::test_plot_hpd[kwargs1] arviz/tests/test_plots_matplotlib.py::test_plot_hpd[kwargs2] arviz/tests/test_plots_matplotlib.py::test_plot_hpd[kwargs3] arviz/tests/test_plots_matplotlib.py::test_plot_hpd[kwargs4] arviz/tests/test_plots_matplotlib.py::test_fast_kde_scipy[limits0] 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