diff --git a/requirements.txt b/requirements.txt
index 25bd9b9..ee5280c 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -5,3 +5,4 @@ scikit-learn
 setuptools_scm
 tables-io[full]
 deprecated
+multipledispatch
diff --git a/src/qp/__init__.py b/src/qp/__init__.py
index f23f038..09bb8f3 100644
--- a/src/qp/__init__.py
+++ b/src/qp/__init__.py
@@ -34,3 +34,5 @@
 from . import packing_utils
 
 from . import test_funcs
+
+from . import projectors
diff --git a/src/qp/projectors/__init__.py b/src/qp/projectors/__init__.py
new file mode 100644
index 0000000..17d9ce7
--- /dev/null
+++ b/src/qp/projectors/__init__.py
@@ -0,0 +1,3 @@
+from .projector_base import ProjectorBase
+from .projector_shifts import ProjectorShifts
+from .projector_moments import ProjectorMoments
diff --git a/src/qp/projectors/projector_base.py b/src/qp/projectors/projector_base.py
new file mode 100644
index 0000000..cb5fe00
--- /dev/null
+++ b/src/qp/projectors/projector_base.py
@@ -0,0 +1,60 @@
+from ..ensemble import Ensemble
+import numpy as np
+from multipledispatch import dispatch
+
+
+class ProjectorBase(object):
+    @dispatch()
+    def __init__(self):
+        self._project_base()
+        self._project()
+
+    @dispatch(np.ndarray, np.ndarray)
+    def __init__(self, zs, pzs):
+        self._project_base(zs, pzs)
+
+    @dispatch(Ensemble)
+    def __init__(self, ens):
+        self._project_base(ens)
+
+    @dispatch()
+    def _project_base(self):
+        raise NotImplementedError
+
+    @dispatch(np.ndarray, np.ndarray)
+    def _project_base(self, zs, pzs):
+        self.pzs = self._normalize(pzs)
+        self.z = zs
+        self.pz_mean = np.mean(self.pzs, axis=0)
+        self.prior = None
+
+    @dispatch(qp.ensemble.Ensemble)
+    def _project_base(self, ens, z=None):
+        if z is None:
+            z = np.linspace(0, 1.5, 45)
+        self.z = z
+        pzs = ens.pdf(z)
+        pzs = ens.objdata()['pdfs']
+        self.pzs = self._normalize(pzs)
+        self.pz_mean = np.mean(self.pzs, axis=0)
+        self.prior = None
+
+    def _normalize(self, pzs):
+        norms = np.sum(pzs, axis=1)
+        pzs /= norms[:, None]  
+        return pzs
+
+    def evaluate_model(self, *args):
+        raise NotImplementedError
+
+    def get_prior(self):
+        if self.prior is None:
+            self.prior = self._get_prior()
+        return self.prior
+
+    def sample_prior(self):
+        prior = self.get_prior()
+        return prior.rvs()
+
+    def save_prior(self):
+        raise NotImplementedError
diff --git a/src/qp/projectors/projector_moments.py b/src/qp/projectors/projector_moments.py
new file mode 100644
index 0000000..391b170
--- /dev/null
+++ b/src/qp/projectors/projector_moments.py
@@ -0,0 +1,57 @@
+import numpy as np
+from ..ensemble import Ensemble
+from multipledispatch import dispatch
+from .projector_base import ProjectorBase
+from numpy.linalg import eig, cholesky
+from scipy.stats import multivariate_normal as mvn
+
+
+class ProjectorMoments(ProjectorBase):
+    @dispatch()
+    def __init__(self):
+        self._project_base()
+        self._project()
+
+    @dispatch(np.ndarray, np.ndarray)
+    def __init__(self, zs, pzs):
+        self._project_base(zs, pzs)
+        self._project()
+
+    @dispatch(Ensemble)
+    def __init__(self, ens):
+        self._project_base(ens)
+        self._project()
+
+    def _project(self):
+        self.pz_cov = self._get_cov()
+        self.pz_chol = cholesky(self.pz_cov)
+
+    def _get_cov(self):
+        cov = np.cov(self.pzs, rowvar=False)
+        if not self._is_pos_def(cov):
+            print('Warning: Covariance matrix is not positive definite')
+            print('The covariance matrix will be regularized')
+            jitter = 1e-15 * np.eye(cov.shape[0])
+            w, v = eig(cov+jitter)
+            w = np.real(np.abs(w))
+            v = np.real(v)
+            cov = v @ np.diag(np.abs(w)) @ v.T
+            cov = np.tril(cov) + np.triu(cov.T, 1)
+            if not self._is_pos_def(cov):
+                print('Warning: regularization failed')
+                print('The covariance matrix will be diagonalized')
+                cov = np.diag(np.diag(cov))
+        return cov
+
+    def _is_pos_def(self, A):
+        return np.all(np.linalg.eigvals(A) > 0)
+
+    def evaluate_model(self, pz, alpha):
+        z = pz[0]
+        pz = pz[1]
+        return [z, pz + self.pz_chol @ alpha]
+
+    def _get_prior(self):
+        return mvn(np.zeros_like(self.pz_mean),
+                   np.ones_like(self.pz_mean))
+
diff --git a/src/qp/projectors/projector_shifts.py b/src/qp/projectors/projector_shifts.py
new file mode 100644
index 0000000..11be278
--- /dev/null
+++ b/src/qp/projectors/projector_shifts.py
@@ -0,0 +1,44 @@
+import numpy as np
+from ..ensemble import Ensemble
+from multipledispatch import dispatch
+from .projector_base import ProjectorBase
+from scipy.interpolate import interp1d
+from scipy.stats import multivariate_normal
+
+
+class ProjectorShifts(ProjectorBase):
+    @dispatch()
+    def __init__(self):
+        self._project_base()
+        self._project()
+
+    @dispatch(np.ndarray, np.ndarray)
+    def __init__(self, zs, pzs):
+        self._project_base(zs, pzs)
+        self._project()
+
+    @dispatch(Ensemble)
+    def __init__(self, ens):
+        self._project_base(ens)
+        self._project()
+
+    def _project(self):
+        self.shift = self._find_shift()
+
+    def evaluate_model(self, pz, shift):
+        z = pz[0]
+        pz = pz[1]
+        z_shift = z + shift
+        pz_shift = interp1d(z_shift, pz,
+                            kind='linear',
+                            fill_value='extrapolate')(z)
+        return [z, pz_shift]
+
+    def _find_shift(self):
+        stds = np.std(self.pzs, axis=1)  # std of each pz
+        s_stds = np.std(stds)            # std of the z-std
+        m_stds = np.mean(stds)           # mean of the z-std
+        return s_stds / m_stds
+
+    def _get_prior(self):
+        return multivariate_normal([0], [self.shift**2])
diff --git a/src/qp/projectors/tests/__init__.py b/src/qp/projectors/tests/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/src/qp/projectors/tests/dummy.npz b/src/qp/projectors/tests/dummy.npz
new file mode 100644
index 0000000..b0f54d8
Binary files /dev/null and b/src/qp/projectors/tests/dummy.npz differ
diff --git a/src/qp/projectors/tests/test_projector_base.py b/src/qp/projectors/tests/test_projector_base.py
new file mode 100644
index 0000000..f93229a
--- /dev/null
+++ b/src/qp/projectors/tests/test_projector_base.py
@@ -0,0 +1,35 @@
+import qp
+import numpy as np
+import rail_projector.projectors as rp
+
+
+def make_qp_ens(file):
+    zs = file['zs']
+    pzs = file['pzs']
+    dz = np.mean(np.diff(zs))
+    zs_edges = np.append(zs - dz/2, zs[-1] + dz/2)
+    q = qp.Ensemble(qp.hist, data={"bins":zs_edges, "pdfs":pzs})
+    return q
+
+def test_base_from_qp():
+    file = np.load('rail_projector/tests/dummy.npz')
+    ens = make_qp_ens(file)
+    projector = rp.ProjectorBase(ens)
+    m, n = projector.pzs.shape
+    k, = projector.z.shape
+    pzs = file['pzs']
+    pzs /= np.sum(pzs, axis=1)[:, None]
+    assert n == k
+    assert np.allclose(projector.pz_mean, np.mean(pzs, axis=0))
+
+def test_base_from_arrs():
+    file = np.load('rail_projector/tests/dummy.npz')
+    zs = file['zs']
+    pzs = file['pzs']
+    projector = rp.ProjectorBase(zs, pzs)
+    m, n = projector.pzs.shape
+    k, = projector.z.shape
+    pzs = file['pzs']
+    pzs /= np.sum(pzs, axis=1)[:, None]
+    assert n == k
+    assert np.allclose(projector.pz_mean, np.mean(pzs, axis=0))
\ No newline at end of file
diff --git a/src/qp/projectors/tests/test_projector_moments.py b/src/qp/projectors/tests/test_projector_moments.py
new file mode 100644
index 0000000..d903074
--- /dev/null
+++ b/src/qp/projectors/tests/test_projector_moments.py
@@ -0,0 +1,39 @@
+import qp
+import numpy as np
+import rail_projector.projectors as rp
+
+
+def make_qp_ens(file):
+    zs = file['zs']
+    pzs = file['pzs']
+    dz = np.mean(np.diff(zs))
+    zs_edges = np.append(zs - dz/2, zs[-1] + dz/2)
+    q = qp.Ensemble(qp.hist, data={"bins":zs_edges, "pdfs":pzs})
+    return q
+
+
+def make_projector():
+    file = np.load('rail_projector/tests/dummy.npz')
+    ens = make_qp_ens(file)
+    return rp.ProjectorMoments(ens)
+
+
+def test_prior():
+    projector = make_projector()
+    prior = projector.get_prior()
+    assert prior is not None
+
+
+def test_sample_prior():
+    projector = make_projector()
+    pz = projector.sample_prior()
+    assert len(pz) == len(projector.pz_mean)
+
+
+def test_model():
+    projector = make_projector()
+    shift = projector.sample_prior()
+    input = np.array([projector.z, projector.pz_mean])
+    output = projector.evaluate_model(input, shift)
+    assert (projector.z == output[0]).all()
+    assert len(output[1]) == len(projector.pz_mean)
diff --git a/src/qp/projectors/tests/test_projector_shifts.py b/src/qp/projectors/tests/test_projector_shifts.py
new file mode 100644
index 0000000..1cc5f25
--- /dev/null
+++ b/src/qp/projectors/tests/test_projector_shifts.py
@@ -0,0 +1,39 @@
+import qp
+import numpy as np
+import rail_projector.projectors as rp
+
+
+def make_qp_ens(file):
+    zs = file['zs']
+    pzs = file['pzs']
+    dz = np.mean(np.diff(zs))
+    zs_edges = np.append(zs - dz/2, zs[-1] + dz/2)
+    q = qp.Ensemble(qp.hist, data={"bins":zs_edges, "pdfs":pzs})
+    return q
+
+
+def make_projector():
+    file = np.load('rail_projector/tests/dummy.npz')
+    ens = make_qp_ens(file)
+    return rp.ProjectorShifts(ens)
+
+
+def test_prior():
+    projector = make_projector()
+    prior = projector.get_prior()
+    assert prior is not None
+
+
+def test_sample_prior():
+    projector = make_projector()
+    shift = projector.sample_prior()
+    assert len([shift]) == len([projector.shift])
+
+
+def test_model():
+    projector = make_projector()
+    shift = projector.sample_prior()
+    input = np.array([projector.z, projector.pz_mean])
+    output = projector.evaluate_model(input, shift)
+    assert (projector.z == output[0]).all()
+    assert len(output[1]) == len(projector.pz_mean)