data = {0 -> 0, 50 -> 3, 100 -> 10, 150 -> 5};
p = Predict[data, Method -> {"GaussianProcess", "CovarianceType" -> "SquaredExponential"}];
rw = Accumulate /@ 
   RandomVariate[NormalDistribution[0, 0.5], {1000, 50}];
pos1 = Flatten[Position[rw[[All, -2]], # ] & /@ Select[rw[[All, -2]], Abs[# - 3] < 1 &] ];
pos2 = Flatten[Position[rw[[All, -2]], # ] & /@ Select[rw[[All, -2]], Abs[# - 7] < 1 &] ];
pos3 = Flatten[Position[rw[[All, -2]], # ] & /@ Select[rw[[All, -2]], Abs[# + 5] < 1 &] ];
n = Dimensions[pos2][[1]]
p0 = Table[
   Legended[Show[ListPlot[rw[[pos1]][[1 ;; n, 1 ;; Max[3, t] ]], Joined -> True, PlotStyle -> Directive[Black, Opacity[0.2]], DataRange -> {0.9, Max[3, t]} ]
     ,
     ListPlot[List @@@ data, PlotStyle -> Directive[Purple, PointSize[0.03]] ]
     , PlotRange -> {{0, 160}, {-10, 20}}
     ]
    , Column[{LineLegend[{Purple}, {"Prediction"}], LineLegend[{Orange}, {"Credible Interval"}], PointLegend[{Purple}, {"Data"}]}]
    ]
   , {t, 0, 50, 5}];
p1 = Table[
   Legended[Show[ListPlot[rw[[pos1]][[1 ;; n ]], Joined -> True, PlotStyle -> Directive[Black, Opacity[0.2]], DataRange -> {0.9, 50} ]
     ,
     ListPlot[rw[[pos2]][[All, 1 ;; Max[3, t]]] + 3, Joined -> True, PlotStyle -> Directive[Black, Opacity[0.2]], DataRange -> {51, 51 + Max[3, t]} ]
     ,
     ListPlot[List @@@ data, PlotStyle -> Directive[Purple, PointSize[0.03]] ], PlotRange -> {{0, 160}, {-10, 20}}
     ]
    , Column[{LineLegend[{Purple}, {"Prediction"}], LineLegend[{Orange}, {"Credible Interval"}], PointLegend[{Purple}, {"Data"}]}]
    ]
   , {t, 0, 50, 5}];
p2 = Table[
   Legended[Show[
     ListPlot[rw[[pos1]][[1 ;; n ]], Joined -> True, PlotStyle -> Directive[Black, Opacity[0.2]], DataRange -> {0.9, 50} ]
     ,
     ListPlot[rw[[pos2]] + 3, Joined -> True, PlotStyle -> Directive[Black, Opacity[0.2]], DataRange -> {51, 100} ]
     ,
     ListPlot[rw[[pos3]][[1 ;; n, 1 ;; Max[3, t]]] + 10, Joined -> True, PlotStyle -> Directive[Black, Opacity[0.2]], DataRange -> {101, 101 + Max[3, t]} ]
     ,
     ListPlot[List @@@ data, PlotStyle -> Directive[Purple, PointSize[0.03]] ], PlotRange -> {{0, 160}, {-10, 20}}
     ]
    , Column[{LineLegend[{Purple}, {"Prediction"}], LineLegend[{Orange}, {"Credible Interval"}], PointLegend[{Purple}, {"Data"}]}]
    ]
   , {t, 0, 50, 5}];
p3 = Table[
   Legended[Show[
     ListPlot[rw[[pos1]][[1 ;; 35 ]], Joined -> True, PlotStyle -> Directive[Black, Opacity[0.2]], DataRange -> {0.9, 50} ]
     ,
     ListPlot[rw[[pos2]] + 3, Joined -> True, PlotStyle -> Directive[Black, Opacity[0.2]], DataRange -> {51, 100} ]
     ,
     ListPlot[rw[[pos3]][[1 ;; 35]] + 10, Joined -> True, PlotStyle -> Directive[Black, Opacity[0.2]], DataRange -> {101, 150} ]
     ,
     Plot[{p[x], p[x] + StandardDeviation[p[x, "Distribution"]], p[x] - StandardDeviation[p[x, "Distribution"]]}, {x, -1, 150}, PlotStyle -> {Directive[Purple, Opacity[t]], Directive[Orange, Opacity[t]], Directive[Orange, Opacity[t]]}, Filling -> {2 -> {3}}, FillingStyle -> Opacity[t/3], Exclusions -> False, PerformanceGoal -> "Speed"]
     ,
     ListPlot[List @@@ data, PlotStyle -> Directive[Purple, PointSize[0.03]] ], PlotRange -> {{0, 160}, {-10, 20}}
     ]
    , Column[{LineLegend[{Purple}, {"Prediction"}], LineLegend[{Orange}, {"Credible Interval"}], PointLegend[{Purple}, {"Data"}]}]
    ]
   , {t, 0, 1, 0.2}];
ListAnimate[p3]
ListAnimate[Join[p0, p1, p2, p3, Table[p3[[-1]], {10}]] ]

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