WPF DataGrid: How do I programmatically select a ComboBox item?

The ComboBoxes in question are inside a DataGrid's column and have been defined as follows:

<DataGridTemplateColumn Header=" Right Column "><DataGridTemplateColumn.CellTemplate><DataTemplate><ComboBox ItemsSource="{Binding Caliber, RelativeSource={RelativeSource AncestorType=Window}, Mode=TwoWay}" DisplayMemberPath="Thickness" SelectedItem="{Binding Thickness, UpdateSourceTrigger=PropertyChanged, Mode=TwoWay}" ></ComboBox></DataTemplate></DataGridTemplateColumn.CellTemplate></DataGridTemplateColumn>

I borrowed the above XAML code from here:

    WPF: Best ComboBox Tutorial Ever

TIA.